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 K64: Variational Quantum AlgorithmsFocus
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Sponsoring Units: DQI Chair: Deliang Bao, Vanderbilt University Room: Room 415 |
Tuesday, March 7, 2023 3:00PM - 3:12PM |
K64.00001: Subspace Diagonalization on Quantum Computers using Eigenvector Continuation Akhil Francis, Anjali A Agrawal, Jack H Howard, Efekan Kokcu, Alexander F Kemper Quantum subspace diagonalization (QSD) methods are quantum-classical hybrid methods, commonly used to find ground and excited state energies by projecting the Hamiltonian to a smaller subspace. In applying these, the choice of subspace basis is critical from the perspectives of basis completeness and efficiency of implementation on quantum computers. In this work, we present Eigenvector Continuation (EC) as a QSD method, where low-energy states of the Hamiltonian at different points in parameter space are chosen as the subspace basis. This unique choice enables rapid evaluation of low-energy spectra, including ground and nearby excited states, with minimal hardware effort. As a particular advantage, EC is able to capture the spectrum across ground state crossovers corresponding to different symmetry sectors of the problem. We demonstrate this method for interacting spin models and molecules. |
Tuesday, March 7, 2023 3:12PM - 3:24PM |
K64.00002: Iteration-free variational quantum eigensolver algorithm Daniel Gunlycke, C Stephen Hellberg, John Stenger We present a variant of the variational quantum eigensolver algorithm that only requires the execution of a set of quantum circuits once rather than at every iteration during the parameter optimization process, thereby significantly reducing the number of needed circuit executions. This iteration-free algorithm relies on an ansatz operator of a particular form that lets the quantum processing unit probe all needed probability mass functions and the classical processing unit perform all the remaining calculations, including those that depend on the variational parameters. If the ansatz requirements can be met, it will provide a large degree of control over the parameter space and allow for the consideration of physically motivated parameter constraints, which could be helpful in striking the right balance between computational cost and accuracy. |
Tuesday, March 7, 2023 3:24PM - 3:36PM Author not Attending |
K64.00003: Relaxational Quantum Eigensolver: State Characterization and Thermometry Alexandar M Liguori-Schremp, George S Grattan, David Rodriguez Perez, Wesley Jones, Peter Graf, Eliot Kapit Many quantum algorithms, such as QAOA or the Variational Quantum Eigensolver (VQE), focus on minimizing a classical or quantum problem Hamiltonian through adiabatic preparation-like ansatze. However, these algorithms typically must race against proliferating gate error, limiting their usefulness for problems needing high circuit depths. Drawing on ideas from bath engineering, open quantum systems, and variational algorithms, we develop an algorithm exhibiting continuous, approximate error correction, which we call the Relaxational Quantum Eigensolver (RQE). In RQE, we weakly couple a second register of auxiliary "shadow" qubits to the primary system in Trotterized evolution, thus engineering an approximate zero-temperature bath by periodically resetting the auxiliary qubits during the algorithm's runtime. Balancing the infinite temperature bath of random gate error, RQE returns states with an average energy equal to a constant fraction of the ground state. In this work we focus on better understanding the steady state, its "temperature" T as a function of error rate, and methods for estimating both T and deviations from thermal behavior. This basic proof of concept demonstrates stabilization of finite temperature states of many-body Hamiltonians against random error. |
Tuesday, March 7, 2023 3:36PM - 4:12PM |
K64.00004: Peptide conformational sampling using the Quantum Approximate Optimization Algorithm Invited Speaker: Sami Boulebnane Protein folding -- the problem of predicting the spatial structure of a protein given its sequence of amino-acids -- has attracted considerable research effort in biochemistry in recent decades. In this work, we explore the potential of quantum computing to solve a simplified version of protein folding. More precisely, we numerically investigate the performance of a variational quantum algorithm, the Quantum Approximate Optimization Algorithm (QAOA), in sampling low-energy conformations of short peptides. We start by benchmarking the algorithm on an even simpler problem: sampling self-avoiding walks, which is a necessary condition for a valid protein conformation. Motivated by promising results achieved by QAOA on this problem, we then apply the algorithm to a more complete version of protein folding, including a simplified physical potential. In this case, based on numerical simulations on 20 qubits, we find less promising results: deep quantum circuits are required to achieve accurate results, and the performance of QAOA can be matched by random sampling up to a small overhead. Overall, these results cast serious doubt on the ability of QAOA to address the protein folding problem in the near term, even in an extremely simplified setting. We believe that the approach and conclusions presented in this work could offer valuable methodological insights on how to systematically evaluate variational quantum optimization algorithms on real-world problems beyond protein folding. |
Tuesday, March 7, 2023 4:12PM - 4:24PM |
K64.00005: TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ansätze Panagiotis G Anastasiou, Yanzhu Chen, Sophia Economou, Edwin Barnes, Nicholas Mayhall Recent progress on variational quantum eigensolver (VQE) algorithms has reduced the resource requirements with an adaptive algorithm for problem-tailored ansatz construction called ADAPT-VQE. The algorithm uses local energy gradient information to iteratively construct a VQE ansatz, one unitary at a time. In this work, we introduce a variation of the algorithm dubbed TETRIS-ADAPT-VQE which modifies the way the ansatz is constructed by adding multiple unitaries with disjoint supports in each iteration. Our algorithm results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary is performed only a fraction of the time. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. |
Tuesday, March 7, 2023 4:24PM - 4:36PM |
