Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session A70: Machine Learning and Quantum SimulationFocus
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Sponsoring Units: DQI Chair: Daoheng Niu, University of Texas at Austin Room: Room 409 |
Monday, March 6, 2023 8:00AM - 8:12AM |
A70.00001: Revealing microcanonical phase diagrams of strongly correlated electrons on quantum computers I Gaurav Gyawali, Mabrur Ahmed, Eric W Aspling, Luke A Ellert-Beck, Michael J Lawler Quantum computers and simulators are promising platforms to simulate the dynamics of quantum many-body systems. Inspired by von Neumann’s time-averaged density matrix and recently developed classical shadow tomography technique, we introduce an approach called time averaged classical shadows(TACS) to study the quantum thermodynamic properties. We show that TACS can be used as an effective representation for unsupervised machine learning methods such as diffusion map to identify the microcanonical phases of strongly interacting electrons. Our results demonstrate that machine learning methods can identify quantum phase transitions from simulated microcanonical dynamics data suggesting quantum computers will be capable of mapping out microcanonical phase diagrams in the near term. In part I of this talk, we will discuss the theoretical underpinnings of our work. |
Monday, March 6, 2023 8:12AM - 8:24AM |
A70.00002: Revealing microcanonical phase diagrams of strongly correlated electrons on quantum computers II Mabrur Ahmed, Gaurav Gyawali, Michael J Lawler One of the earliest conceived advantages quantum computers have over classical computers is in simulating the dynamics of closed quantum systems. In comparison, the problem of ground state computation is harder for it to solve, especially in the case of strongly correlated systems. Here, we devise a method to study the microcanonical phase diagram of strongly correlated quantum systems from dynamics data. We introduce a concept called time-averaged classical shadows (TACS), which borrows from the quantum tomography method called classical shadows, as well as Von Neumann's idea of the time-averaged density matrix, to construct thermal state representations from dynamics data. We simulate microcanonical quantum dynamics for the 1D transverse field Ising model to generate TACS data, then deploy an unsupervised machine learning method called diffusion maps to learn the phases. Our results show that machine learning methods can learn quantum phase transitions from TACS data, suggesting quantum computers will be capable of mapping out microcanonical phase diagrams in the near term. |
Monday, March 6, 2023 8:24AM - 8:36AM |
A70.00003: Adaptive randomized measurement: a practical route to achieve scientific discovery from quantum simulations Wonjun Lee, Cheong Eung Ahn, Hyukjoon Kwon, Gil Young Cho Quantum simulators and computers are powerful platforms for investigating the physics of strongly-correlated quantum systems. To fully utilize their potential, however, one needs to efficiently extract physically relevant features from the simulated many-body states. Here, we propose such an adaptive randomized measurement protocol. Instead of performing fully randomized measurements, our approach adaptively changes its measurement basis at each step, based on Bayesian inference of prior measurement outcomes. We demonstrate the utility of our protocol by applying it to spontaneously symmetry breaking and symmetry-protected topological (SPT) phases, from which we successfully extract the classifying observables such as order parameters and SPT invariants, and to learning stabilizer states. These establish a practical, physics-oriented protocol, which can potentially lead to new scientific discoveries in near-term quantum simulations of strongly-correlated many-body systems. |
Monday, March 6, 2023 8:36AM - 8:48AM |
A70.00004: Quantum variational learning for quantum error-correcting codes Chenfeng Cao Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. However, the majority of these codes are not suitable for near-term quantum devices. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. The cost functions are inspired by the most general and fundamental requirements of a QECC, the Knill-Laflamme conditions. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, degenerate or non-degenerate, pure or impure. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., ((n,2n-6,3))2 for n from 7 to 14. We also found new ((6,2,3))2 and ((7,2,3))2 codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a ((7,3,3))2 code does not exist. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes. |
Monday, March 6, 2023 8:48AM - 9:00AM |
A70.00005: Reconstructing Thermal Quantum Quench Dynamics from Pure States Jason Saroni, Henry S Lamm, Peter P Orth, Thomas Iadecola Simulating the nonequilibrium dynamics of thermal states is a fundamental problem across scales from high energy to condensed matter physics. The exponential complexity of time-evolving such states suggests that quantum computers could solve this problem efficiently. However, even on a quantum computer, this requires evolving an exponentially large number of pure states, one for each element of the density matrix. In this work we show that the necessary number of pure-state evolutions can be reduced to simulating the largest density matrix elements by weight, capturing the density matrix to a specified precision. The number of quantum simulations can be further reduced by leveraging symmetries of the Hamiltonian. This approach paves the way to more accurate thermal-state dynamics simulations on near-term quantum hardware with reduced resources. |
Monday, March 6, 2023 9:00AM - 9:12AM |
A70.00006: Variational learning algorithms for quantum query complexity Zipeng Wu, Bei Zeng, ZHANG CHAO Quantum query complexity plays an important role in studying quantum algorithms, which cap- |
Monday, March 6, 2023 9:12AM - 9:24AM |
A70.00007: The Quantum Fourier Transform Has Small Entanglement Jielun Chen The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would think it can introduce large entanglement to qubit systems and would be difficult to simulate classically. While early results showed QFT indeed has maximal operator entanglement, we show that this is entirely due to the bit reversal in the QFT. The core part of the QFT has Schmidt coefficients decaying exponentially quickly, and thus it can only generate a constant amount of entanglement regardless of the number of qubits. In addition, we show the entangling power of the QFT is the same as the time evolution of a Hamiltonian with exponentially decaying interactions, and thus a variant of the area law for dynamics can be used to understand the low entanglement intuitively. Using the low entanglement property of the QFT, we show that classical simulations of the QFT on a matrix product state with low bond dimension only take time linear in the number of qubits, providing a potential speedup over the classical fast Fourier transform (FFT) on many classes of functions. We demonstrate this speedup in test calculations on some simple functions. For data vectors of length 106 to 108, the speedup can be a few orders of magnitude. |
