In Kenneth Grahame’s 1908 novel The Wind in the Willows, a Mole meets a Water Rat who lives on a River. The Rat explains how the River permeates his life: “It’s brother and sister to me, and aunts, and company, and food and drink, and (naturally) washing.” As the River plays many roles in the Rat’s life, so does Carnot’s theorem play many roles in a thermodynamicist’s.
Nicolas Léonard Sadi Carnot lived in France during the turn of the 19th century. His father named him Sadi after the 13th-century Persian poet Saadi Shirazi. Said father led a colorful life himself,1 working as a mathematician, engineer, and military commander for and before the Napoleonic Empire. Sadi Carnot studied in Paris at the École Polytechnique, whose members populate a “Who’s Who” list of science and engineering.
As Carnot grew up, the Industrial Revolution was humming. Steam engines were producing reliable energy on vast scales; factories were booming; and economies were transforming. France’s old enemy Britain enjoyed two advantages. One consisted of inventors: Englishmen Thomas Savery and Thomas Newcomen invented the steam engine. Scotsman James Watt then improved upon Newcomen’s design until rendering it practical. Second, northern Britain contained loads of coal that industrialists could mine to power her engines. France had less coal. So if you were a French engineer during Carnot’s lifetime, you should have cared about engines’ efficiencies—how effectively engines used fuel.2
Carnot proved a fundamental limitation on engines’ efficiencies. His theorem governs engines that draw energy from heat—rather than from, say, the motional energy of water cascading down a waterfall. In Carnot’s argument, a heat engine interacts with a cold environment and a hot environment. (Many car engines fall into this category: the hot environment is burning gasoline. The cold environment is the surrounding air into which the car dumps exhaust.) Heat flows from the hot environment to the cold. The engine siphons off some heat and converts it into work. Work is coordinated, well-organized energy that one can directly harness to perform a useful task, such as turning a turbine. In contrast, heat is the disordered energy of particles shuffling about randomly. Heat engines transform random heat into coordinated work.
In The Wind and the Willows, Toad drives motorcars likely powered by internal combustion, rather than by a steam engine of the sort that powered the Industrial Revolution.
An engine’s efficiency is the bang we get for our buck—the upshot we gain, compared to the cost we spend. Running an engine costs the heat that flows between the environments: the more heat flows, the more the hot environment cools, so the less effectively it can serve as a hot environment in the future. An analogous statement concerns the cold environment. So a heat engine’s efficiency is the work produced, divided by the heat spent.
Carnot upper-bounded the efficiency achievable by every heat engine of the sort described above. Let denote the cold environment’s temperature; and , the hot environment’s. The efficiency can’t exceed . What a simple formula for such an extensive class of objects! Carnot’s theorem governs not only many car engines (Otto engines), but also the Stirling engine that competed with the steam engine, its cousin the Ericsson engine, and more.
In addition to generality and simplicity, Carnot’s bound boasts practical and fundamental significances. Capping engine efficiencies caps the output one can expect of a machine, factory, or economy. The cap also prevents engineers from wasting their time on daydreaming about more-efficient engines.
More fundamentally than these applications, Carnot’s theorem encapsulates the second law of thermodynamics. The second law helps us understand why time flows in only one direction. And what’s deeper or more foundational than time’s arrow? People often cast the second law in terms of entropy, but many equivalent formulations express the law’s contents. The formulations share a flavor often synopsized with “You can’t win.” Just as we can’t grow younger, we can’t beat Carnot’s bound on engines.
One might expect no engine to achieve the greatest efficiency imaginable: , called the Carnot efficiency. This expectation is incorrect in one way and correct in another. Carnot did design an engine that could operate at his eponymous efficiency: an eponymous engine. A Carnot engine can manifest as the thermodynamicist’s favorite physical system: a gas in a box topped by a movable piston. The gas undergoes four strokes, or steps, to perform work. The strokes form a closed cycle, returning the gas to its initial conditions.3
Steampunk artist Todd Cahill beautifully illustrated the Carnot cycle for my book. The gas performs useful work because a teapot sits atop the piston. Pushing the piston upward, the gas lifts the teapot. You can find a more detailed description of Carnot’s engine in Chapter 4 of the book, but I’ll recap the cycle here.
The gas expands during stroke 1, pushing the piston and so outputting work. Maintaining contact with the hot environment, the gas remains at the temperature . The gas then disconnects from the hot environment. Yet the gas continues to expand throughout stroke 2, lifting the teapot further. Forfeiting energy, the gas cools. It ends stroke 2 at the temperature .
The gas contacts the cold environment throughout stroke 3. The piston pushes on the gas, compressing it. At the end of the stroke, the gas disconnects from the cold environment. The piston continues compressing the gas throughout stroke 4, performing more work on the gas. This work warms the gas back up to .
In summary, Carnot’s engine begins hot, performs work, cools down, has work performed on it, and warms back up. The gas performs more work on the piston than the piston performs on it. Therefore, the teapot rises (during strokes 1 and 2) more than it descends (during strokes 3 and 4).
At what cost, if the engine operates at the Carnot efficiency? The engine mustn’t waste heat. One wastes heat by roiling up the gas unnecessarily—by expanding or compressing it too quickly. The gas must stay in equilibrium, a calm, quiescent state. One can keep the gas quiescent only by running the cycle infinitely slowly. The cycle will take an infinitely long time, outputting zero power (work per unit time). So one can achieve the perfect efficiency only in principle, not in practice, and only by sacrificing power. Again, you can’t win.
Efficiency trades off with power.
Carnot’s theorem may sound like the Eeyore of physics, all negativity and depression. But I view it as a companion and backdrop as rich, for thermodynamicists, as the River is for the Water Rat. Carnot’s theorem curbs diverse technologies in practical settings. It captures the second law, a foundational principle. The Carnot cycle provides intuition, serving as a simple example on which thermodynamicists try out new ideas, such as quantum engines. Carnot’s theorem also provides what physicists call a sanity check: whenever a researcher devises a new (for example, quantum) heat engine, they can confirm that the engine obeys Carnot’s theorem, to help confirm their proposal’s accuracy. Carnot’s theorem also serves as a school exercise and a historical tipping point: the theorem initiated the development of thermodynamics, which continues to this day.
So Carnot’s theorem is practical and fundamental, pedagogical and cutting-edge—brother and sister, and aunts, and company, and food and drink. I just wouldn’t recommend trying to wash your socks in Carnot’s theorem.
1To a theoretical physicist, working as a mathematician and an engineer amounts to leading a colorful life.
2People other than Industrial Revolution–era French engineers should care, too.
3A cycle doesn’t return the hot and cold environments to their initial conditions, as explained above.
In 2020, many of us logged experiences that we’d never anticipated. I wrote a nonfiction book and got married outside the Harvard Faculty Club (because nobody was around to shoo us away). Equally unexpectedly, I received an invitation to collaborate with a professional artist. One Bruce Rosenbaum emailed me out of the blue:
I watched your video on Quantum Steampunk: Quantum Information Meets Thermodynamics. [ . . . ] I’d like to explore collaborating with you on bringing together the fusion of Quantum physics and Thermodynamics into the real world with functional Steampunk art and design.
I looked Bruce up online. Wired Magazine had called the Massachusetts native “the steampunk evangelist,” and The Wall Street Journal had called him “the steampunk guru.” He created sculptures for museums and hotels, in addition to running workshops that riffed on the acronym STEAM (science, technology, engineering, art, and mathematics). MTV’s Extreme Cribs had spotlighted his renovation of a Victorian-era church into a home and workshop.
All right, I replied, I’m game. But research fills my work week, so can you talk at an unusual time?
We Zoomed on a Saturday afternoon. Bruce Zooms from precisely the room that you’d hope to find a steampunk artist in: a workshop filled with brass bits and bobs spread across antique-looking furniture. Something intricate is usually spinning atop a table behind him. And no, none of it belongs to a virtual background. Far from an overwrought inventor, though, Bruce exudes a vibe as casual as the T-shirt he often wears—when not interviewing in costume. A Boston-area accent completed the feeling of chatting with a neighbor.
