arXiv:2305.04425 · The Journal of Physical Chemistry A

Modular Cluster Circuits for the Variational Quantum Eigensolver

Seyed Ehsan Ghasempouri, Gerhard W. Dueck, Stijn De Baerdemacker

Published Sep 20, 2023• 6 citations

Abstract

The variational quantum eigensolver algorithm recently became a popular method to compute the quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the quantum circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that must be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H 2, (H 2 ) 2, and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights into the construction of the circuit in a resonating valence bond picture.

DOI: 10.1021/acs.jpca.3c03015

Related papers

Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

Feng Zhang, Niladri Gomes, Noah Berthusen +4 more

Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled-cluster Ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point-group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit by a factor of 4–8. With these strategies, VQE calculations on a noise-free quantum simulator achieve energies within a few meVs of those obtained with the full unitary coupled-cluster Ansatz with single and double excitations for the H4-square, H4-chain, and H6-hexagon molecules, while the number of cnot gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore, we introduced an efficient “score” parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first. Using the H4 square and H4 chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational Ansatz.

Jan 1, 202127 citations

Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

Feng Zhang, Niladri Gomes, Noah Berthusen +4 more

Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing.Based on the variational quantum eigensolver (VQE) with unitary coupled-cluster Ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point-group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace.In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit by a factor of 4-8.With these strategies, VQE calculations on a noise-free quantum simulator achieve energies within a few meVs of those obtained with the full unitary coupled-cluster Ansatz with single and double excitations for the H 4 -square, H 4 -chain, and H 6 -hexagon molecules, while the number of CNOT gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35.Furthermore, we introduced an efficient "score" parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first.Using the H 4 square and H 4 chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational Ansatz.

arXiv:2006.11213Physical Review ResearchJan 13, 202133 citations

Computing electronic correlation energies using linear depth quantum circuits

Chong Hian Chee, Adrian Matthew Mak, Daniel Leykam +2 more

Abstract Efficient computation of molecular energies is an exciting application of quantum computing for quantum chemistry, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing variational quantum algorithms, which require deep entangling quantum circuit ansatzes to capture correlations, to small molecules. Here we demonstrate a variational NISQ-friendly algorithm that generates a set of Hartree–Fock ansatzes using multiple shallow circuits with depth linear in the number of qubits to estimate electronic correlation energies via perturbation theory up to the second order. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. The number of shallow circuits required for our algorithms scales O ( N 5 ) , with N being the system size, thus enabling the study of larger molecules compared to other approaches, where circuit depth or number of qubits required become prohibitive for NISQ devices.

arXiv:2207.03949Quantum Science and TechnologyJan 16, 20244 citations

Variational quantum eigensolver with reduced circuit complexity

Yu Zhang, Łukasz Cincio, Christian F. A. Negre +6 more

Abstract The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices.

arXiv:2106.07619npj Quantum InformationAug 12, 202274 citations

Offline Quantum Circuit Pruning for Quantum Chemical Calculations

Satoshi Imamura, Akihiko Kasagi, Eiji Yoshida

A variational quantum eigensolver (VQE) designed for noisy intermediate-scale quantum (NISQ) computers is a promising hybrid quantum-classical algorithm for quantum chemical calculations (QCC). Its accuracy and computational cost strongly depend on an ansatz, and unitary coupled-cluster (UCC) ansatze are well-known chemistry-inspired ansatze that can achieve a high accuracy for QCC. However, UCC-based quantum circuits have a high depth and a lot of 2-qubit controlled NOT (CNOT) gates which are sensitive to noises, leading to the low accuracy of VQE running on NISQ computers. To address this issue, we propose a novel offline quantum circuit pruning technique that reduces the number of CNOT gates and depth of UCC-based quantum circuits by reducing the number of excitation operators per parameter to a user-specified value. It is applied only once before VQE is executed (i.e., offline), which is the advantage over state-of-the-art quantum circuit pruning techniques. The evaluation using a quantum computer simulator with a noise model based on a real NISQ device shows that our offline pruning technique improves the accuracy of UCCSD-VQE while sustaining the potential accuracy of the UCCSD ansatz and has a synergy with a well-known noise mitigation method called zero noise extrapolation (ZNE).

IEEE International Conference on Quantum Computing and Engineering (QCE)Sep 17, 20235 citations

Sparse Simulation of VQE Circuits

Damian S. Steiger, Thomas Häner, Scott N. Genin +1 more

The Variational Quantum Eigensolver (VQE) is a promising algorithm for future Noisy Intermediate-Scale Quantum (NISQ) devices to simulate chemical systems. In this paper, we consider the classical simulation of the iterative Qubit Coupled Cluster (iQCC) ansatz. To this end, we implement a multi-threaded sparse wave function simulator and simulate iQCC circuits with up to 80 qubits and 980 entanglers to compare our results to experimental values and previous approximate simulations. In contrast to previous iQCC simulations, e.g., for computing the emission spectra of a phosphorescent emitting material, our approach features a variational guarantee, such that the resulting energies are true upper bounds on the exact energies. Additionally, our method is two orders of magnitude more memory efficient because it does not store the transformed Hamiltonians. Our theoretical analysis also enables the construction of ansätze with a limited number of nonzero amplitudes, for which our simulator can obtain exact results.This will allow one to generate complex benchmarking instances for future NISQ devices and simulators.

arXiv:2404.10047Apr 15, 20240 citations