[Paper Review] Large-scale sparse wavefunction circuit simulator for applications with the variational quantum eigensolver

J. Wayne Mullinax, Norm M. Tubman|arXiv (Cornell University)|Jan 13, 2023

Quantum Computing Algorithms and Architecture7 citations

TL;DR

This paper presents a classical sparse wavefunction circuit simulator that enables large-scale variational quantum eigensolver (VQE) optimization for molecular systems up to 64 qubits using double-zeta basis sets. By combining truncated UCCSD ansatz with wavefunction amplitude truncation and MP2-based parameter initialization, the method achieves efficient, high-precision classical simulation of quantum circuits, demonstrating robust convergence and enabling realistic benchmarking of VQE performance on near-term quantum hardware.

ABSTRACT

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 sparse wavefunction 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.

Motivation & Objective

• To enable large-scale classical simulation of variational quantum eigensolver (VQE) circuits for molecular systems beyond the reach of exact simulators.
• To address the challenge of barren plateaus and high-parameter optimization in near-term quantum hardware by shifting much of the variational parameter optimization to classical high-performance computing.
• To demonstrate that approximate classical simulation with sparse wavefunction techniques can accurately recover correlation energy and benchmark VQE performance for systems with tens of thousands of variational parameters.
• To provide a practical framework for testing and refining quantum circuit ansätze before deployment on noisy quantum processors.
• To validate the utility of the UCCSD ansatz with double-zeta basis sets on large systems using classical resources, paving the way for quantum advantage in quantum chemistry.

Proposed method

• Uses a factorized form of the unitary coupled cluster singles and doubles (UCCSD) ansatz, decomposed into sequential single and double excitation operators.
• Applies MP2 amplitudes as initial variational parameters for double excitations and sets single excitation parameters to zero.
• Employs wavefunction truncation after each UCC factor application, retaining only the N_CUT largest-amplitude determinants to control Hilbert space complexity.
• Truncates the UCCSD ansatz to M_D double excitations and includes all M_S single excitations, ordered by initial MP2 amplitude magnitude.
• Utilizes the SU(2) algebraic simplification of exponential UCC factors to enable efficient classical evaluation of each UCC operation.
• Employs the SLSQP optimizer in SciPy for variational parameter optimization, with full configuration interaction (FCI), CISD, CCD, CCSD, and CCSD(T) reference energies computed via PySCF.

Experimental results

Research questions

• RQ1 Can classical sparse wavefunction simulation effectively approximate VQE optimization for large molecular systems with up to 64 qubits and double-zeta basis sets?
• RQ2 How does wavefunction truncation and UCCSD ansatz truncation affect the convergence and accuracy of electronic energy calculations in large-scale VQE simulations?
• RQ3 To what extent can MP2-based parameter initialization and sequential application of UCC factors reduce the risk of barren plateaus in large-scale variational quantum optimization?
• RQ4 Can classical simulations using this approach reliably benchmark the performance of VQE circuits before deployment on noisy intermediate-scale quantum (NISQ) devices?
• RQ5 What is the impact of basis set quality (e.g., cc-pVDZ) on the accuracy and resource requirements of classical VQE simulations for large molecules?

Key findings

• The method successfully simulates UCCSD-based VQE circuits for molecules up to 64 qubits using a single computational node, without requiring large-scale parallelization.
• Wavefunction truncation at N_CUT = 1000 determinants effectively limits Hilbert space growth while preserving electronic energy convergence, enabling scalable simulation.
• The use of MP2 amplitudes as initial parameters ensures rapid convergence of the variational optimization, reducing the risk of barren plateaus in large circuits.
• For NH3, the method recovers over 90% of the correlation energy using only 100 double excitations, demonstrating effective control of wavefunction complexity.
• Benchmarking against CCSD(T) shows that the classical simulator achieves chemical accuracy (within 1 kcal/mol) for all eight molecules studied, including H2O, N2, and CH4.
• The approach enables the use of double-zeta basis sets (e.g., cc-pVDZ) in large-scale simulations, which are essential for accurate molecular energy prediction but previously infeasible with exact simulators.