Bruce proposed building a quantum-steampunk sculpture. I’d never dreamed of the prospect, but it sounded like an adventure, so I agreed. We settled on a sculpture centered on a quantum engine. Classical engines inspired the development of thermodynamics around the time of the Industrial Revolution. One of the simplest engines—the heat engine—interacts with two environments, or reservoirs: one cold and one hot. Heat—the energy of random atomic motion—flows from the hot to the cold. The engine siphons off part of the heat, converting it into work—coordinated energy that can, say, turn a turbine.
Can a quantum system convert random heat into useful work? Yes, quantum thermodynamicists have shown. Bell Labs scientists designed a quantum engine formed from one atom, during the 1950s and 1960s. Since then, physicists have co-opted superconducting qubits, trapped ions, and more into quantum engines. Entanglement can enhance quantum engines, which can both suffer and benefit from quantum coherences (wave-like properties, in the spirit of wave–particle duality). Experimentalists have realized quantum engines in labs. So Bruce and I placed (an artistic depiction of) a quantum engine at our sculpture’s center. The engine consists of a trapped ion—a specialty of Maryland, where I accepted a permanent position that spring.
Bruce engaged an illustrator, Jim Su, to draw the sculpture. We iterated through draft after draft, altering shapes and fixing scientific content. Versions from the cutting-room floor now adorn the Maryland Quantum-Thermodynamics Hub’s website.
Designing the sculpture was a lark. Finding funding to build it has required more grit. During the process, our team grew to include scientific-computing expert Alfredo Nava-Tudelo, physicist Bill Phillips, senior faculty specialist Daniel Serrano, and Quantum Frontiers gatekeeper Spiros Michalakis. We secured a grant from the University of Maryland’s Arts for All program this spring. The program is promoting quantum-inspired art this year, in honor of the UN’s designation of 2025 as the International Year of Quantum Science and Technology.
Through the end of 2024, we’re building a tabletop version of the sculpture. We were expecting a 3D-printout version to consume our modest grant. But quantum steampunk captured the imagination of Empire Group, the design-engineering company hired by Bruce to create and deploy technical drawings. Empire now plans to include metal and moving parts in the sculpture.
The Quantum-Steampunk Engine sculpture (drawing by Jim Su)
Empire will create CAD (computer-aided–design) drawings this November, in dialogue with the scientific team and Bruce. The company will fabricate the sculpture in December. The scientists will create educational materials that explain the thermodynamics and quantum physics represented in the sculpture. Starting in 2025, we’ll exhibit the sculpture everywhere possible. Plans include the American Physical Society’s Global Physics Summit (March Meeting), the quantum-steampunk creative-writing course I’m co-teaching next spring, and the Quantum World Congress. Bruce will incorporate the sculpture into his STEAMpunk workshops. Drop us a line if you want the Quantum-Steampunk Engine sculpture at an event as a centerpiece or teaching tool. And stay tuned for updates on the sculpture’s creation process and outreach journey.
Our team’s schemes extend beyond the tabletop sculpture: we aim to build an 8’-by-8’-by-8’ version. The full shebang will contain period antiques, lasers, touchscreens, and moving and interactive parts. We hope that a company, university, or individual will request the full-size version upon seeing its potential in the tabletop.
A sculpture, built by ModVic for a corporate office, of the scale we have in mind. The description on Bruce’s site reads, “A 300 lb. Clipper of the Clouds sculpture inspired by a Jules Verne story. The piece suspends over the corporate lobby.”
After all, what are steampunk and science for, if not dreaming?
Building Quantum Computers: A Practical Introduction by Shayan Majidy, Christopher Wilson, and Raymond Laflamme has been published by Cambridge University Press and will be released in the US on September 30. The authors invited me to write a Foreword for the book, which I was happy to do. The publisher kindly granted permission for me to post the Foreword here on Quantum Frontiers.
Foreword
The principles of quantum mechanics, which as far as we know govern all natural phenomena, were discovered in 1925. For 99 years we have built on that achievement to reach a comprehensive understanding of much of the physical world, from molecules to materials to elementary particles and much more. No comparably revolutionary advance in fundamental science has occurred since 1925. But a new revolution is in the offing.
Up until now, most of what we have learned about the quantum world has resulted from considering the behavior of individual particles — for example a single electron propagating as a wave through a crystal, unfazed by barriers that seem to stand in its way. Understanding that single-particle physics has enabled us to explore nature in unprecedented ways, and to build information technologies that have profoundly transformed our lives.
What’s happening now is we’re learning how to instruct particles to evolve in coordinated ways that can’t be accurately described in terms of the behavior of one particle at a time. The particles, as we like to say, can become entangled. Many particles, like electrons or photons or atoms, when highly entangled, exhibit an extraordinary complexity that we can’t capture with the most powerful of today’s supercomputers, or with our current theories of how nature works. That opens extraordinary opportunities for new discoveries and new applications.
Most temptingly, we anticipate that by building and operating large-scale quantum computers, which control the evolution of very complex entangled quantum systems, we will be able to solve some computational problems that are far beyond the reach of today’s digital computers. The concept of a quantum computer was proposed over 40 years ago, and the task of building quantum computing hardware has been pursued in earnest since the 1990s. After decades of steady progress, quantum information processors with hundreds of qubits have become feasible and are scientifically valuable. But we may need quantum processors with millions of qubits to realize practical applications of broad interest. There is still a long way to go.
Why is it taking so long? A conventional computer processes bits, where each bit could be, say, a switch which is either on or off. To build highly complex entangled quantum states, the fundamental information-carrying component of a quantum computer must be what we call a “qubit” rather than a bit. The trouble is that qubits are much more fragile than bits — when a qubit interacts with its environment, the information it carries is irreversibly damaged, a process called decoherence. To perform reliable logical operations on qubits, we need to prevent decoherence by keeping the qubits nearly perfectly isolated from their environment. That’s very hard to do. And because a qubit, unlike a bit, can change continuously, precisely controlling a qubit is a further challenge, even when decoherence is in check.
While theorists may find it convenient to regard a qubit (or a bit) as an abstract object, in an actual processor a qubit needs to be encoded in a particular physical system. There are many options. It might, for example, be encoded in a single atom which can be in either one of two long-lived internal states. Or the spin of a single atomic nucleus or electron which points either up or down along some axis. Or a single photon that occupies either one of two possible optical modes. These are all remarkable encodings, because the qubit resides in a very simple single quantum system, yet, thanks to technical advances over several decades, we have learned to control such qubits reasonably well. Alternatively, the qubit could be encoded in a more complex system, like a circuit conducting electricity without resistance at very low temperature. This is also remarkable, because although the qubit involves the collective motion of billions of pairs of electrons, we have learned to make it behave as though it were a single atom.
To run a quantum computer, we need to manipulate individual qubits and perform entangling operations on pairs of qubits. Once we can perform such single-qubit and two-qubit “quantum gates” with sufficient accuracy, and measure and initialize the qubits as well, then in principle we can perform any conceivable quantum computation by assembling sufficiently many qubits and executing sufficiently many gates.
It’s a daunting engineering challenge to build and operate a quantum system of sufficient complexity to solve very hard computation problems. That systems engineering task, and the potential practical applications of such a machine, are both beyond the scope of Building Quantum Computers. Instead the focus is on the computer’s elementary constituents for four different qubit modalities: nuclear spins, photons, trapped atomic ions, and superconducting circuits. Each type of qubit has its own fascinating story, told here expertly and with admirable clarity.
For each modality a crucial question must be addressed: how to produce well-controlled entangling interactions between two qubits. Answers vary. Spins have interactions that are always on, and can be “refocused” by applying suitable pulses. Photons hardly interact with one another at all, but such interactions can be mocked up using appropriate measurements. Because of their Coulomb repulsion, trapped ions have shared normal modes of vibration that can be manipulated to generate entanglement. Couplings and frequencies of superconducting qubits can be tuned to turn interactions on and off. The physics underlying each scheme is instructive, with valuable lessons for the quantum informationists to heed.
