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arXiv:2007.10515

A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz

Alexander Cowtan, Will Simmons, Duncan, Ross

Published Jul 20, 2020• 34 citations
arXivHTMLPDF

Abstract

We describe a compilation strategy for Variational Quantum Eigensolver (VQE) algorithms which use the Unitary Coupled Cluster (UCC) ansatz, designed to reduce circuit depth and gate count. This is achieved by partitioning Pauli exponential terms into mutually commuting sets. These sets are then diagonalised using Clifford circuits and synthesised using the phase polynomial formalism. This strategy reduces cx depth by 75.4% on average, and by up to 89.9%, compared to naive synthesis for a variety of molecules, qubit encodings and basis sets.

DOI
10.48550/arxiv.2007.10515

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We describe a compilation strategy for Variational Quantum Eigensolver (VQE) algorithms which use the Unitary Coupled Cluster (UCC) ansatz, designed to reduce circuit depth and gate count. This is achieved by partitioning Pauli exponential terms into mutually commuting sets. These sets are then diagonalised using Clifford circuits and synthesised using the phase polynomial formalism. This strategy reduces cx depth by 75.4% on average, and by up to 89.9%, compared to naive synthesis for a variety of molecules, qubit encodings and basis sets.
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.
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.
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.
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.
The Unitary Coupled Cluster with Singles and Doubles (UCCSD) ansatz is a widely used kernel in quantum chemistry and variational quantum eigensolver (VQE) algorithms, but its execution on near-term superconducting quantum processors is hindered by high gate costs and limited qubit connectivity. Existing compilation approaches either adopt simultaneous synthesis, which efficiently diagonalizes excitations but ignores connectivity, or individual synthesis, which enforces connectivity-awareness but sacrifices optimization opportunities. In this work, we propose a connectivity-aware compiler framework for UCCSD kernels that combines the efficiency of simultaneous synthesis with the practicality of connectivity constraints. First, we introduce blockwise qubit mapping, which groups program qubits into excitation-specific blocks and maps them to internally connected regions of the hardware graph. Second, we design connectivity-aware synthesis rules that diagonalize excitations directly on the mapped hardware graph, reducing the number of SWAP gates. We implement our framework and evaluate it on molecular and random UCCSD kernels using Google Sycamore’s and IBMQ Manhattan’s connectivity. Compared with state-of-the-art compilers, our approach reduces CNOT count by up to 34% and circuit depth by 49%, while improving VQE accuracy under noise.
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.