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 B70: Classical-Assisted Quantum ComputationFocus
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Sponsoring Units: DQI Chair: Yuxuan Zhang, The University of Texas at Austin Room: Room 409 |
Monday, March 6, 2023 11:30AM - 11:42AM |
B70.00001: Contextual Subspace Variational Quantum Eigensolver Peter J Love, William M Kirby, Andrew Tranter, Alexis P Ralli, Timothy Weaving, Peter V Coveney We describe the contextual subspace variational quantum eigensolver (CS-VQE), an approximation method based on the standard variational quantum eigensolver (VQE). CS-VQE obtains a classical approximation to the ground state energy by solving a hidden variables model for a noncontextual approximation to the Hamiltonian. This approximation is then used to construct a smaller VQE instance that computes quantum corrections to this classical approximation in a contextual subspace. CS-VQE is an example of a genuinely hybrid NISQ algorithm in the sense that part of the answer is computed on the classical computer and part of the answer on the quantum computer. |
Monday, March 6, 2023 11:42AM - 11:54AM |
B70.00002: Characterization of variational quantum algorithms using free fermions Gabriel Matos, Chris N Self, Konstantinos Meichanetzidis, Zlatko Papic, Henrik Dreyer We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional lattice -- with and without decoupled angles -- is able to prepare all fermionic Gaussian states respecting the symmetries of the circuit. Leveraging these results, we numerically study the interplay between these symmetries and the locality of the target state, and find that an absence of symmetries makes nonlocal states easier to prepare. An efficient classical simulation of Gaussian states, with system sizes up to $80$ and deep circuits, is employed to study the behavior of the circuit when it is overparameterized. In this regime of optimization, we find that the number of iterations to converge to the solution scales linearly with system size. Moreover, we observe that the number of iterations to converge to the solution decreases exponentially with the depth of the circuit, until it saturates at a depth which is quadratic in system size. Finally, we conclude that the improvement in the optimization can be explained in terms of of better local linear approximations provided by the gradients. |
Monday, March 6, 2023 11:54AM - 12:06PM |
B70.00003: How well does the Variational Quantum Eigensolver algorithm perform for a random fermionic Hamiltonian? Thomas Scaffidi, Arijit Haldar, Omid Tavakol Given a random q-local fermionic Hamiltonian, how well does the Variational Quantum Eigensolver (VQE) algorithm perform? In this talk, we propose field theory techniques as a novel tool to answer this question in the limit of large N, where N is the number of fermions. For typical quantum chemistry Hamiltonians, Hartree-Fock usually already recovers r~99% of the ground state energy, and the remaining 1% is partially recovered by more sophisticated techniques like coupled clusters. However, the situation is completely different for the random q-local fermionic Hamiltonians we consider (with q>2). In that case, we show that Hartree-Fock states have a vanishing approximation ratio r=0% in the large-N limit. This means the ground state energy is entirely attributed to strong correlations, and that achieving a non-zero approximation ratio is already an achievement. This prompts us to propose an ansatz inspired by the variational coupled cluster algorithm for which we demonstrate an approximation ratio of r~62%. Finally, we propose to use the same large-N techniques to benchmark other ansatzes which are tractable on a quantum computer, like the unitary coupled cluster states. |
Monday, March 6, 2023 12:06PM - 12:18PM |
B70.00004: A variational quantum-classical ansatz to study quantum systems Stefano Barison, Filippo Vicentini, Giuseppe Carleo In recent years, simulations of quantum chemical and physical systems has been successfully carried out on quantum hardware. |
Monday, March 6, 2023 12:18PM - 12:30PM |
B70.00005: Quantum-Selected Configuration Interaction: Exact diagonalization of Hamiltonians in a subspace selected by quantum computers Keita Kanno, Masaya Kohda, Ryosuke Imai, Sho Koh, Yuya O Nakagawa In this work, we propose a new hybrid quantum-classical algorithm for calculating the ground- and excited-state energies of molecular Hamiltonians. For calculating the ground-state energies on noisy intermediate-scale quantum (NISQ) devices, variational quantum eigensolver (VQE) is most widely used. However, although VQE is designed to work on the noisy devices, it still suffers the physical and statistical errors. Most critically, the effect of the noises spoils the "variational" nature of VQE; due to the errors, the resulting energy is not guaranteed to be higher or equal to the exact ground-state energy, which makes it hard to assess the quality of the VQE calculation. |
Monday, March 6, 2023 12:30PM - 12:42PM |
B70.00006: Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes Benchen Huang, Nan Sheng, Marco Govoni, Giulia Galli We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum eigensolvers (VQE). We combine a qubit-efficientencoding scheme [1] mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz [2] and noise-mitigation techniques [3]. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the NV center in diamond and the double vacancy in silicon carbide (SiC) and tackling a defect as complex as VSiin SiC for the first time[4]. |
Monday, March 6, 2023 12:42PM - 12:54PM |
B70.00007: Polyhedral Structure of Penalty Constants in Quadratic Unconstrained Binary Optimization and Applications to Quantum Computing. Rodolfo Alexander A Quintero Ospina, Luis F Zuluaga, Tamás Terlaky, Juan C Vera In recent years, the study of Quadratic Unconstrained Binary Optimization (QUBO) problems has regained importance because it provides a unified framework to model and solve many combinatorial optimization problems (COPT); in particular, several quantum computing algorithms (like QAOA, VQE, quantum annealing algorithms, etc.) can be used to solve QUBO models. In this talk, we will present a polyhedral characterization of the penalty constants that arise when penalization methods are used to reformulate linear and quadratic integer programs as QUBO problems. As a result, we are able to recover previous reformulations and techniques used in the literature; and also obtain QUBO constructions that give a bijective correspondence between their optimal solutions and the ones corresponding to the original problem. |