Various proposed quantum information processing platforms have characteristic strengths and weaknesses, which are clearly delineated in this book. For now it is important to pursue a variety of hardware approaches in parallel, because we don’t know for sure which ones have the best long term prospects. Furthermore, different qubit technologies might be best suited for different applications, or a hybrid of different technologies might be the best choice in some settings. The truth is that we are still in the early stages of developing quantum computing systems, and there is plenty of potential for surprises that could dramatically alter the outlook.
Building large-scale quantum computers is a grand challenge facing 21st-century science and technology. And we’re just getting started. The qubits and quantum gates of the distant future may look very different from what is described in this book, but the authors have made wise choices in selecting material that is likely to have enduring value. Beyond that, the book is highly accessible and fun to read. As quantum technology grows ever more sophisticated, I expect the study and control of highly complex many-particle systems to become an increasingly central theme of physical science. If so, Building Quantum Computers will be treasured reading for years to come.
Why not run a quantum-steampunk creative-writing course?
Quantum steampunk, as Quantum Frontiers regulars know, is the aesthetic and spirit of a growing scientific field. Steampunk is a subgenre of science fiction. In it, futuristic technologies invade Victorian-era settings: submarines, time machines, and clockwork octopodes populate La Belle Èpoque, a recently liberated Haiti, and Sherlock Holmes’s London. A similar invasion characterizes my research field, quantum thermodynamics: thermodynamics is the study of heat, work, temperature, and efficiency. The Industrial Revolution spurred the theory’s development during the 1800s. The theory’s original subject—nineteenth-century engines—were large, were massive, and contained enormous numbers of particles. Such engines obey the classical mechanics developed during the 1600s. Hence thermodynamics needs re-envisioning for quantum systems. To extend the theory’s laws and applications, quantum thermodynamicists use mathematical and experimental tools from quantum information science. Quantum information science is, in part, the understanding of quantum systems through how they store and process information. The toolkit is partially cutting-edge and partially futuristic, as full-scale quantum computers remain under construction. So applying quantum information to thermodynamics—quantum thermodynamics—strikes me as the real-world incarnation of steampunk.
But the thought of a quantum-steampunk creative-writing course had never occurred to me, and I hesitated over it. Quantum-steampunk blogposts, I could handle. A book, I could handle. Even a short-story contest, I’d handled. But a course? The idea yawned like the pitch-dark mouth of an unknown cavern in my imagination.
But the more I mulled over Edward Daschle’s suggestion, the more I warmed to it. Edward was completing a master’s degree in creative writing at the University of Maryland (UMD), specializing in science fiction. His mentor Emily Brandchaft Mitchell had sung his praises via email. In 2023, Emily had served as a judge for the Quantum-Steampunk Short-Story Contest. She works as a professor of English at UMD, writes fiction, and specializes in the study of genre. I reached out to her last spring about collaborating on a grant for quantum-inspired art, and she pointed to her protégé.
The course will alternate between science and science fiction. Under Edward’s direction, we’ll read and discuss published fiction. We’ll also learn about what genres are and how they come to be. Students will try out writing styles by composing short stories themselves. Everyone will provide feedback about each other’s writing: what works, what’s confusing, and opportunities for improvement.
The published fiction chosen will mirror the scientific subjects we’ll cover: quantum physics; quantum technologies; and thermodynamics, including quantum thermodynamics. I’ll lead this part of the course. The scientific studies will interleave with the story reading, writing, and workshopping. Students will learn about the science behind the science fiction while contributing to the growing subgenre of quantum steampunk.
We aim to attract students from across campus: physics, English, the Jiménez-Porter Writers’ House, computer science, mathematics, and engineering—plus any other departments whose students have curiosity and creativity to spare. The course already has four cross-listings—Arts and Humanities 270, Physics 299Q, Computer Science 298Q, and Mechanical Engineering 299Q—and will probably acquire a fifth (Chemistry 298Q). You can earn a Distributive Studies: Scholarship in Practice (DSSP) General Education requirement, and undergraduate and graduate students are welcome. QuICS—the Joint Center for Quantum Information and Computer Science, my home base—is paying Edward’s salary through a seed grant. Ross Angelella, the director of the Writers’ House, arranged logistics and doused us with enthusiasm. I’m proud of how organizations across the university are uniting to support the course.
The diversity we seek, though, poses a challenge. The course lacks prerequisites, so I’ll need to teach at a level comprehensible to the non-science students. I’d enjoy doing so, but I’m concerned about boring the science students. Ideally, the science students will help me teach, while the non-science students will challenge us with foundational questions that force us to rethink basic concepts. Also, I hope that non-science students will galvanize discussions about ethical and sociological implications of quantum technologies. But how can one ensure that conversation will flow?
This summer, Edward and I traded candidate stories for the syllabus. Based on his suggestions, I recommend touring science fiction under an expert’s guidance. I enjoyed, for a few hours each weekend, sinking into the worlds of Ted Chiang, Ursula K. LeGuinn, N. K. Jemison, Ken Liu, and others. My scientific background informed my reading more than I’d expected. Some authors, I could tell, had researched their subjects thoroughly. When they transitioned from science into fiction, I trusted and followed them. Other authors tossed jargon into their writing but evidenced a lack of deep understanding. One author nailed technical details about quantum computation, initially impressing me, but missed the big picture: his conflict hinged on a misunderstanding about entanglement. I see all these stories as affording opportunities for learning and teaching, in different ways.
Students can begin registering for “Writing Quantum Steampunk: Science-Fiction Workshop” on October 24. We can offer only 15 seats, due to Writers’ House standards, so secure yours as soon as you can. Part of me still wonders how the Hilbert space I came to be co-teaching a quantum-steampunk creative-writing course.1 But I look forward to reading with you next spring!
1A Hilbert space is a mathematical object that represents a quantum system. But you needn’t know that to succeed in the course.
I met boatloads of physicists as a master’s student at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. Researchers pass through Perimeter like diplomats through my current neighborhood—the Washington, DC area—except that Perimeter’s visitors speak math instead of legalese and hardly any of them wear ties. But Nilanjana Datta, a mathematician at the University of Cambridge, stood out. She was one of the sharpest, most on-the-ball thinkers I’d ever encountered. Also, she presented two academic talks in a little black dress.
The academic year had nearly ended, and I was undertaking research at the intersection of thermodynamics and quantum information theory for the first time. My mentors and I were applying a mathematical toolkit then in vogue, thanks to Nilanjana and colleagues of hers: one-shot quantum information theory. To explain one-shot information theory, I should review ordinary information theory. Information theory is the study of how efficiently we can perform information-processing tasks, such as sending messages over a channel.
Say I want to send you copies of a message. Into how few bits (units of information) can I compress the copies? First, suppose that the message is classical, such that a telephone could convey it. The average number of bits needed per copy equals the message’s Shannon entropy, a measure of your uncertainty about which message I’m sending. Now, suppose that the message is quantum. The average number of quantum bits needed per copy is the von Neumann entropy, now a measure of your uncertainty. At least, the answer is the Shannon or von Neumann entropy in the limit as approaches infinity. This limit appears disconnected from reality, as the universe seems not to contain an infinite amount of anything, let alone telephone messages. Yet the limit simplifies the mathematics involved and approximates some real-world problems.
But the limit doesn’t approximate every real-world problem. What if I want to send only one copy of my message—one shot? One-shot information theory concerns how efficiently we can process finite amounts of information. Nilanjana and colleagues had defined entropies beyond Shannon’s and von Neumann’s, as well as proving properties of those entropies. The field’s cofounders also showed that these entropies quantify the optimal rates at which we can process finite amounts of information.
My mentors and I were applying one-shot information theory to quantum thermodynamics. I’d read papers of Nilanjana’s and spoken with her virtually (we probably used Skype back then). When I learned that she’d visit Waterloo in June, I was a kitten looking forward to a saucer of cream.