K64.00006: Variational quantum chemistry requires gate-error probabilities below the fault-tolerance threshold David R Arvidsson-Shukur, Kieran Dalton, Christopher K Long, Crispin H Barnes, Normann Mertig, Yordan Yordanov, Charles G Smith The variational quantum eigensolver (VQE) is a leading contender for useful quantum advantages in the NISQ era. The interplay between quantum processors and classical optimisers is believed to make the VQE noise resilient. In this talk, we probe this hypothesis in two ways. First, we present full density-matrix simulations to rank the noise resilience of leading VQE algorithms. Second, we show that, for a wide range of small molecules, even the best-performing VQE algorithms require gate-error probabilities on the order of 10-5 to reach chemical accuracy. This is significantly below the fault-tolerance threshold of most error-correction protocols. Therefore, our results indicate that useful implementation of gate-based VQEs on pre-error-correction hardware is unlikely. |
Tuesday, March 7, 2023 4:36PM - 4:48PM |
K64.00007: Improved QOCA ansatz using an adapt-VQE approach Camille Le Calonnec, Maxime Dion, Alexandre Choquette, Alexandre Blais One of the most promising applications of quantum computers in the NISQ era is quantum simulation, especially using variational quantum algorithms. The implementation, as well as the convergence of those algorithms, are however highly dependent on the choice of circuit ansatz. One example is the Quantum Optimal Control inspired Ansatz [Choquette et al. (2021)] where circuits constitute of two blocks: one that encodes the problem Hamiltonian, taking into account the symetries of the problem, and a second block which purposely break the symetries of the problem in hope of finding shortcuts in the Hilbert space. It performs well when applied to the Fermi Hubbard model and H20 compared to other well-established. However some questions remained unanswered: what are the drive terms that matter and how should they be ordered? Can we make the circuits shallower? In this talk we address these questions and show that the circuit depth and the number of CNOTs can be reduce by combining the QOCA ansatz with the adaptive method adapt-VQE [Grimsley et al. (2019)]. |
Tuesday, March 7, 2023 4:48PM - 5:00PM |
K64.00008: Implementing pulse-based VQE (ctrl-VQE) algorithm on NISQ devices. Chenxu Liu, Ayush Asthana, Tongyu Zhao, Raymond W Simmonds, Nicholas Mayhall, Edwin Barnes, Sophia Economou Unlike the gate-based Variational Quantum Eigensolvers (VQE), ctrl-VQE directly uses control pulse parameters as variational parameters, which can greatly reduce the ground state preparation time [1]. Here we present the minimum time control pulses for ctrl-VQE to prepare target molecular ground states for a given device’s Hamiltonian [2]. We noticed that the leakage outside the computational space can speed up the state preparation. Furthermore, we explore its application on NISQ devices by studying the effects of the experimental imperfections of ctrl-VQE in parametrically-coupled transmon devices [3]. |
Tuesday, March 7, 2023 5:00PM - 5:12PM |
K64.00009: Variational quantum eigensolver ansatz for the J1-J2-model Verena Feulner, Michael J Hartmann The ground state properties of the two-dimensional J1-J2 model are very challenging to analyze via classical numerical methods due to the high level of frustration. This makes the model a promising candidate for which quantum computers could be helpful to possibly explore regimes that classical computers cannot reach. The J1-J2 model is a quantum spin model composed of Heisenberg interactions along the rectangular lattice edges and along diagonal edges between next-nearest-neighbor spins. We propose an ansatz for the variational quantum eigensolver to approximate the ground state of an antiferromagnetic J1-J2 Hamiltonian for different lattice sizes and different ratios of J1 and J2. Moreover, we demonstrate that this ansatz can work without the need for gates along the diagonal next-nearest-neighbor interactions. This simplification is of great importance for solid-state-based hardware with qubits on a rectangular grid, where it eliminates the need for SWAP gates. In addition, we provide an extrapolation for the number of gates and parameters needed for larger lattice sizes, showing that these are expected to grow linearly in the qubit number up to lattice sizes which eventually can no longer be treated with classical computers. |
Tuesday, March 7, 2023 5:12PM - 5:24PM |
K64.00010: Unbiased Quantum Simulation with Feynman's iη Prescription Woo-Ram Lee, Ryan Scott, Vito W Scarola Quantum phase estimation is a paradigm of unbiased quantum simulation designed to yield exact results for intractable models. However, this approach is, in practice, hindered by high demand for deep circuits and error-correcting codes. Biased quantum simulation, including variational quantum eigensolvers, was developed as an alternative approach using shallow circuits, but only provides approximate ground-state energy estimates. In this work, we revisit unbiased quantum simulation in the context of quantum phase estimation while introducing Feynman's iη prescription. We show that this prescription relaxes the otherwise stringent conditions on circuit depth. As a specific application, we develop a hybrid quantum gap estimation algorithm to estimate the energy gap of the transverse-field Ising model. We show that the gap estimation algorithm tolerates a common noise channel, one and two-qubit depolarizing noise. We demonstrate the result of noisy quantum simulation using IBM quantum hardware, and discuss the impact of noise channels on gap estimation. |
Tuesday, March 7, 2023 5:24PM - 5:36PM |
K64.00011: Orbital Optimized ADAPT-VQE for molecular simulation on NISQ devices Ayush Asthana, Sophia Economou, Edwin Barnes, Nicholas Mayhall Molecular simulation using Variational Quantum Eigensolvers (VQEs) is expected to be a promising application on NISQ devices. Our group's proposed ADAPT-VQE algorithm has shown great promise in this regard as it is quasi-optimally compact in the number of parameters and is expected to be resilient to local minima and barren plateaus. I will present our group's new developments that deal with including orbital relaxation along with iterative ansatz construction in ADAPT-VQE. This can be thought of as a way to classically rotate the orbitals such that the current ansatz captures more correlation energy, ideally speeding the convergence of ADAPT-VQE. I will discuss the benefits of using orbital optimization in VQEs along with the opportunities it presents in simulating molecular ground and excited states on near-term quantum computers. |
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