Jekyll2024-03-06T09:10:02-08:00http://threeplusone.com/feed.xmlGavin E. CrooksBespoke research on the physics of informationGavin E. CrooksUpcoming: 2024-03-20, U. Chicago, Computations in Science Seminar2024-02-22T00:00:00-08:002024-02-22T00:00:00-08:00http://threeplusone.com/news/Upcoming<h2 id="upcoming-seminars-and-presentations">Upcoming Seminars and Presentations</h2>
<ul>
<li>2024-03-20, U. Chicago, Computations in Science Seminar</li>
</ul>Gavin E. Crooks* Upcoming: 2024-03-20, U. Chicago, Computations in Science SeminarTalk: U. Maryland Physics Colloquium: Thermodynamic Linear Algebra2024-02-13T00:00:00-08:002024-02-13T00:00:00-08:00http://threeplusone.com/talks/Maryland-TLA<p><a href="/talks/2024-02-13-Maryland.pdf">Slides</a></p>
<p><strong>Abstract</strong></p>
<p><a href="/assets/images/thermola.jpg" class="align-right"><img src="/assets/images/thermola.jpg" alt="cr" /></a>
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities, so this approach remains long-term in timescale. Here we consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.
At first sight, thermodynamics and linear algebra seem to be unrelated fields. In this work, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.</p>Gavin E. CrooksWe consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.Talk: Rutgers University 125th Statistical Mathematics Conference: Thermodynamic Linear Algebra2023-12-18T00:00:00-08:002023-12-18T00:00:00-08:00http://threeplusone.com/talks/Rutgers-TLA<p><a href="/talks/2023-12-Rutgers.pdf">Slides</a></p>
<p><strong>Abstract</strong></p>
<p><a href="/assets/images/thermola.jpg" class="align-right"><img src="/assets/images/thermola.jpg" alt="cr" /></a>
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities, so this approach remains long-term in timescale. Here we consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.
At first sight, thermodynamics and linear algebra seem to be unrelated fields. In this work, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.</p>Gavin E. CrooksWe consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.Presentation: NeurIPS 2023 (New Orleans) Physics Colloquium: Thermodynamic AI and Thermodynamic Linear Algebra2023-12-16T00:00:00-08:002023-12-16T00:00:00-08:00http://threeplusone.com/talks/NeurIPS-TLA<p><a href="/talks/2023-12-Neurips.pdf">Presentation</a></p>
<p><strong>Abstract</strong></p>
<p><a href="/talks/2023-12-Neurips.pdf" class="align-right"><img src="/assets/images/Neurips_poster.png" alt="cr" /></a>
Many Artificial Intelligence (AI) algorithms are inspired by physics and employ
stochastic fluctuations, such as generative diffusion models, Bayesian neural 6
networks, and Monte Carlo inference. These algorithms are currently run on digital hardware, ultimately limiting their scalability and overall potential. Here, we propose a novel computing device, called Thermodynamic AI hardware, that could accelerate such algorithms. Thermodynamic AI hardware can be viewed as a novel form of computing, since it uses novel fundamental building blocks, called stochastic units (s-units), which naturally evolve over time via stochastic trajectories. In addition to these s-units, Thermodynamic AI hardware employs a Maxwell’s demon device that guides the system to
B. Gaussian sampling
produce non-trivial states. We provide a few simple physical architectures for
building these devices, such as RC electrical circuits. Moreover, we show that this same hardware can be used to accelerate various linear algebra primitives.
We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations.</p>Gavin E. CrooksWe consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.Talk: Berkeley Physics Colloquium: Thermodynamic Linear Algebra2023-11-13T00:00:00-08:002023-11-13T00:00:00-08:00http://threeplusone.com/talks/Berkeley-Physics-TLA<table>
<tbody>
<tr>
<td><a href="/talks/2023-11-13-Berkeley-Physics-TLA.pdf">Slides</a></td>
<td><a href="https://www.youtube.com/watch?v=dyxRB-nLKac&list=PLt7hlrB4U1m3ZvY-LT-3MRaxjyR1o6K2S&index=6">Youtube</a></td>
</tr>
</tbody>
</table>
<p><strong>Abstract</strong></p>
<p><a href="/assets/images/thermola.jpg" class="align-right"><img src="/assets/images/thermola.jpg" alt="cr" /></a>
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities, so this approach remains long-term in timescale. Here we consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.