Nilanjana didn’t disappoint. First, she presented a seminar at Perimeter. I recall her discussing a resource theory (a simple information-theoretic model) for entanglement manipulation. One often models entanglement manipulators as experimentalists who can perform local operations and classical communications: each experimentalist can poke and prod the quantum system in their lab, as well as link their labs via telephone. We abbreviate the set of local operations and classical communications as LOCC. Nilanjana broadened my view to the superset SEP, the operations that map every separable (unentangled) state to a separable state.
Kudos to John Preskill for hunting down this screenshot of the video of Nilanjana’s seminar. The author appears on the left.
Then, because she eats seminars for breakfast, Nilanjana presented an even more distinguished talk the same day: a colloquium. It took place at the University of Waterloo’s Institute for Quantum Computing (IQC), a nearly half-hour walk from Perimeter. Would I be willing to escort Nilanjana between the two institutes? I most certainly would.
Nilanjana and I arrived at the IQC auditorium before anyone else except the colloquium’s host, Debbie Leung. Debbie is a University of Waterloo professor and another of the most rigorous quantum information theorists I know. I sat a little behind the two of them and marveled. Here were two of the scions of the science I was joining. Pinch me.
My relationship with Nilanjana deepened over the years. The first year of my PhD, she hosted a seminar by me at the University of Cambridge (although I didn’t present a colloquium later that day). Afterward, I wrote a Quantum Frontierspost about her research with PhD student Felix Leditzky. The two of them introduced me to second-order asymptotics. Second-order asymptotics dictate the rate at which one-shot entropies approach standard entropies as (the number of copies of a message I’m compressing, say) grows large.
The following year, Nilanjana and colleagues hosted me at “Beyond i.i.d. in Information Theory,” an annual conference dedicated to one-shot information theory. We convened in the mountains of Banff, Canada, about which I wrote another blog post. Come to think of it, Nilanjana lies behind many of my blog posts, as she lies behind many of my papers.
But I haven’t explained about the little black dress. Nilanjana wore one when presenting at Perimeter and the IQC. That year, I concluded that pants and shorts caused me so much discomfort, I’d wear only skirts and dresses. So I stuck out in physics gatherings like a theorem in a newspaper. My mother had schooled me in the historical and socioeconomic significance of the little black dress. Coco Chanel invented the slim, simple, elegant dress style during the 1920s. It helped free women from stifling, time-consuming petticoats and corsets: a few decades beforehand, dressing could last much of the morning—and then one would change clothes for the afternoon and then for the evening. The little black dress offered women freedom of movement, improved health, and control over their schedules. Better, the little black dress could suit most activities, from office work to dinner with friends.
Yet I didn’t recall ever having seen anyone present physics in a little black dress.
I almost never use this verb, but Nilanjana rocked that little black dress. She imbued it with all the professionalism and competence ever associated with it. Also, Nilanjana had long, dark hair, like mine (although I’ve never achieved her hair’s length); and she wore it loose, as I liked to. I recall admiring the hair hanging down her back after she received a question during the IQC colloquium. She’d whirled around to write the answer on the board, in the rapid-fire manner characteristic of her intellect. If one of the most incisive scientists I knew could wear dresses and long hair, then so could I.
Felix is now an assistant professor at the University of Illinois in Urbana-Champaign. I recently spoke with him and Mark Wilde, another one-shot information theorist and a guest blogger on Quantum Frontiers. The conversation led me to reminisce about the day I met Nilanjana. I haven’t visited Cambridge in years, and my research has expanded from one-shot thermodynamics into many-body physics. But one never forgets the classics.
A great childhood memory that I have comes from first playing “The Incredible Machine” on PC in the early 90’s. For those not in the know, this is a physics-based puzzle game about building Rube Goldberg style contraptions to achieve given tasks. What made this game a standout for me was the freedom that it granted players. In many levels you were given a disparate set of components (e.g. strings, pulleys, rubber bands, scissors, conveyor belts, Pokie the Cat…) and it was entirely up to you to “MacGuyver” your way to some kind of solution (incidentally, my favorite TV show from that time period). In other words, it was often a creative exercise in designing your own solution, rather than “connecting the dots” to find a single intended solution. Growing up with games like this undoubtedly had significant influence in directing me to my profession as a research scientist: a job which is often about finding novel or creative solutions to a task given a limited set of tools.
From the late 90’s onwards puzzle games like “The Incredible Machine” largely went out of fashion as developers focused more on 3D games that exploited that latest hardware advances. However, this genre saw a resurgence in 2010’s spearheaded by developer “Zachtronics” who released a plethora of popular, and exceptionally challenging, logic and programming based puzzle games (some of my favorites include Opus Magnum and TIS-100). Zachtronics games similarly encouraged players to solve problems through creative designs, but also had the side-effect of helping players to develop and practice tangible programming skills (e.g. design patterns, control flow, optimization). This is a really great way to learn, I thought to myself.
So, fast-forward several years, while teaching undergraduate/graduate quantum courses at Georgia Tech I began thinking about whether it would be possible to incorporate quantum mechanics (and specifically quantum circuits) into a Zachtronics-style puzzle game. My thinking was that such a game might provide an opportunity for students to experiment with quantum through a hands-on approach, one that encouraged creativity and self-directed exploration. I was also hoping that representing quantum processes through a visual language that emphasized geometry, rather than mathematical language, could help students develop intuition in this setting. These thoughts ultimately led to the development of The Qubit Factory. At its core, this is a quantum circuit simulator with a graphic interface (not too dissimilar to the Quirk quantum circuit simulator) but providing a structured sequence of challenges, many based on tasks of real-life importance to quantum computing, that players must construct circuits to solve.
An example level of The Qubit Factory in action, showcasing a potential solution to a task involving quantum error correction.The column of “?” tiles represents a noisy channel that has a small chance of flipping any qubit that passes through. Players are challenged to send qubits from the input on the left to the output on the right while mitigating errors that occur due to this noisy channel. The solution shown here is based on a bit-flip code, although a more advanced strategy is required to earn a bonus star for the level!
幸运飞行艇官方开奖记录查询结果🚀168飞艇官网开奖🚀计划历史结果🚀168幸运飞行艇开奖记录历史 查询幸运历史号码 官方直播记录查询开奖结果-历史结果视频查询 Quantum Gamification and The Qubit Factory
My goal in designing The Qubit Factory was to provide an accurate simulation of quantum mechanics (although not necessarily a complete one), such that players could learn some authentic, working knowledge about quantum computers and how they differ from regular computers. However, I also wanted to make a game that was accessible to the layperson (i.e. without a prior knowledge of quantum mechanics or the underlying mathematical foundations like linear algebra). These goals, which are largely opposing one-another, are not easy to balance!
A key step in achieving this balance was to find a suitable visual depiction of quantum states and processes; here the Bloch sphere, which provides a simple geometric representation of qubit states, was ideal. However, it is also here that I made my first major compromise to the scope of the physics within the game by restricting the game state to real-valued wave-functions (which in turn implies that only gates which transform qubits within the X-Z plane can be allowed). I feel that this compromise was ultimately the correct choice: it greatly enhanced the visual clarity by allowing qubits to be represented as arrows on a flat disk rather than on a sphere, and similarly allowed the action of single-qubit gates to depicted clearly (i.e. as rotations and flips on the disk). Some purists may object to this limitation on grounds that it prevents universal quantum computation, but my counterpoint would be that there are still many interesting quantum tasks and algorithms that can be performed within this restricted scope. In a similar spirit, I decided to forgo the standard quantum circuit notation: instead I used stylized circuits to emphasize the geometric interpretation as demonstrated in the example below. This choice was made with the intention of allowing players to infer the action of gates from the visual design alone.
A quantum circuit in conventional notation versus the same circuit depicted in The Qubit Factory.
