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| 1 | +--- |
| 2 | +layout: post |
| 3 | +title: "Anti-quantum algorithms" |
| 4 | +categories: research |
| 5 | +--- |
| 6 | + |
| 7 | +It has been about 6 months since my last blog post. |
| 8 | +I have been busy since then with various projects, both associated with my job and my personal research program, |
| 9 | + but I haven't had any bloggable results until now. |
| 10 | +I had intended to start blogging more on thoughts and opinions that aren't connected to research results, |
| 11 | + but my thoughts got caught up in a slow-burning existential career crisis that I didn't really want to blog about until they had converged. |
| 12 | +I will be discussing these thoughts in my next blog post in the near future. |
| 13 | + |
| 14 | +I'd also like to briefly take stock of how what I've actually been up to matches the plans that I articulated in my last blog post. |
| 15 | +I noted a queue of 4 planned papers. |
| 16 | +The first paper was an electronic structure application of the Cauchy kernel paper that was the subject of my last post. |
| 17 | +I ended up putting that on hold, |
| 18 | + but I will now be finishing that up for the SIAM Annual Meeting in July (I was invited to present a talk and hopefully the conference won't be cancelled). |
| 19 | +The second paper was a final revision of the [quantum Metropolis algorithm paper](https://arxiv.org/abs/1903.01451) that I presented at the 2019 APS March Meeting. |
| 20 | +I heavily revised the paper and improve it substantially, |
| 21 | + but I uncovered an important technical problem at the end of the revision process |
| 22 | + (the repeat-until-success loop of the algorithm has a fat tail of success probabilities that can cause a divergence in average run times) |
| 23 | + that will necessitate yet another major revision later this year. |
| 24 | +The third paper was a very old project on designing molecules with extremely low ionization potentials, |
| 25 | + which I resumed technical work on but had to pause as the 2020 APS March Meeting grew closer. |
| 26 | +The fourth paper is the subject of this blog post. |
| 27 | +As suggested by this mismatch between intent and outcomes, |
| 28 | + scientific research is often fraught by large uncertainties and frequent delays. |
| 29 | + |
| 30 | +This post is mainly about my latest preprint, ["Robust decompositions of quantum states"](https://arxiv.org/abs/2003.04171), |
| 31 | + which I was planning to speak about at the 2020 APS March Meeting before it was cancelled because of the global coronavirus outbreak. |
| 32 | +I'm trying to make the best of this situation, and I've instead [recorded my talk on YouTube](https://youtu.be/sUka7hj5e_E). |
| 33 | +Perhaps it will eventually reach a wider audience than it would have at the conference. |
| 34 | +Indirectly, this project has an exceptionally long history. |
| 35 | +I started trying to develop new computational methods for simulating quantum many-body systems before I even started graduate school in 2002. |
| 36 | +Like many of my research passions, I had a lot of enthusiasm, lofty goals, and high standards, which resulted in a steady stream of failed ideas for years on end. |
| 37 | +I was particularly obsessed with trying to solve the 2D Hubbard model, |
| 38 | + which was and still is an important, unsolved model of strong electron correlations and possibly electron-mediated superconductivity. |
| 39 | +My modus operandi at the time was to focus on whatever methodological idea seemed promising at the moment, |
| 40 | + mess around with it and stress test it in some way until it inevitably broke, |
| 41 | + and then brainstorm up a new idea to focus on that was informed by the past failures. |
| 42 | +At times, the churn on this approach became super high, and ideas sometimes wouldn't last more than a day. |
| 43 | +Those were fun times, but I wasn't able to produce papers from this process, which I eventually acknowledged to be a serious career problem. |
| 44 | +As a post-doc, I decided to commit to one last, best idea for treating strong quantum correlations that only produced [an incomplete preprint](https://arxiv.org/abs/1003.2596) |
| 45 | + after the preliminary numerical results that I generated turned out to be absolutely terrible. |
| 46 | +After that, I stopped working on strong-correlation methods and started working on more modest weak-correlation methods based on the random-phase approximation (RPA). |
| 47 | +My RPA work was a lot more successful, and I ended up with [a published paper](https://doi.org/10.1063/1.4855255) that I am still quite proud of. |
| 48 | +Unfortunately, I had to stop working on RPA methods when my funding for electronic structure research at Sandia National Labs suddenly dried up, |
| 49 | + and I was pushed into working on quantum computing research instead. |
| 50 | + |
| 51 | +Working on quantum computing research at Sandia National Labs was a frustrating experience. |
| 52 | +I was very interested in developing simulation methods for quantum systems, |