At first sight, thermodynamics and linear algebra seem to be unrelated fields. In this work, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.</p>Gavin E. CrooksWe consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.Talk: Berkeley Stat. Mech. Seminar: Thermodynamic Linear Algebra2023-10-25T00:00:00-07:002023-10-25T00:00:00-07:00http://threeplusone.com/talks/thermola<p><a href="talks/2023-10-Stat-Mech-Seminar-Thermodynamic-Linear-Algebra.pdf">Slides</a></p>
<p><strong>Abstract</strong></p>
<p><a href="/assets/images/thermola.jpg" class="align-right"><img src="/assets/images/thermola.jpg" alt="cr" /></a>
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities, so this approach remains long-term in timescale. Here we consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.
At first sight, thermodynamics and linear algebra seem to be unrelated fields. In this work, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.</p>Gavin E. CrooksWe consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.Preprint: Thermodynamic Linear Algebra2023-08-10T00:00:00-07:002023-08-10T00:00:00-07:00http://threeplusone.com/pubs/thermola<p>Maxwell Aifer, Kaelan Donatella, Max Hunter Gordon, Thomas Ahle, Daniel Simpson, Gavin E. Crooks, Patrick J. Coles</p>
<p>arXiv:2308.05660</p>
<p>[
<a href="http://arxiv.org/pdf/2308.05660.pdf">Full text</a> |
<a href="http://arxiv.org/abs/2308.05660">arXiv</a> ]</p>
<p><strong>Abstract</strong></p>
<p><a href="/assets/images/thermola.jpg" class="align-right"><img src="/assets/images/thermola.jpg" alt="cr" /></a>
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities, so this approach remains long-term in timescale. Here we consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.
At first sight, thermodynamics and linear algebra seem to be unrelated fields. In this work, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for (1) solving linear systems of equations, (2) computing matrix inverses, (3) computing matrix determinants, and (4) solving Lyapunov equations. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.</p>Gavin E. CrooksWe consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra.Article: Protein–ligand binding free-energy calculations with ARROW – A purely first-principles parameterized polarizable force field2022-12-05T00:00:00-08:002022-12-05T00:00:00-08:00http://threeplusone.com/pubs/arrow<p>Grzegorz Nawrocki, Igor Leontyev, Serzhan Sakipov, Mikhail Darkhovskiy, Igor Kurnikov, Leonid Pereyaslavets, Ganesh Kamath, Ekaterina Voronina, Oleg Butin, Alexey Illarionov, Michael Olevanov, Alexander Kostikov, Ilya Ivahnenko, Dhilon S. Patel, Subramanian K. R. S. Sankaranarayanan, Maria G. Kurnikova, Christopher Lock, Gavin E. Crooks, Michael Levitt, Roger D. Kornberg, and Boris Fain, J. Chem. Theory Comput (2022)</p>
<p>[
<a href="https://threeplusone.com/pubs/Nawrocki2022a.pdf">Full text</a> ]</p>
<p><strong>Abstract</strong></p>
<p><a href="/assets/images/arrow.png" class="align-right"><img src="/assets/images/arrow.png" alt="cr" /></a></p>
<p>Protein−ligand binding free-energy calculations
using molecular dynamics (MD) simulations have emerged as a
powerful tool for in silico drug design. Here, we present results
obtained with the ARROW force field a multipolar
polarizable and physics-based model with all parameters fitted
entirely to high-level ab initio quantum mechanical (QM)
calculations. ARROW has already proven its ability to determine
solvation free energy of arbitrary neutral compounds with
unprecedented accuracy. The ARROW FF parameterization is
now extended to include coverage of all amino acids including charged groups, allowing molecular simulations of a series of protein−
ligand systems and prediction of their relative binding free energies. We ensure adequate sampling by applying a novel technique that
is based on coupling the Hamiltonian Replica exchange (HREX) with a conformation reservoir generated via potential softening and
nonequilibrium MD. ARROW provides predictions with near chemical accuracy (mean absolute error of ∼0.5 kcal/mol) for two of
the three protein systems studied here (MCL1 and Thrombin). The third protein system (CDK2) reveals the difficulty in accurately
describing dimer interaction energies involving polar and charged species. Overall, for all of the three protein systems studied here,
ARROW FF predicts relative binding free energies of ligands with a similar accuracy level as leading nonpolarizable force fields.</p>Gavin E. CrooksProtein−ligand binding free-energy calculations using molecular dynamics (MD) simulations have emerged as a powerful tool for in silico drug design. Here, we present results obtained with the ARROW force field a multipolar polarizable and physics-based model with all parameters fitted entirely to high-level ab initio quantum mechanical (QM) calculations.Tech. Note 009 v0.8: On Measures of Information and Entropy 009 v0.82021-12-10T00:00:00-08:002021-12-10T00:00:00-08:00http://threeplusone.com/pubs/on-info-009-080<p><img src="/assets/images/info.png" alt="info" class="align-right" />
A brief overview of information measures on classical, discrete probability distributions.
