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arXiv:2301.05666 · Quantum

Beyond MP2 initialization for unitary coupled cluster quantum circuits

Mark R. Hirsbrunner, Diana Chamaki, J. Wayne Mullinax, Norm M. Tubman

Published Nov 26, 2024• 16 citations
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Abstract

The unitary coupled cluster (UCC) ansatz is a promising tool for achieving high-precision results using the variational quantum eigensolver (VQE) algorithm in the NISQ era. However, results on quantum hardware are thus far very limited and simulations have only accessed small system sizes. We advance the state of the art of UCC simulations by utilizing an efficient sparse wavefunction circuit solver and studying systems up to 64 qubits. Here we report results obtained using this solver that demonstrate the power of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction, among others. Our approach enables meaningful benchmarking of the UCC ansatz, a crucial step in assessing the utility of VQE for achieving quantum advantage.

DOI
10.22331/q-2024-11-26-1538

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The unitary coupled cluster (UCC) ansatz is a promising tool for achieving high-precision results using the variational quantum eigensolver (VQE) algorithm in the NISQ era. However, results on quantum hardware are thus far very limited and simulations have only accessed small system sizes. We advance the state of the art of UCC simulations by utilizing an efficient sparse wavefunction circuit solver and studying systems up to 64 qubits. Here we report results obtained using this solver that demonstrate the power of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction, among others. Our approach enables meaningful benchmarking of the UCC ansatz, a crucial step in assessing the utility of VQE for achieving quantum advantage.
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized circuits, but this becomes increasingly challenging with circuit size. As a consequence, the utility of large-scale circuit optimization is relatively unknown. In this work we demonstrate that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner such that we can bridge the resources that we have from high performance computing and see a direct transition to quantum advantage. We show this through the sparse wave function circuit solvers, which we detail here, and demonstrate a region of efficient classic simulation. With such tools, we can avoid the many problems that plague circuit optimization for circuits with hundreds of qubits using only practical and reasonable classical computing resources. These tools allow us to probe the true benefit of variational optimization approaches on quantum computers, thus opening the window to what can be expected with near term hardware for physical systems. We demonstrate this with a unitary coupled cluster ansatz on various molecules up to 64 qubits with tens of thousands of variational parameters.
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.
Abstract Variational quantum eigensolver (VQE) with a unitary coupled cluster (UCC) ansatz has been suggested as a promising method for electronic structure calculations on future quantum computers. However, the complexity of the excitation terms for UCC with the single and double excitations (UCCSD) ansatz is up‐bounded to , where N is the number of electrons and M is the number of spin orbitals. The gate complexity of quantum circuit for the UCCSD ansatz is up‐bounded to using the Jordan–Wigner transformation. These complexities significantly limit the implementation of UCCSD on current Noisy Intermediate‐Scale Quantum (NISQ) devices. Herein, we developed a k‐QUpCCGSD ansatz which is based on the generalized paired double excitation operators and the particle preserving exchange gate. The former reduces the number of the excitation operators, the latter reduces the number of qubit gates for transforming excitation operators to quantum circuit. The gate complexity of the proposed k‐QUpCCGSD ansatz is up‐bounded to , which significantly reduce the complexity of the VQE algorithm on NISQ devices. The performance of the proposed ansatz on VQE is demonstrated by calculating ground‐state dissociation energy curves of the H6, LiH, H2O, and BeH2 molecules with the STO‐3G minimal basis set, and the accuracy is evaluated by comparing to the full configuration interaction (FCI) benchmarks. Moreover, we compare the number of quantum gates, especially the CNOT gates, and accuracies of various ansatzes. The assessments have shown that the accuracy of qubit unitary coupled cluster (QUCC) ansatzes is slightly worse than that of the UCC ones, but the circuit complexity of QUCC is much less than that of UCC. Among the tested QUCC ansatzes, k‐QUpCCGSD achieves higher accuracy with fewer quantum gates than QUCCSD, and k‐QUpCCGSD is a promising ansatz for VQE calculation on NISQ devices.
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 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.
The Variational Quantum Eigensolver (VQE) is a quantum algorithm used to find the ground state energy of a given Hamiltonian. The key component of VQE is the ansatz, which is a trial wavefunction that the algorithm uses to approximate the ground state. Designing a good ansatz can significantly improve the performance of the VQE algorithm. Typical ansatz structures include the Unitary Coupled Cluster (UCC) ansatz and the Hardware-Efficient Ansatz (HEA). The primary distinction between these two structures lies in their dependence on the problem and hardware. The UCC ansatz is tailored to the target Hamiltonian, whereas the HEA is determined by the hardware topology. We believe that an intermediate approach could combine the benefits of the UCC ansatz while introducing additional parameters to increase its expressiveness and capability. In this paper, we propose utilizing a diffusion model to facilitate the generation of ansatz. We create a sequence of UCC ansatzes as training data and input this data into the diffusion model. The model then generates quantum circuits that have a similar structure to the input data. These quantum circuits are subsequently tested using a VQE task to evaluate their performance. This approach provides a systematic method for generating ansatzes that maintain a similar structure while incorporating additional parameters, enhancing their expressiveness and capability. We validate on small molecules that the diffusion model can help prepare ansatz circuits for VQE.