Surfing the Singularity - The Universe Computes

Just back from the IEEE Computer Society Quantum Week in Montreal, and besides eating my weight in pastry and bagels [1], it was a great conference. The collective hardware roadmaps from the major players leaves us thinking the big wave in quantum computing is not here yet, but soon - perhaps in 5 years time for scientific applications, and within a decade for commercial utility. While the current software continues to be sparse and low-level, there are inklings of software engineers starting to build up a stack in anticipation of needing one. But besides that, and at the risk of sounding like the other hot topic - AI marketeer hype [2] - there is the sense with quantum of being present at a new phase in computing at least, if not something larger still.

The concept of the computing universe is still just a hypothesis; nothing has been proved. However, I am confident that this idea can help unveil the secrets of nature. - Konrad Zuse, 1969 [3]

It seems, at its core, that the universe computes. Conch shells grow in logarithmic spirals, bees and orb weavers understand structural geometry. Many animals - not including Mr. Ed or Clever Hans [4], but including primates, fish, and rats - have been shown to use simple arithmetic or approximations, and in other cases can show ability to order objects in a list. There are lizards and sea shells with surface patterns constructed by cellular automata processes - simple rules which can produce complex structures, like Conway's "Game of Life". Ducks, using an inherently quantum mechanical biological process, can see magnetic fields giving them a kind of "heads up" display when migrating. [5]

Our own eyes are themselves literally photon detectors, our retinas and optic nerves pre-processing the signals before they even get to the brain. DNA stores vast amounts of information in simple patterns of four "letters" (effectively two classical bits), recipes to manufacture from the raw material of the universe a wide array of proteins for all manner of biological purposes, including of course growing your own brain. Humans can themselves perform the manual calculations necessary to build bridges and other structures which can span and withstand the forces of nature for centuries. Its also not hard to see computation of a kind in plants and their systemic networks of roots. Is the universe computing, or is the universe doing the only thing it can based on the rules? Water flowing downhill. Lightning finding its own path of least resistance. Entangled electrons separated at distance flipping their spin in response to their partner, in real time. [7]

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An Entangled History

Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical. - Richard Feynman [8]

I think I can safely say that nobody understands quantum mechanics. - Richard Feynman [9]

In the 1920s physicists like Heisenberg, Born, Pauli, and Schrödinger convinced their peers of the validity of a new formulation of the laws of physics they called (in German) "quantum mechanics", describing the behavior of nature and the universe even below the scale of atoms. This then led computing pioneer John Von Neumann in the 1930s to solidify some of the necessary maths to perform discrete quantum mechanical calculations. Von Neumann, a member of the Manhattan Project, would go on to formulate the hardware architecture for today's "classical" computers, the approach to computing being challenged by quantum computing today.

Since then, mostly notably in the 1940s with the Manhattan Project, humans have shown an increasing ability to harness the basic quantum physics into a new range of applications. We learned how to make superconductors, and how to park and manipulate individual atoms like tinkertoys [10], and now we've learned how to use these skills to make computers, with most immediate applications in modeling quantum systems like atoms and molecules, as Nobel laureate and Manhattan Project member Feynman predicted more than 40 years ago. We learned how to make lasers and LEDs, and we can now also harness photons for computing. The scientists have had nearly a century to refine their theories, and are now handing off to the engineers to prove the depth of human understanding by building things in the real world, with the business people eagerly waiting on the sidelines in anticipation (think: MRI machines). It seems that the universe computes - we now endeavor to make use of that knowledge for our own human purposes.

Qubits, Gates, and Error Everywhere

What is a qubit? Like the early video game Q*bert which showed a simulated 3D world on a 2D screen back in 1982, a qubit is a little hard to visualize as it goes deeper than a classical binary bit - much deeper. While a bit can be either a zero or a one but nothing else, a qubit can model the probability of a zero or a one and probabilistically anything in between. It might be a zero, or it might be a one, with some probability of each. It might start off a zero, and then noise from the environment might cause it to drift, or it might move off the zero purposefully as a result of acting on the qubit with one of several kinds of single and multi-qubit gates. Like gates in classical computing, a quantum gate can flip the qubit, or unique to quantum just nudge it a little. As in classical computing, its the acting on the qubit by gates which results in the computing. A native quantum program is a circuit, a directed graph, composed of gates.