Tech. Note 009 v0.8
[ <a href="/info">Full Text</a> ]</p>Gavin E. CrooksA brief overview of information measures on classical, discrete probability distributions. Tech. Note 009 v0.8 [ Full Text ]Article: Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule2021-02-02T00:00:00-08:002021-02-02T00:00:00-08:00http://threeplusone.com/pubs/SPSR2<p>Leonardo Banchi and Gavin E. Crooks, Quantum 5 356 (2021)
[
<a href="https://arxiv.org/pdf/2005.10299">Full text</a> |
<a href="https://arxiv.org/abs/2005.10299">arXiv</a>
<a href="https://quantum-journal.org/views/qv-2021-01-26-50/">Perspective</a> ]</p>
<hr />
<p>The Parameter Shift Rule is a cunning, recently developed method for evaluation gradients of quantum circuits on a quantum computer. But it has two problems. The first is aesthetic: The derivation has always felt somewhat convoluted to me, although I did my best to explain why the PSR works in a <a href="/pubs/gradients/">previous paper</a>. The second issues is that the PSR isn’t universal. It only works for certain gates with a special mathematical structure. Again, in a previous paper I described one approach to circumvent that limitation, but that approach itself has limitations.</p>
<p>Last November I was invited to <a href="https://qhack.ai/">QHACK’19</a>, a quantum hackathon hosted by <a href="https://www.xanadu.ai/">Xanadu AI</a>. I gave a <a href="https://www.youtube.com/watch?v=cobp2Sf5f3o">short talk</a> on gate decompositions and the Parameter Shift Rule, and there met <a href="https://leonardobanchi.github.io/">Leonardo Banchi</a>, who also gave a talk on related subjects. Over the next couple of days we fell to chatting, and the collaboration leading to the current paper was born. Leonardo had two key insights. The first was that we should derive the PSR starting from the superoperator formalism of quantum mechanics.</p>
<p><a href="/assets/images/superop.png" class="align-center"><img src="/assets/images/superop.png" alt="cr" /></a></p>
<p>The standard Dirac notation with bra’s and ket’s and unitaries is fine for describing pure quantum dynamics followed by a single measurement. But for anything <a href="/pubs/Crooks2008a.pdf">more complicated than that</a> the Dirac formalism gets really tricky really quickly. Instead we should use density matrices and describe the dynamics with superoperators. Even if the dynamics is still pure and not noisy, superoperators can still provide a simpler representation. This step makes the derivation of the PSR feel much more natural to me.</p>
<p>The second trick is the following operator identity, which is due to Wilcox in the 1960’s.</p>
<p><a href="/assets/images/Wilcox1966.png" class="align-center"><img src="/assets/images/Wilcox1966.png" alt="cr" /></a></p>
<p>Taking derivatives of exponentials of functions is easy standard calculus. But life gets harder if you want to take derivatives of exponentials of operators. This Wilcox identity neatly solved that problem. Putting this math together with the superoperator description of the dynamics, and we get a general expression for evaluating gradients of quantum gates, which we have called the <a href="/pubs/Banchi2020a.pdf">Stochastic Parameter Shift Rule</a>.</p>
<p>For the technical details, please see our paper. But for a introductory operational overview, take a look at this great <a href="https://pennylane.ai/qml/demos/tutorial_stochastic_parameter_shift.html">PennyLane tutorial</a> from the folks at Xanadu AI, and this perspective <a href="https://quantum-journal.org/views/qv-2021-01-26-50/">Gradients just got more flexible</a> by Johannes Jakob Meyer .</p>
<p><a href="/assets/images/SPSR2.png" class="align-center"><img src="/assets/images/SPSR2.png" alt="cr" /></a></p>
<hr />
<p><strong>Abstract</strong></p>
<p>Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.</p>Gavin E. CrooksThe Parameter Shift Rule is a cunning, recently developed method for evaluation gradients of quantum circuits on a quantum computer. But it has two problems...