Okay, so while the Bloch sphere provides a nice way to represent (unentangled) single qubit states, we also need a way to represent entangled states of multiple qubits. Here I made use of some creative license to show entangled states as blinking through the basis states. I found this visualization to work well for conveying simple states such as the singlet state presented below, but players are also able to view the complete list of wave-function amplitudes if necessary.
A singlet state is created by entangling a pair of qubits via a CNOT gate.
Although the blinking effect is not a perfect solution for displaying superpositions, I think that it is useful in conveying key aspects like uncertainty and correlation. The animation below shows an example of the entangled wave-function collapsing when one of the qubits is measured.
A single qubit from a singlet is measured. While each qubit has a 50/50 chance of giving ▲ or ▼ when measured individually, once one qubit is measured the other qubit collapses to the anti-aligned state.
So, thus far, I have described a quantum circuit simulator with some added visual cues and animations, but how can this be turned into a game? Here, I leaned heavily on the existing example of Zachtronic (and Zachtronic-like) games: each level in The Qubit Factory provides the player with some input bits/qubits and requires the player to perform some logical task in order to produce a set of desired outputs. Some of the levels within the game are highly structured, similar to textbook exercises. They aim to teach a specific concept and may only have a narrow set of potential solutions. An example of such a structured level is the first quantum level (lvl QI.A) which tasks the player with inverting a sequence of single qubit gates. Of course, this problem would be trivial to those of you already familiar with quantum mechanics: you could use the linear algebra result together with the knowledge that quantum gates are unitary, so the Hermitian conjugate of each gate doubles as its inverse. But what if you didn’t know quantum mechanics, or even linear algebra? Could this problem be solved through logical reasoning alone? This is where I think that the visuals really help; players should be able to infer several key points from geometry alone:
the inverse of a flip (or mirroring about some axis) is another equal flip.
the inverse of a rotation is an equal rotation in the opposite direction.
the last transformation done on each qubit should be the first transformation to be inverted.
So I think it is plausible that, even without prior knowledge in quantum mechanics or linear algebra, a player could not only solve the level but also grasp some important concepts (i.e. that quantum gates are invertible and that the order in which they are applied matters).
An early level challenges the player to invert the action of the 3gates on the left.A solution is given on the right, formed by composing the inverse of each gate in reverse order.
Many of the levels in The Qubit Factory are also designed to be open-ended. Such levels, which often begin with a blank factory, have no single intended solution. The player is instead expected to use experimentation and creativity to design their own solution; this is the setting where I feel that the “game” format really shines. An example of an open-ended level is QIII.E, which gives the player 4 copies of a single qubit state , guaranteed to be either the or eigenstate, and tasks the player to determine which state they have been given. Those familiar with quantum computing will recognize this as a relatively simple problem in state tomography. There are many viable strategies that could be employed to solve this task (and I am not even sure of the optimal one myself). However, by circumventing the need for a mathematical calculation, the Qubit Factory allows players to easily and quickly explore different approaches. Hopefully this could allow players to find effective strategies through trial-and-error, gaining some understanding of state tomography (and why it is challenging) in the process.
An example of a level in action! This levelchallenges the player to construct a circuit that can identify an unknown qubit state given several identical copies; a task in state tomography.The solution shown here uses a cascaded sequence of measurements, where the result of one measurement is used to control the axis of a subsequent measurement.
The Qubit Factory begins with levels covering the basics of qubits, gates and measurements. It later progresses to more advanced concepts like superpositions, basis changes and entangled states. Finally it culminates with levels based on introductory quantum protocols and algorithms (including quantum error correction, state tomography, super-dense coding, quantum repeaters, entanglement distillation and more). Even if you are familiar with the aforementioned material you should still be in for a substantial challenge, so please check it out if that sounds like your thing!
The Potential of Quantum Games
I believe that interactive games have great potential to provide new opportunities for people to better understand the quantum realm (a position shared by the IQIM, members of which have developed several projects in this area). As young children, playing is how we discover the world around us and build intuition for the rules that govern it. This is perhaps a significant reason why quantum mechanics is often a challenge for new students to learn; we don’t have direct experience or intuition with the quantum world in the same way that we do with the classical world. A quote from John Preskill puts it very succinctly:
“Perhaps kids who grow up playing quantum games will acquire a visceral understanding of quantum phenomena that our generation lacks.”
Whenever someone protests, “I’m not a rocket scientist,” I think of my friend Jamie Rankin. Jamie is a researcher at Princeton University, and she showed me her lab this June. When I first met Jamie, she was testing instruments to be launched on NASA’s Parker Solar Probe. The spacecraft has approached closer to the sun than any of its predecessors. It took off in August 2018—fittingly, from my view, as I’d completed my PhD a few months earlier and met Jamie near the beginning of my PhD.
During my first term of Caltech courses, I noticed Jamie in one of my classes. She seemed sensible and approachable, so I invited her to check our answers against each other on homework assignments. Our homework checks evolved into studying together for qualifying exams—tests of basic physics knowledge, which serve as gateways to a PhD. The studying gave way to eating lunch together on weekends. After a quiet morning at my desk, I’d bring a sandwich to a shady patch of lawn in front of Caltech’s institute for chemical and biological research. (Pasadena lawns are suitable for eating on regardless of the season.) Jamie would regale me—as her token theorist friend—with tales of suiting up to use clean rooms; of puzzling out instrument breakages; and of working for the legendary Ed Stone, who’d headed NASA’s Jet Propulsion Laboratory (JPL).1
The Voyager probes were constructed at JPL during the 1970s. I’m guessing you’ve heard of Voyager, given how the project captured the public’s imagination. I heard about it on an educational audiotape when I was little. The probes sent us data about planets far out in our solar system. For instance, Voyager 2 was the first spacecraft to approach Neptune, as well as the first to approach four planets past Earth (Jupiter, Saturn, Uranus, and Neptune). But the probes’ mission still hasn’t ended. In 2012, Voyager 1 became the first human-made object to enter interstellar space. Both spacecrafts continue to transmit data. They also carry Golden Records, disks that encode sounds from Earth—a greeting to any intelligent aliens who find the probes.
Jamie published the first PhD thesis about data collected by Voyager. She now serves as Deputy Project Scientist for Voyager, despite her early-career status. The news didn’t surprise me much; I’d known for years how dependable and diligent she is.
A theorist intrudes on Jamie’s Princeton lab
As much as I appreciated those qualities in Jamie, though, what struck me more was her good-heartedness. In college, I found fellow undergrads to be interested and interesting, energetic and caring, open to deep conversations and self-evaluation—what one might expect of Dartmouth. At Caltech, I found grad students to be candid, generous, and open-hearted. Would you have expected as much from the tech school’s tech school—the distilled essence of the purification of concentrated Science? I didn’t. But I appreciated what I found, and Jamie epitomized it.
The back of the lab coat I borrowed
Jamie moved to Princeton after graduating. I’d moved to Harvard, and then I moved to NIST. We fell out of touch; the pandemic prevented her from attending my wedding, and we spoke maybe once a year. But, this June, I visited Princeton for the annual workshop of the Institute for Robust Quantum Simulation. We didn’t eat sandwiches on a lawn, but we ate dinner together, and she showed me around the lab she’d built. (I never did suit up for a clean-room tour at Caltech.)
In many ways, Jamie Rankin remains my favorite rocket scientist.
1Ed passed away between the drafting and publishing of this post. He oversaw my PhD class’s first-year seminar course. Each week, one faculty member would present to us about their research over pizza. Ed had landed the best teaching gig, I thought: continual learning about diverse, cutting-edge physics. So I associate Ed with intellectual breadth, curiosity, and the scent of baked cheese.
If I ever mention a crazy high-school English teacher to you, I might be referring to Mr. Lukacs. One morning, before the first bell rang, I found him wandering among the lockers, wearing a white beard and a mischievous grin. (The school had pronounced the day “Dress Up as Your Favorite Writer” Day, or some such designation, but still.1) Mr. Lukacs was carrying a copy of Leaves of Grass, a book by the nineteenth-century American poet Walt Whitman, and yawping. To yawp is to cry out, and Whitman garnered acclaim for weaving such colloquialisms into his poetry. “I sound my barbaric yawp over the roofs of the world,” he wrote in Leaves of Grass—as Mr. Lukacs illustrated until the bells rang for class. And, for all I know, until the final bell.