| 53 | + but funding for electronic structure research in very pragmatic and heavily applied environments like Sandia and the other DOE weapons labs (Livermore and Los Alamos) |
| 54 | + has been on a long slow-and-steady decline because such methods just don't have enough practical value. |
| 55 | +One of the big rationales for quantum computing, both at Sandia and more broadly, |
| 56 | + is to improve our ability to simulate quantum systems, |
| 57 | + but it is absolutely bizarre, counterintuitive, and counterproductive that we would be increasing our investment in developing |
| 58 | + quantum algorithms for quantum computers that we don't have yet while steadily decreasing our investment in developing classical algorithms |
| 59 | + for classical computers that we have plenty of and are arguably using very inefficiently. |
| 60 | +As a trendy research topic, quantum computing gets the benefit of the doubt, while the older and no-longer-trendy topic of electronic structure doesn't anymore. |
| 61 | +It is especially bizarre given that researchers generally agree that |
| 62 | + (1) a lot of methodology is shared, so that improvements to classical algorithms will have residual benefits for quantum algorithms, |
| 63 | + (2) quantum computers will likely supplement or accelerate simulations that mostly occur on classical computers, and |
| 64 | + (3) the benefits of quantum computers for quantum simulation are asymptotic in accuracy and system size, |
| 65 | + so they might not have any benefits at all for the accuracies and system sizes that people normally deal with. |
| 66 | +While I learned about quantum algorithm development and made numerous attempts at developing new quantum algorithms at Sandia, |
| 67 | + I also tried my best to inject classical algorithm development wherever I could get away with it. |
| 68 | +This was also an excuse to return to research in strong-correlation methods, now considering a broader set of tools and ingredients |
| 69 | + including classical algorithms, both deterministic and stochastic, and quantum algorithms. |
| 70 | + |
| 71 | +I did not have a clear agenda or program of research when I started working in quantum computing. |
| 72 | +At first, I spent a lot of time just learning the subject and catching up with several decades of research. |
| 73 | +Eventually, after a period of more exploratory efforts, I settled into a program of quantum computing research |
| 74 | + that I have now carried with me beyond my time at Sandia. |
| 75 | +The premise is that someday, once we finally have large digital quantum computers in a few decades or so, |
| 76 | + we will carry out atomistic simulations containing both classical and quantum degrees of freedom |
| 77 | + that are distributed over classical and quantum computers. |
| 78 | +I am interested in delineating these classical/quantum boundaries in both simulation and computation: |
| 79 | + (1) what degrees of freedom should be treated classically, semi-classically, or fully quantum mechanically and |
| 80 | + (2) how should we partition the simulation between classical and quantum computers and how should they be coupled together? |
| 81 | +My approach to resolving these boundaries right now is a two-pronged attack |
| 82 | + aimed at developing better classical algorithms to push on the classical side of the boundary |
| 83 | + and better quantum algorithms to push on the quantum side of the boundary, |
| 84 | + so that the boundary is resolved evenly from both sides. |
| 85 | + |
| 86 | +The quantum side of this research program is much farther along, as it was developed first. |
| 87 | +For now, it mainly consists of two parts: quantum error correction (QEC) algorithms and quantum Metropolis algorithms. |
| 88 | +The overall cost of quantum computing depends on multiple layers: the underlying physical qubit technology, |
| 89 | + the QEC layer, and the algorithms layer. |
| 90 | +For reasons of long-term career stability, I am very loath to commit to a specific physical qubit technology, |
| 91 | + so I've instead focused on the other two layers. |
| 92 | +I wrote several papers on QEC at Sandia, and I find the topic to be very interesting, but it just isn't a very popular research topic right now. |
| 93 | +While I have a lot of ideas for future projects, my QEC research has been on hold for several years now, |
| 94 | + and I don't plan to return to it until a logical qubit has been experimentally realized. |
| 95 | +My interest in QEC is now more about patenting essential components of future quantum computers rather than purely academic curiosity, |
| 96 | + and there is no point in starting a patent clock in a world without logical qubits. |
| 97 | +Instead, I've been working on quantum algorithms for preparing thermal states. |
| 98 | +This started at Sandia, where I tried to develop a quantum analog of the Langevin thermostat. |
| 99 | +The development of a quantum Langevin thermostat turned into a horrible technical slog (that I might eventually recount in this blog), |
| 100 | + but it eventually evolved into the development of a quantum Metropolis algorithm that I released a [preprint](https://arxiv.org/abs/1903.01451) |