Monday, March 6, 2023 12:54PM - 1:06PM |
B70.00008: Construction of Anti-Symmetrized Variational Quantum States with Real Space Representation on Quantum Circuits Takahiro Horiba, Soichi Shirai, Hirotoshi Hirai For quantum chemistry simulations on quantum computers, the variational quantum eigensolver (VQE) is widely adopted. The usual VQE is based on the second quantization, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is the first quantization, which offers the possibility of achieving smaller scaling with respect to the number of basis sets than the second quantization. A major difficulty with the first quantization is how to construct anti-symmetrized many-body wave functions on quantum circuits. In this work, we propose a method to construct an anti-symmetrized variational quantum state based on a real space basis. The proposed circuit can generate the superposition of exponentially many Slater determinants, i.e., multireference states, by repeatedly applying the one-body circuit and the two-body circuit alternately to the seed state. We performed the VQE with the proposed circuit to obtain the potential energy curve of a one-dimensional hydrogen molecule and obtained the energy values which agree with the result of the exact diagonalization. Although the challenges of measurement and calculation costs in evaluating energy expectations exist, our work may pave the way to future quantum simulations on quantum computers. |
Monday, March 6, 2023 1:06PM - 1:18PM |
B70.00009: Power Flow Contingency Analysis with NISQ-era Hybrid Quantum Algorithms Palash Goiporia, Michael Perlin, Pranav Gokhale, Frederic T Chong The US electric grid currently powers nearly 130 million households, making it essential that its operation is not interrupted by environmental factors and cybersecurity threats. We present a path towards a quantum advantage in utilities security through a hybrid quantum-classical algorithm for performing power system contingency analysis. The core of the quantum advantage lies in a Hybrid Multiple Phase Estimation Algorithm (HMPEA), which can be applied to solve a linearized model of power flow in an energy grid. We discuss how, in the era of noisy intermediate-scale quantum (NISQ) devices, HMPEA provides a more realistic approach to quantum contingency analysis than standard quantum algorithms such as HHL. We outline how this problem would be approached classically, using HHL, and using HMPEA, studying parameters such as theoretical accuracy, time complexity, qubit requirements, circuit depth, and ability to scale to large power grids in the NISQ era. Finally, we address the problem of how to best distribute quantum resources across the grid to maximize the reliability of contingency analysis. |
Monday, March 6, 2023 1:18PM - 1:30PM |
B70.00010: Quantum Approximate Optimization Algorithm with Sparsified Phase Operator Xiaoyuan Liu, Ruslan Shaydulin, Ilya Safro The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate algorithm for demonstrating quantum advantage in optimization using near-term quantum computers. However, QAOA has high requirements on gate fidelity due to the need to encode the objective function in the phase separating operator, requiring a large number of gates that potentially do not match the hardware connectivity. Using the MaxCut problem as the target, we demonstrate numerically that an easier way to implement an alternative phase operator can be used in lieu of the phase operator encoding the objective function, as long as the ground state is the same. We observe that if the ground state energy is not preserved, the approximation ratio obtained by QAOA with such a phase separating operator is likely to decrease. Moreover, we show that a better alignment of the low energy subspace of the alternative operator leads to better performance. Leveraging these observations, we propose a sparsification strategy that reduces the resource requirements of QAOA. We also compare our sparsification strategy with some other classical graph sparsification methods and demonstrate the efficacy of our approach. |
Monday, March 6, 2023 1:30PM - 1:42PM |
B70.00011: Circuit knitting toolbox and quantum serverless Iskandar Sitdikov During the near term quantum computers era of quantum computing, while quantum computers are still very noisy, it will be important to work in a direction of composable solutions that reduces the size of given problems and handles problem execution on classical-quantum backends. |
Monday, March 6, 2023 1:42PM - 2:18PM |
B70.00012: Virtual two-qubit gates realized by quasi-probability sampling of single-qubit operations Invited Speaker: Kosuke Mitarai Two-qubit gates are essential components of quantum computation. They are, however, often more challenging to implement experimentally than single qubit gates and also constrained by the physical connectivity of qubits. To aid this problem on the software side, we describe a strategy to decompose a two-qubit gate by quasi-probability sampling of single-qubit operations. Required operations are projective measurements of a qubit in Pauli basis, and π/2 rotation around the x, y, and z axes. The required number of sampling to get an expectation value of a target observable scales exponentially to the number of 'cuts' performed, as expected. The proposed technique enables us to perform 'virtual' gates between a distant pair of qubits, where there is no direct interaction and thus many swap gates are inevitable otherwise. Our findings can provide a resource reduction scheme suitable for first-generation quantum devices. |
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