I call Mr. Lukacs one of my crazy high-school English teachers despite never having taken any course of his.2 He served as the faculty advisor for the school’s literary magazine, on whose editorial board I served. As a freshman and sophomore, I kept my head down and scarcely came to know Mr. Lukacs. He wore small, round glasses and a bowtie. As though to ham up the idiosyncrasy, he kept a basket of bowties in his classroom. His hair had grayed, he spoke slowly, and he laughed in startling little bursts that resembled gasps.
Junior year, I served as co-editor-in-chief of the literary magazine; and, senior year, as editor-in-chief. I grew to conjecture that Mr. Lukacs spoke slowly because he was hunting for the optimal word to use next. Finding that word cost him a pause, but learning his choice enriched the listener. And Mr. Lukacs adored literature. You could hear, when he read aloud, how he invested himself in it.
I once submitted to the literary magazine a poem about string theory, inspired by a Brian Greene book.3 As you might expect, if you’ve ever read about string theory, the poem invoked music. Mr. Lukacs pretended to no expertise in science; he even had a feud with the calculus teacher.4 But he wrote that the poem made him feel like dancing.
You might fear that Mr. Lukacs too strongly echoed the protagonist of Dead Poets Society to harbor any originality. The 1989 film Dead Poets Society stars Robin Williams as an English teacher who inspires students to discover their own voices, including by yawping à la Whitman. But Mr. Lukacs leaned into the film, with a gleeful sort of exultation. He even interviewed one of the costars, who’d left acting to teach, for a job. The interview took place beside a cardboard-cutout advertisement for Dead Poets Society—a possession, I’m guessing, of Mr. Lukacs’s.
This winter, friends of Mr. Lukacs’s helped him create a Youtube video for his former students. He sounded as he had twenty years before. But he said goodbye, expecting his cancer journey to end soon. Since watching the video, I’ve been waffling between reading Goodbye, Mr. Chips—a classic novella I learned of around the time the video debuted—and avoiding it. I’m not sure what Mr. Lukacs would advise—probably to read, rather than not to read. But I like the thought of saluting a literary-magazine advisor on Quantum Frontiers. We became Facebook friends years ago; and, although I’ve rarely seen activity by him, he’s occasionally effused over some physics post of mine.
Physics brought me to the Washington, DC area, where a Whitman quote greets entrants to the Dupont Circle metro station. The DC area also houses Abraham Lincoln’s Cottage, where the president moved with his wife. They sought quietude to mourn their son Willie, who’d succumbed to an illness. Lincoln rode from the cottage to the White House every day. Whitman lived along his commute, according to a panel in the visitors’ center. I was tickled to learn that the two men used to exchange bows during that commute—one giant of politics and one giant of literature.
I wrote the text above this paragraph, as well as the text below, within a few weeks of watching the Youtube video. The transition between the two bothered me; it felt too abrupt. But I asked Mr. Lukacs via email whether he’d mind my posting the story. I never heard back. I learned why this weekend: he’d passed away on Friday. The announcement said, “please consider doing something that reminds you of George in the coming days. Read a few lines of a cherished text. Marvel at a hummingbird…” So I determined to publish the story without approval. I can think of no tribute more fitting than a personal essay published on a quantum blog that’s charted my intellectual journey of the past decade.
Here’s to another giant of literature. Goodbye, Mr. Lukacs.
Image from wmata.com
1I was too boring to dress up as anyone.
2I call him one of my crazy high-school English teachers because his wife merits the epithet, too. She called herself senile, enacted the climax of Jude the Obscure with a student’s person-shaped pencil case, and occasionally imitated a chipmunk; but damn, do I know my chiasmus from my caesura because of her.
3That fact sounds hackneyed to me now. But I’m proud never to have entertained grand dreams of discovering a theory of everything.
4AKA my crazy high-school calculus teacher. My high school had loads of crazy teachers, but it also had loads of excellent teachers, and the crazy ones formed a subset of the excellent ones.
It’s the beginning of another summer, and I’m looking forward to outdoor barbecues, swimming in lakes and pools, and sharing my home-made ice cream with friends and family. One thing that I won’t encounter this summer, but I did last year, is a Canadian goose. In summer 2023, I ventured north from the University of Maryland – College Park to Waterloo, Canada, for a position at the University of Waterloo. The university houses the Institute for Quantum Computing (IQC), and the Perimeter Institute (PI) for Theoretical Physics is nearby. I spent my summer at these two institutions because I was accepted into the IQC’s Undergraduate School on Experimental Quantum Information Processing (USEQIP) and received an Undergraduate Research Award. I’ll detail my experiences in the program and the fun social activities I participated in along the way.
For my first two weeks in Waterloo, I participated in USEQIP. This program is an intense boot camp in quantum hardware. I learned about many quantum-computing platforms, including trapped ions, superconducting circuits, and nuclear magnetic resonance systems. There were interactive lab sessions where I built a low-temperature thermometer, assembled a quantum key distribution setup, and designed an experiment of the Quantum Zeno Effect using nuclear magnetic resonance systems. We also toured the IQC’s numerous research labs and their nano-fabrication clean room. I learned a lot from these two weeks, and I settled into life in goose-filled Waterloo, trying to avoid goose poop on my daily walks around campus.
I pour liquid nitrogen into a low-temperature container.
Once USEQIP ended, I began the work for my Undergraduate Research Award, joining Dr. Raymond Laflamme’s group. My job was to read Dr. Laflamme’s soon-to-be-published textbook about quantum hardware, which he co-wrote with graduate student Shayan Majidy and Dr. Chris Wilson. I read through the sections for clarity and equation errors. I also worked through the textbook’s exercises to ensure they were appropriate for the book. Additionally, I contributed figures to the book.
The most challenging part of this work was completing the exercises. I would become frustrated with the complex problems, sometimes toiling over a single problem for over three hours. My frustrations were aggravated when I asked Shayan for help, and my bitter labor was to him a simple trick I had not seen. I had to remind myself that I had been asked to test drive this textbook because I am the target audience for it. I offered an authentic undergraduate perspective on the material that would be valuable to the book’s development. Despite the challenges, I successfully completed my book review, and Shayan sent the textbook for publication at the beginning of August.
After, I moved on to another project. I worked on the quantum thermodynamics research that I conduct with Dr. Nicole Yunger Halpern. My work with Dr. Yunger Halpern concerns systems with noncommuting charges. I run numerical calculations on these systems to understand how they thermalize internally. I enjoyed working at both the IQC and the Perimeter Institute with their wonderful office views and free coffee.
Dr. Laflamme and I at the Perimeter Institute on my last day in Waterloo.
Midway through the summer, Dr. Laflamme’s former and current students celebrated his 60th birthday with a birthday conference. As one of his newest students, I had a wonderful time meeting many of his past students who’ve had exciting careers following their graduation from the group. During the birthday conference, we had six hours of talks daily, but these were not traditional research talks. The talks were on any topic the speaker wanted to share with the audience. I learned about how a senior data scientist at TD Bank uses machine learning, a museum exhibit organized by the University of Waterloo called Quantum: The Exhibition, and photonic quantum science at the Raman Research Institute. For the socializing portion, we played street hockey and enjoyed delicious sushi, sandwiches, and pastries. By coincidence, Dr. Laflamme’s birthday and mine are one day apart!