| 101 | + on shortly before starting this blog. |
| 102 | +The quantum Metropolis algorithm is very promising but still has a few outstanding technical problems, |
| 103 | + and I expect to finish it and release a final version of the paper later this summer. |
| 104 | + |
| 105 | +The classical side of this research program also started at Sandia, but it was much slower to develop. |
| 106 | +The basic premise of the project was that noise and uncertainty in quantum systems must inevitably drive them to some kind of classical limit |
| 107 | + that is described by classical physics and is efficient to simulate on classical computers. |
| 108 | +As quantum systems are driven towards that limit, they should become easier to simulate on classical computers even while retaining much of their quantum identity. |
| 109 | +There are some very nice results in quantum information theory that embody this concept very clearly. |
| 110 | +Perhaps the best example are quantum stabilizer circuits (Clifford gates with qubit preparation and measurement operations) |
| 111 | + that include T gates (a non-Clifford gate that enables universal quantum computation) with polarizing noise. |
| 112 | +When the noise in the T gates is smaller than a known threshold, |
| 113 | + the noise can be "distilled" away to a negligible amount using a process known as magic state distillation, |
| 114 | + which is an important ingredient in many plans for digital quantum computers. |
| 115 | +As the threshold is approached, the efficiency of magic state distillation drops to zero (a diverging number of noisy T gates is needed to distill out a low-noise T gate). |
| 116 | +When the noise is at or above the threshold, these circuits can be efficiently simulated on a classical computer |
| 117 | + and are no longer capable of universal quantum computation. |
| 118 | +While this is a very compelling result, it has very little to do with physical quantum devices or any applications other than QEC. |
| 119 | +With a lot of popular interest in using noisy quantum devices for quantum simulation tasks without any QEC, |
| 120 | + I wanted to develop a comparable result that was relevant to simulation (i.e. showing that noise made quantum simulation tasks easier for classical computers). |
| 121 | +For a long time, this project was too hung up on trying to model specific instances of analog quantum simulators, |
| 122 | + but realistic noise is messy and does not directly make systems easier to simulate. |
| 123 | +In fact, a lot of experimental noise is actually very difficult to model and simulate, |
| 124 | + and makes some noisy quantum systems even harder to simulate than their idealized versions. |
| 125 | +I finally started to make progress when I gave up on realistic physical noise |
| 126 | + and decided to design noise that was tailored to making quantum systems easier to simulate. |
| 127 | +This noise was based on qubit measurements, which introduced a stochastic component that effectively made it a type of quantum Monte Carlo method. |
| 128 | +I had always discounted stochastic algorithms in my previous attempts at developing strong-correlation solvers |
| 129 | + because of the inherently high cost of reducing sampling errors, |
| 130 | + but here it was natural and inevitable in mimicking the capabilities of quantum computing hardware. |
| 131 | + |
| 132 | +In a way, the development of classical algorithms to simulate quantum systems by introducing noise that saps them of their inherent quantum computing power |
| 133 | + is kind of like developing "anti-quantum" algorithms, at least for the purposes of a catchy title for a blog post. |
| 134 | +As I will discuss more in my next blog post, I now feel a strong need to consolidate my research into a more narrowly focused technical path. |
| 135 | +My end goal on the timescale of several years is still to develop a new generation of semiempirical models, |
| 136 | + but that research area is extremely unpopular now (making it impossible to get any sort of support for it or career benefit from it) |
| 137 | + and in need of a major technical overhaul. |
| 138 | +Right now, I believe that further developing the results of this project, both the theory and software implementation, |
| 139 | + will both help with the technical overhaul of semiempirical models (by distinguishing between Hamiltonian model errors and correlation model errors) |
| 140 | + and be a direct benefactor of it (by gaining access to simple model Hamiltonians that are quantitative representations of real molecules and materials). |
| 141 | +I'm trying to balance my research program so that it aligns as much as possible with what I want to work on and what I believe to be the best science that I am capable of doing |
| 142 | + while also maintaining connections to popular research topics that give me a better chance of eventually finding financial support to sustain a research career |
| 143 | + that is presently in a slow but inevitable decline. |
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