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arXiv:2108.10912

Reducing Unitary Coupled Cluster Circuit Depth by Classical Stochastic Amplitude Pre-Screening

Maria-Andreea Filip, Nathan Fitzpatrick, David Muñoz Ramo, Alex J. W. Thom

Published Aug 24, 2021• 0 citations
arXivHTMLPDF

Abstract

Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH$_2$, N$_2$ and N$_2$H$_2$ molecules giving sub-milliHartree errors.

DOI
10.48550/arxiv.2108.10912

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Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH2_22​, N2_22​ and N2_22​H2_22​ molecules giving sub-milliHartree errors.
Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with sub-milliHartree errors in the CH2_22​, N2_22​ and N2_22​H2_22​ molecules.
Unitary coupled cluster (UCC) approaches are an appealing route to utilizing quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared with the exponential scaling required on classical computers. Current noisy intermediate scale quantum computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the variational quantum eigensolver (VQE) approach. We present a combined classical-quantum approach where a stochastic classical UCC preprocessing step is used to determine the important excitations in the UCC Ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH2,N2{\mathrm{CH}}_{2}, {\mathrm{N}}_{2}CH2​,N2​, and N2H2{\mathrm{N}}_{2}{\mathrm{H}}_{2}N2​H2​ molecules giving submillihartree errors.
Quantum computation represents a revolutionary approach to solving problems in quantum chemistry. However, due to the limited quantum resources in the current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for large chemical systems remain a major task. In this work, we demonstrate that the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes in the algorithm of the variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are first prescreened from the operator pool according to its contribution to the total energy. The quantum circuit ansatz is then iteratively constructed until convergence of the final energy to a typical accuracy. For demonstration, this method has been successfully applied to molecular and periodic systems. Particularly, a reduction of 50%-98% in the number of operators is observed while retaining the accuracy of the original UCCSD operator pools. This method can be straightforwardly extended to general parametric variational ansatzes.
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).
Abstract Quantum computing is an exciting area, which has grown at an astonishing rate in the last decade. It is specially promising for the computational and theoretical chemistry area. One algorithm has received a lot of attention lately, the variational quantum eigensolver (VQE). Is is used to solve electronic structure problems and it is suitable to the noisy intermediate-scale quantum (NISQ) hardware. VQE calculations require ansatze and one of the most known is the unitary coupled-cluster (UCC). It uses the chosen basis set to generate a circuit which will be iteratively minimized. The present work investigates the circuit depth as a function of basis sets and molecular size. It has been shown that for the current quantum devices, only the smallest molecules and basis sets are tractable. The H2 molecule with the cc-pVTZ and aug-cc-pVTZ basis sets have circuit depths in the order of 106 to 107 gates and the C2H6 molecule with 3-21G basis set has a circuit depth of 2.2 ×108 gates. At the same time the analysis demonstrate that the H2 molecule with STO-3G basis set, requires at least 500 shots to reduce the error and that, although error mitigation schemes can diminish the error, they were not able to completely negate it.
Abstract The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.