How fast can we flip a qubit? Heisenberg 100 years ago gave us a way to compute the lower bound on the time to flip a spin given an energy - in short, its fast. But this doesn't even tell the whole performance story because of superposition and the ability of wide circuits to act on multiple qubits simultaneously - the speed advantage of quantum over classical can be exponential, albeit application-specific, making a class of problems which would be classically uncomputable in any human lifetime now well within reach.

The main challenge in realizing these potentials is the noise. Qubits are noisy, meaning they don't stay fixed where you think you last left them, and the seemingly magical entanglement also can show decoherence over time and distance. The gates necessary for computation can themselves introduce noisy error, as can the act of measuring the qubit to sample the solution result. Software algorithms can also just be estimates, and thus introduce their own error term relative to experiment. The prevalence of error in quantum computing means the algorithms themselves must be aware the results might be unpredictable, might need to be computed more then once to improve confidence, and might need to allocate and use a good number of precious qubits just to help mitigate the errors. We call the period we are in today the "NISQ era", meaning, noisy intermediate scale quantum computing.

Beyond the noise, how do we quantify "scale" or other metrics for sizing up the capabilities of quantum computers, now, in future, and as compared to classical? One aspect of the problem is that when comparing quantum to classical we're not comparing apples to apples, and even within "quantum apples" as we have seen, there are different kinds. [12] In one simple measure we can count qubits, but we must also know their error rate, and we must notice something about their connectedness - some quantum hardware use an all-to-all grid, and others use other topologies - racetracks and the like. And qubits can fail. Because of the limitations of qubits in the NISQ era the connectedness matters, is necessary to be known at time of circuit transpilation, and may result in swaps or other strategies employed by the transpiler toolchain to minimize errors due to the physical layout. Qubit coherence in superposition can be measured and reported as a hardware spec. Quantum volume is a number which expresses the size of a circuit N qubits wide by d gates deep which can be executed on a given machine. Gate errors especially for 2-qubit gates can be reported by the vendor. CLOPS - circuit layer operations per second - is another proposed metric which takes into consideration the time to prepare the qubits, execute the gates, and take the measurement of the result. [13] The US government in the form of Defense Advanced Research Projects Agency (DARPA) has gotten into the game of studying this varied performance landscape, towards being able to help pick winners and losers and accelerate innovation with funding awards. [14]

Quantum Hardware Roadmap

I build quantum computers that store information on individual atoms and then massage the normal interactions between atoms to make them compute. - Seth Lloyd [15]

This year's IEEE Quantum Week was an opportunity to see and hear from most of the major players in quantum computing R&D - those focused on quantum processors, systems control, networking, and software. The software topic we'll leave as a topic of a future blog, but focusing on hardware, the vendors collectively represented multiple distinct technical mechanisms to making a quantum computing machine. There's superconducting qubits from US companies like IBM Quantum , Google , and Rigetti Computing, which refrigerate and maintain the qubit between a ground and an excited state. Trapped ion computers from companies like IonQ and Quantinuum , and neutral atom computers from QuEra Computing Inc. use novel methods to again cool the system qubits to near absolute zero. But there are quantum computers which also operate quite differently. Quantum annealing, or algorithmically simulating an adiabatic process for slowly evolving a system to an optimal state, could be simulated on one of the above general quantum machines, or shown more directly on a specialized quantum machine from a Canadian company like D-Wave. Xanadu, also based in Canada, performs its quantum tricks with photonics. And while Google may jump the gun on announcing successes from time to time, they and Microsoft and others are working on a "topological qubit" based on previously only-hypothesized Majorana particles which provide the great advantage relative to other qubit implementations of being able to be controlled digitally. [16, 17]

Staying within the NISQ era as the machines scale up, a good chunk of the available qubits will continue to be allocated to error correction schemes, a task which may later as these systems mature be allocated to a software layer. At 100s of useful error-corrected qubits we can start to gain real scientific utility from quantum computing - begin to do research with quantum rather than research about quantum. Vendors such as Quantinuum promise a fully connected machine of that size in 5 years. In 10 years, vendors expect to deliver machines with 1000s of QEC, which will usher in commercial utility, and the era of "cryptographically relevant" quantum computing (i.e. DARPA wants the US to get there first [18]).