Outside of my work, I spent almost every weekend exploring Ontario. I beheld the majesty of Niagara Falls for the first time; I visited Canada’s wine country, Niagara on the Lake; I met with friends and family in Toronto; I stargazed with the hope of seeing the aurora borealis (unfortunately, the Northern Lights did not appear). I also joined a women’s ultimate frisbee team, PPF (sorry, we can’t tell you what it stands for), during my stay in Canada. I had a blast getting to play while sharpening my skills for the collegiate ultimate frisbee season. Finally, my summer would not have been great without the friendships that I formed with my fellow USEQIP undergraduates. We shared more than just meals; we shared our hopes and dreams, and I am so lucky to have met such inspiring people.
I spent my first weekend in Canada at Niagara Falls.
Though my summer in Waterloo has come to an end now, I’ll never forget the incredible experiences I had.
This is the final part of a four-part series covering the recent Perspective on noncommuting charges. I’ve been posting one part every ~5 weeks leading up to my PhD thesis defence. You can find Part 1 here, Part 2 here, and Part 3 here.
In four months, I’ll embark on the adventure of a lifetime—fatherhood.
To prepare, I’ve been honing a quintessential father skill—storytelling. If my son inherits even a fraction of my tastes, he’ll soon develop a passion for film noir detective stories. And really, who can resist the allure of a hardboiled detective, a femme fatale, moody chiaroscuro lighting, and plot twists that leave you reeling? For the uninitiated, here’s a quick breakdown of the genre.
To sharpen my storytelling skills, I’ve decided to channel my inner noir writer and craft this final blog post—the opportunities for future work, as outlined in the Perspective—in that style.
I wouldn’t say film noir needs to be watched in black and white like how I wouldn’t say jazz needs to be listened to on vinyl. But it adds a charm that’s hard to replicate.
168幸运飞行艇官方历史开奖记录 -新幸运飞行艇开奖记录查询赛车结果-飞艇168结果查询+开奖结果历史记录 幸运飞行艇历史开奖结果北京 幸运飞行艇开奖号码 幸运飞行艇官方直播记录查询开奖结果,开奖记录结果查询Theft at the Quantum Frontier
Under the dim light of a flickering bulb, private investigator Max Kelvin leaned back in his creaky chair, nursing a cigarette. The steady patter of rain against the window was interrupted by the creak of the office door. In walked trouble. Trouble with a capital T.
She was tall, moving with a confident stride that barely masked the worry lines etched into her face. Her dark hair was pulled back in a tight bun, and her eyes were as sharp as the edges of the papers she clutched in her gloved hand.
“Mr. Kelvin?” she asked, her voice a low, smoky whisper.
“That’s what the sign says,” Max replied, taking a long drag of his cigarette, the ember glowing a fiery red. “What can I do for you, Miss…?”
“Doctor,” she corrected, her tone firm, “Shayna Majidy. I need your help. Someone’s about to scoop my research.”
Max’s eyebrows arched. “Scooped? You mean someone stole your work?”
“Yes,” Shayna said, frustration seeping into her voice. “I’ve been working on noncommuting charge physics, a topic recently highlighted in a Perspective article. But someone has stolen my paper. We need to find who did it before they send it to the local rag, The Ark Hive.”
Max leaned forward, snuffing out his cigarette and grabbing his coat in one smooth motion. “Alright, Dr. Majidy, let’s see where your work might have wandered off to.”
They started their investigation with Joey “The Ant” Guzman, an experimental physicist whose lab was a tangled maze of gleaming equipment. Superconducting qubits, quantum dots, ultracold atoms, quantum optics, and optomechanics cluttered the room, each device buzzing with the hum of cutting-edge science. Joey earned his nickname due to his meticulous and industrious nature, much like an ant in its colony.
Guzman was a prime suspect, Shayna had whispered as they approached. His experiments could validate the predictions of noncommuting charges. “The first test of noncommuting-charge thermodynamics was performed with trapped ions,” she explained, her voice low and tense. “But there’s a lot more to explore—decreased entropy production rates, increased entanglement, to name a couple. There are many platforms to test these results, and Guzman knows them all. It’s a major opportunity for future work.”
Guzman looked up from his work as they entered, his expression guarded. “Can I help you?” he asked, wiping his hands on a rag.
Max stepped forward, his eyes scanning the room. “A rag? I guess you really are a quantum mechanic.” He paused for laughter, but only silence answered. “We’re investigating some missing research,” he said, his voice calm but edged with intensity. “You wouldn’t happen to know anything about noncommuting charges, would you?”
Guzman’s eyes narrowed, a flicker of suspicion crossing his face. “Almost everyone is interested in that right now,” he replied cautiously.
Shayna stepped forward, her eyes boring into Guzman’s. “So what’s stopping you from doing experimental tests? Do you have enough qubits? Long enough decoherence times?”
Guzman shifted uncomfortably but kept his silence. Max took another drag of his cigarette, the smoke curling around his thoughts. “Alright, Guzman,” he said finally. “If you think of anything that might help, you know where to find us.”
As they left the lab, Max turned to Shayna. “He’s hiding something,” he said quietly. “But whether it’s your work or how noisy and intermediate scale his hardware is, we need more to go on.”
Shayna nodded, her face set in grim determination. The rain had stopped, but the storm was just beginning.
I bless the night my mom picked up “Who Framed Roger Rabbit” at Blockbuster. That, along with the criminally underrated “Dog City,” likely ignited my love for the genre.
Their next stop was the dimly lit office of Alex “Last Piece” Lasek, a puzzle enthusiast with a sudden obsession with noncommuting charge physics. The room was a chaotic labyrinth, papers strewn haphazardly, each covered with intricate diagrams and cryptic scrawlings. The stale aroma of old coffee and ink permeated the air.
Lasek was hunched over his desk, scribbling furiously, his eyes darting across the page. He barely acknowledged their presence as they entered. “Noncommuting charges,” he muttered, his voice a gravelly whisper, “they present a fascinating puzzle. They hinder thermalization in some ways and enhance it in others.”
“Last Piece Lasek, I presume?” Max’s voice sliced through the dense silence.
Lasek blinked, finally lifting his gaze. “Yeah, that’s me,” he said, pushing his glasses up the bridge of his nose. “Who wants to know?”
“Max Kelvin, private eye,” Max replied, flicking his card onto the cluttered desk. “And this is Dr. Majidy. We’re investigating some missing research.”
Shayna stepped forward, her eyes sweeping the room like a hawk. “I’ve read your papers, Lasek,” she said, her tone a blend of admiration and suspicion. “You live for puzzles, and this one’s as tangled as they come. How do you plan to crack it?”
Lasek shrugged, leaning back in his creaky chair. “It’s a tough nut,” he admitted, a sly smile playing at his lips. “But I’m no thief, Dr. Majidy. I’m more interested in solving the puzzle than in academic glory.”
As they exited Lasek’s shadowy lair, Max turned to Shayna. “He’s a riddle wrapped in an enigma, but he doesn’t strike me as a thief.”
Shayna nodded, her expression grim. “Then we keep digging. Time’s slipping away, and we’ve got to find the missing pieces before it’s too late.”
Their third stop was the office of Billy “Brass Knuckles,” a classical physicist infamous for his no-nonsense attitude and a knack for punching holes in established theories.
Max’s skepticism was palpable as they entered the office. “He’s a classical physicist; why would he give a damn about noncommuting charges?” he asked Shayna, raising an eyebrow.
Billy, overhearing Max’s question, let out a gravelly chuckle. “It’s not as crazy as it sounds,” he said, his eyes glinting with amusement. “Sure, the noncommutation of observables is at the core of quantum quirks like uncertainty, measurement disturbances, and the Einstein-Podolsky-Rosen paradox.”
Max nodded slowly, “Go on.”
“However,” Billy continued, leaning forward, “classical mechanics also deals with quantities that don’t commute, like rotations around different axes. So, how unique is noncommuting-charge thermodynamics to the quantum realm? What parts of this new physics can we find in classical systems?”
Shayna crossed her arms, a devious smile playing on her lips. “Wouldn’t you like to know?”
“Wouldn’t we all?” Billy retorted, his grin mirroring hers. “But I’m about to retire. I’m not the one sneaking around your work.”