Monday, March 6, 2023 9:24AM - 9:36AM |
A70.00008: Quantum Boundary Integral Algorithm for linear and nonlinear PDEs in Quantum Computation of Fluid Dynamics Sachin Satish Bharadwaj, Balu Nadiga, Stephan Eidenbenz, K. R Sreenivasan The advent of quantum computing (QC) and its potential in solving certain classes of problems with large computational speed-ups compared to its classical counterparts, kindles one to try utilizing such abilities to solve fluid flow problems. Though there has been an influx of new and improved quantum algorithms, recent efforts in this direction also point to critical caveats that need addressing, especially to be able to simulate fluid flows. For instance, the class of Quantum Linear System Algorithms (QLSA) has evolved greatly over time with its origins stemming from the HHL (Harrow-Hassidim-Lloyd) algorithm, that aims at solving linear system of equations with a significant speedup, which inherently also reflects the linearity of quantum mechanics itself. However fluid flows are mostly nonlinear. The aim of this work is to explore how one could reformulate the problem to leverage the advantage of QLSA to encode the nonlinearities, while also preserving the speed-up. |
Monday, March 6, 2023 9:36AM - 9:48AM |
A70.00009: Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations Yong-Xin Yao, Jo~{a}o Getelina, Niladri Gomes, Thomas Iadecola, Peter P Orth Scalable quantum algorithms to simulate quantum many-body systems in thermal equilibrium are under active research. Here we develop a quantum version of the minimally entangled typical thermal states algorithm to compute finite temperature properties of quantum systems. We adopt a recently developed adaptive variational approach to realize high-fidelity state propagation along the imaginary time axis at each thermal step. The algorithm leverages highly compact, dynamically generated, problem-specific quantum circuits, which are suitable for current and near-term quantum hardware. Through thermal energy calculations of integrable and nonintegrable spin models in one and two dimensions, we demonstrate approximately linear system-size scaling of the circuit complexity for our benchmark systems. Finally, we showcase the approach by mapping out representative points on a two-phase critical line of a 2D quantum spin model. |
Monday, March 6, 2023 9:48AM - 10:00AM |
A70.00010: Using the Variational Quantum Thermalizer as an Impurity Solver Johannes Selisko, Maximilian Amsler, Thomas Hammerschmidt, Ralf Drautz, Thomas Eckl The simulation of strongly correlated fermionic systems could potentially benefit from quantum computers which inherently exhibit quantum properties. Calculating a Green's function for an impurity model in the framework of dynamical mean field theory (DMFT) incorporating a quantum device is a particularly efficient way to treat extended materials. We present a novel quantum algorithm to solve such quantum impurity problems, using a hybrid quantum-classical approach. Our solver uses a variational quantum thermalizer to calculate the eigenstates of the system and their energies. Using these states, the Lehmann representation of the impurity Green's function can be measured on quantum devices. By considering the effect of shot noise and quantum errors, which are prevalent on experimental NISQ hardware, we carefully analyze DMFT results for the Bethe lattice and conclude that our algorithm is well suited for current NISQ devices. Finally, we present results from a full DFT+DMFT cycle for real materials systems which show good agreement with reference calculations from classical methods like exact diagonalization and quantum Monte Carlo methods. |
Monday, March 6, 2023 10:00AM - 10:12AM |
A70.00011: Green's function approach to quantum chemistry on a quantum computer via dynamical self-energy mapping Christina Daniel, Barbara Jones, James K Freericks We propose a low-depth circuit for quantum chemistry based on the dynamical self-energy mapping (DSEM) paradigm, where a sparse Hamiltonian is created that shares the same dynamical part of the self energy as that of the molecule (evaluated with a simple approximate method). DSEM then assumes the exact self-energy of the sparse model will approximate the dynamical part of the self-energy of the molecule accurately. As a first step in this approach, we illustrate how this procedure can work on a quantum computer, by simulating the following process classically: (i) generate the lesser and greater Green's functions in the time domain; (ii) process the temporal data with compressive sensing to determine the retarded Green's function in the frequency domain; (iii) extract the imaginary part of the self-energy by determining the weights and frequencies of the corresponding delta functions, and (iv) verify the accuracy by computing the ground-state energy. We illustrate part of this algorithm with the Hubbard model on a ring. |
Monday, March 6, 2023 10:12AM - 10:24AM |
A70.00012: Koopman operator learning for accelerating quantum optimization and machine learning Di Luo, Jiayu Shen, Rumen Dangovski, Marin Soljacic Finding efficient optimization methods is crucial for quantum optimization and machine learning on near-term quantum computers. It is costly to obtain gradients on quantum computers in comparison to classical computers, since the sample complexity scales linearly with the number of parameters and measurements. In this paper, we connect the natural gradient method in quantum optimization with Koopman operator theory, which is a powerful framework for predicting nonlinear dynamics. We propose a data-driven Koopman operator learning approach for accelerating quantum optimization and machine learning. To predict parameter updates on quantum computers, we develop new methods including the sliding window dynamic mode decomposition (DMD) and the neural-network-based DMD. We apply our methods both on simulations and real quantum hardware. We demonstrate successful acceleration of gradient optimization on the variational quantum eigensolver, including the quantum Ising model and the quantum Heisenberg model, as well as quantum machine learning applications. |
Monday, March 6, 2023 10:24AM - 11:00AM |
A70.00013: Neural-network-enabled hybrid classical-quantum computing Invited Speaker: Giuseppe Carleo Using quantum and classical computational techniques in a unified framework is key to solving problems that cannot be easily addressed by quantum computations alone. |
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