In the meantime, certain scientific domains, those which study things most closely associated with real quantum systems, will be early adopters of the technology. Molecular biology. Chemistry, for example, studying better ways to perform synthetic nitrogen fixation (think: energy-costly ammonia production for fertilizers).

Conclusion

The quantum hardware industry is in its infancy. From this gaggle of eager go-getters it’s reasonable to assume there will be technical and business winners and losers. For reasons of national security, governments will ramp up their involvement. But current machines are small, flaky, and limited in usefulness. It will be 5 to 10 years before there are quantum computers being used more commonly. A new but also a familiar approach to software will be needed - more on that in a future blog. Until utility some industries will be early leaders, ready to capitalize on an exponential increase in computing capability, one which promises to get us closer to harnessing the grand computing engine of the universe which is all around and within.

References & Trivia

[0] Photo by Ben Wicks on Unsplash

[1] Montreal bagels: https://www.mtl.org/en/experience/the-famous-montreal-bagel

[2] Gartner AI Hype Cycle 2024 explained: https://www.youtube.com/watch?v=qXKYOR3KqxQ

[3] "Calculating Space", Konrad Zuse, 1969, https://philpapers.org/archive/ZUSRR.pdf Its worth noting that while having worked for Ford Motor Co. in his early career, and like Von Neumann doing very important early work on computers, Zuse was a conscripted employee of the German Nazi government from 1939-1945.

[4] Clever Hans: https://www.horsejournals.com/popular/history-heritage/clever-hans

[5] "How Migrating Birds Use Quantum Effects to Navigate", Scientific American, April 2022, https://www.scientificamerican.com/article/how-migrating-birds-use-quantum-effects-to-navigate/

[6] A variation on Conway's Game of Life, https://stackoverflow.com/questions/70019538/simple-animation-for-conways-game-of-life-with-funcanimation

[7] "Real-Time Imaging of Quantum Entanglement", 2013, https://youtu.be/wGkx1MUw2TU?si=mnIExRs2ZOwv46Bh, but not strangely enough "Entanglement between superconducting qubits and a tardigrade", https://arxiv.org/pdf/2112.07978

[8] "Simulating Physics with Computers", International Journal of Theoretical Physics vol 21, transcript of a talk at MIT by Richard Feynman, 1981, https://s2.smu.edu/~mitch/class/5395/papers/feynman-quantum-1981.pdf

[9] "The Character of Physical Law", transcript of lectures by Richard Feynman at Cornell U, 1967, https://archive.org/details/characterofphysi0000feyn/page/12/mode/2up

[10] "2 Researchers Spell 'I.B.M.' Atom by Atom", New York Times, April 5, 1990,https://timesmachine.nytimes.com/timesmachine/1990/04/05/356490.html?pageNumber=41

[11] "Qubit Bloch Sphere Visualization", Casey Duckering, https://raw.githubusercontent.com/cduck/bloch_sphere/master/examples/xyss_gate.gif

[12] Its apple picking season here in New York: https://www.applesfromny.com/varieties/

[13] "Driving quantum performance: more qubits, higher Quantum Volume, and now a proper measure of speed", https://www.ibm.com/quantum/blog/circuit-layer-operations-per-second

[14] DARPA Quantum Benchmarking Initiative, https://www.darpa.mil/work-with-us/quantum-benchmarking-initiative

[15] "The Computational Universe", Seth Lloyd, 2002, https://www.edge.org/conversation/seth_lloyd-the-computational-universe

[16] "Google Claims To Achieve Quantum Supremacy — IBM Pushes Back", https://www.npr.org/2019/10/23/772710977/google-claims-to-achieve-quantum-supremacy-ibm-pushes-back

[17] "A route to scalable Majorana qubits", https://phys.org/news/2024-06-route-scalable-majorana-qubits.html

[18] "DARPA's quantum computing is powered by ... FOMO", https://www.theregister.com/2023/02/02/darpa_quantum_microsoft/