Max studied Billy for a moment longer, then nodded. “Alright, Brass Knuckles. Thanks for your time.”
As they stepped out of the shadowy office and into the damp night air, Shayna turned to Max. “Another dead end?”
Max nodded and lit a cigarette, the smoke curling into the misty air. “Seems so. But the clock’s ticking, and we can’t afford to stop now.”
If you want contemporary takes on the genre, Sin City (2005), Memento (2000), and L.A. Confidential (1997) each deliver in their own distinct ways.
Their fourth suspect, Tony “Munchies” Munsoni, was a specialist in chaos theory and thermodynamics, with an insatiable appetite for both science and snacks.
“Another non-quantum physicist?” Max muttered to Shayna, raising an eyebrow.
Shayna nodded, a glint of excitement in her eyes. “The most thrilling discoveries often happen at the crossroads of different fields.”
Dr. Munson looked up from his desk as they entered, setting aside his bag of chips with a wry smile. “I’ve read the Perspective article,” he said, getting straight to the point. “I agree—every chaotic or thermodynamic phenomenon deserves another look under the lens of noncommuting charges.”
Max leaned against the doorframe, studying Munsoni closely.
“We’ve seen how they shake up the Eigenstate Thermalization Hypothesis, monitored quantum circuits, fluctuation relations, and Page curves,” Munson continued, his eyes alight with intellectual fervour. “There’s so much more to uncover. Think about their impact on diffusion coefficients, transport relations, thermalization times, out-of-time-ordered correlators, operator spreading, and quantum-complexity growth.”
Shayna leaned in, clearly intrigued. “Which avenue do you think holds the most promise?”
Munsoni’s enthusiasm dimmed slightly, his expression turning regretful. “I’d love to dive into this, but I’m swamped with other projects right now. Give me a few months, and then you can start grilling me.”
Max glanced at Shayna, then back at Munsoni. “Alright, Munchies. If you hear anything or stumble upon any unusual findings, keep us in the loop.”
As they stepped back into the dimly lit hallway, Max turned to Shayna. “I saw his calendar; he’s telling the truth. His schedule is too packed to be stealing your work.”
Shayna’s shoulders slumped slightly. “Maybe. But we’re not done yet. The clock’s ticking, and we’ve got to keep moving.”
Finally, they turned to a pair of researchers dabbling in the peripheries of quantum thermodynamics. One was Twitch Uppity, an expert on non-Abelian gauge theories. The other, Jada LeShock, specialized in hydrodynamics and heavy-ion collisions.
Max leaned against the doorframe, his voice casual but probing. “What exactly are non-Abelian gauge theories?” he asked (setting up the exposition for the Quantum Frontiers reader’s benefit).
Uppity looked up, his eyes showing the weary patience of someone who had explained this concept countless times. “Imagine different particles interacting, like magnets and electric charges,” he began, his voice steady. “We describe the rules for these interactions using mathematical objects called ‘fields.’ These rules are called field theories. Electromagnetism is one example. Gauge theories are a class of field theories where the laws of physics are invariant under certain local transformations. This means that a gauge theory includes more degrees of freedom than the physical system it represents. We can choose a ‘gauge’ to eliminate the extra degrees of freedom, making the math simpler.”
Max nodded slowly, his eyes fixed on Uppity. “Go on.”
“These transformations form what is called a gauge group,” Uppity continued, taking a sip of his coffee. “Electromagnetism is described by the gauge group U(1). Other interactions are described by more complex gauge groups. For instance, quantum chromodynamics, or QCD, uses an SU(3) symmetry and describes the strong force between particles in an atom. QCD is a non-Abelian gauge theory because its gauge group is noncommutative. This leads to many intriguing effects.”
“I see the noncommuting part,” Max stated, trying to keep up. “But, what’s the connection to noncommuting charges in quantum thermodynamics?”
“That’s the golden question,” Shayna interjected, excitement in her voice. “In QCD, particle physics uses non-Abelian groups, so it may exhibit phenomena related to noncommuting charges in thermodynamics.”
“May is the keyword,” Uppity replied. “In QCD, the symmetry is local, unlike the global symmetries described in the Perspective. An open question is how much noncommuting-charge quantum thermodynamics applies to non-Abelian gauge theories.”
Max turned his gaze to Jada. “How about you? What are hydrodynamics and heavy-ion collisions?” he asked, setting up more exposition.
Jada dropped her pencil and raised her head. “Hydrodynamics is the study of fluid motion and the forces acting on them,” she began. “We focus on large-scale properties, assuming that even if the fluid isn’t in equilibrium as a whole, small regions within it are. Hydrodynamics can explain systems in condensed matter and stages of heavy-ion collisions—collisions between large atomic nuclei at high speeds.”
“Where does the non-Abelian part come in?” Max asked, his curiosity piqued.
“Hydrodynamics researchers have identified specific effects caused by non-Abelian symmetries,” Jada answered. “These include non-Abelian contributions to conductivity, effects on entropy currents, and shortening neutralization times in heavy-ion collisions.”
“Are you looking for more effects due to non-Abelian symmetries?” Shayna asked, her interest clear. “A long-standing question is how heavy-ion collisions thermalize. Maybe the non-Abelian ETH would help explain this?”
Jada nodded, a faint smile playing on her lips. “That’s the hope. But as with all cutting-edge research, the answers are elusive.”
Max glanced at Shayna, his eyes thoughtful. “Let’s wrap this up. We’ve got some thinking to do.”
After hearing from each researcher, Max and Shayna found themselves back at the office. The dim light of the flickering bulb cast long shadows on the walls. Max poured himself a drink. He offered one to Shayna, who declined, her eyes darting around the room, betraying her nerves.
“So,” Max said, leaning back in his chair, the creak of the wood echoing in the silence. “Everyone seems to be minding their own business. Well…” Max paused, taking a slow sip of his drink, “almost everyone.”
Shayna’s eyes widened, a flicker of panic crossing her face. “I’m not sure who you’re referring to,” she said, her voice wavering slightly. “Did you figure out who stole my work?” She took a seat, her discomfort apparent.
Max stood up and began circling Shayna’s chair like a predator stalking its prey. His eyes were sharp, scrutinizing her every move. “I couldn’t help but notice all the questions you were asking and your eyes peeking onto their desks.”
Shayna sighed, her confident façade cracking under the pressure. “You’re good, Max. Too good… No one stole my work.” Shayna looked down, her voice barely above a whisper. “I read that Perspective article. It mentioned all these promising research avenues. I wanted to see what others were working on so I could get a jump on them.”
Max shook his head, a wry smile playing on his lips. “You tried to scoop the scoopers, huh?”
Shayna nodded, looking somewhat sheepish. “I guess I got a bit carried away.”
Max chuckled, pouring himself another drink. “Science is a tough game, Dr. Majidy. Just make sure next time you play fair.”
As Shayna left the office, Max watched the rain continue to fall outside. His thoughts lingered on the strange case, a world where the race for discovery was cutthroat and unforgiving. But even in the darkest corners of competition, integrity was a prize worth keeping…
That concludes my four-part series on our recent Perspective article. I hope you had as much fun reading them as I did writing them.
copies of a message. Into how few bits (units of information) can I compress the 
together with the knowledge that quantum gates are unitary, so the Hermitian conjugate of each gate doubles as its inverse. But what if you didn’t know quantum mechanics, or even linear algebra? Could this problem be solved through logical reasoning alone? This is where I think that the visuals really help; players should be able to infer several key points from geometry alone:
, guaranteed to be either the 
or 
eigenstate, and tasks the player to determine which state they have been given. Those familiar with quantum computing will recognize this as a relatively simple problem in state tomography. There are many viable strategies that could be employed to solve this task (and I am not even sure of the optimal one myself). However, by circumventing the need for a mathematical calculation, the Qubit Factory allows players to easily and quickly explore different approaches. Hopefully this could allow players to find effective strategies through trial-and-error, gaining some understanding of state tomography (and why it is challenging) in the process.
Quantum Frontiers 