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Large-scale sparse wavefunction circuit simulator for applications with the variational quantum eigensolver
J. Wayne Mullinax, Norm M. Tubman
TL;DR
Optimizing parameterized circuits at large scale remains challenging, including on noisy quantum hardware. This paper uses a classical sparse-wavefunction solver with a UCCSD ansatz; it handles systems requiring up to 64 qubits on one node, with untruncated minimal-basis results close to CCSD(T) except for CH2O.
Problem
Optimizing parameterized circuits becomes difficult at large scale, and noisy quantum hardware presents challenges including barren plateaus.
Source: §I · p. 1Method
A classical sparse-wavefunction circuit solver uses the UCCSD ansatz, with practical truncation of the ansatz and wavefunction.
Source: §II · p. 3, §III · p. 5Results
The solver handled systems requiring up to 64 qubits on one node; untruncated minimal-basis UCCSD energies differed from CCSD(T) by less than 1 millihartree except for CH2O.
Source: §II · p. 2, §III · p. 5Takeaways & Limitations
For the studied molecular systems, exploiting wavefunction sparseness limits computation to important parts of Hilbert space and permits double-zeta quality basis sets.
Source: §III · p. 5
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
The performance of variational algorithms beyond small systems remains uncertain as circuit optimization becomes challenging at scale. This work adapts a classical unitary coupled cluster algorithm to sparse circuit simulation, aiming to shift parameter optimization toward classical resources and examine systems up to 64 qubits.
I. INTRODUCTION
- Although variational algorithms have broad applicability, their expected performance beyond small problems remains an open question as system sizes grow.Recent large-system algorithm simulations have used sparse-wavefunction approximations adapted from classical simulation techniques.Source: §I · p. 1
- The proposed approach shifts much of variational-parameter optimization to classical hardware and uses approximate circuit simulation to address optimization challenges on noisy quantum hardware.The authors identify realistic benchmarking beyond 20 qubits and reducing expensive quantum-hardware optimization as potential applications.Source: §I · p. 1
- The proposed paradigm uses high-precision classical simulation to find convergence regions before quantum hardware refines the optimization.The authors identify enormous parameter counts and wavefunction size as bottlenecks for exact simulators, which they say handle approximately 30 qubits.Source: §I · p. 1
- The study investigates electronic-energy convergence with double-zeta basis sets for systems up to 64 qubits.The authors describe this as a starting point for understanding wavefunction optimization with non-trivial basis sets.Source: §I · p. 2
II. RESULTS AND DISCUSSION
The section evaluates sparse classical UCCSD optimization across molecular settings, including its accuracy, convergence, and wavefunction complexity. It also examines whether approximate optimizations can provide useful starting parameters for quantum-hardware simulations.
II. RESULTS AND DISCUSSION
- The solver applies factorized UCCSD exponentials one at a time, retaining single and double excitations and using individual factors that can be evaluated efficiently on classical hardware.Source: §II · p. 2
- Less than 1 millihartree difference between UCCSD and CCSD(T) occurs for untruncated STO-3G cases except CH2O; truncated setups can underestimate correlation energy by up to 40 millihartree.The authors describe the larger truncation errors as significant while motivating the approach as a way to generate parameters for further refinement on quantum hardware.Source: §II · pp. 2–3
- At 64 qubits, NH3 correlation energies converged as NCUT increased from 1,000 to 5,000, while curves leveled off at NCUT = MD, suggesting over-parameterization when MD > NCUT.The system's Hilbert space contains 4.1×10^10 determinants, motivating the approximate simulator.Source: §II · p. 3
- The classical wavefunction entropy rises to 0.26 across 315 UCCSD factors, while quantum-circuit entropy oscillates above 3.0 across more than 50,000 gates; its minima match the classical curve.The comparison is for NH3 with STO-3G and no truncation.Source: §II · pp. 3–4, Figure 4 · p. 5
- As UCCSD factors are applied, entropy approximately levels off when the factor index reaches NCUT, supporting wavefunction truncation as a way to control complexity in these approximate optimizations.Small variations after each operator are attributed to truncation, and the discarded portion is reported to make no significant contribution.Source: §II · p. 4
- Parameters optimized with smaller wavefunctions recovered additional correlation energy as the wavefunction grew; unoptimized MP2 and CCSD starts enveloped optimized curves at all five NCUT values.The authors say further investigation is needed to validate the proposed advantage of starting with CCSD amplitudes.Source: §II · p. 4
III. CONCLUSION
The work presents a sparse-wavefunction UCCSD solver for classical hardware and reports calculations for systems requiring up to 64 qubits on a single computational node. Its benchmarks and NH3 study examine approximate UCCSD performance and show that controlling wavefunction complexity is key to these classical optimizations.
III. CONCLUSION
- The sparse-wavefunction UCCSD solver handles systems requiring up to 64 qubits, and all reported calculations ran on a single computational node.The approach uses wavefunction sparsity to limit resources to important parts of Hilbert space and allows double-zeta basis sets.Source: §III · p. 5
- The eight-molecule benchmarks assess approximate UCCSD against conventional coupled-cluster theory using double-zeta basis sets.The conclusion also reports convergence behavior for recovering NH3 correlation energy under these approximations.Source: §III · p. 5
- The NH3 study shows that controlling wavefunction complexity is key to performing classical UCCSD optimizations.It examines convergence of correlation-energy recovery under the stated approximations.Source: §III · p. 5
IV. METHODS
The methods use a factorized UCCSD ansatz, initialized and ordered from MP2 amplitudes, with truncation of both the ansatz and determinant wavefunction. The implementation specifies its orbital and basis-set scope and uses established chemistry and optimization software.
IV. METHODS
- The factorized UCCSD ansatz uses individual exponential factors that can be efficiently evaluated classically following the simplified form of Chen, Cheng, and Freericks.The work truncates the excitation operator to MS single and MD double excitations.Source: §IV · p. 5
- Double-excitation parameters start from MP2 amplitudes and are ordered by magnitude; all single factors are retained while MD limits the doubles.After each factor, if the determinant count exceeds NMAX, only the NCUT determinants with largest amplitudes are kept; the ansatz-selection approach could extend to ADAPT-VQE.Source: §IV · p. 5
- The implementation is limited to 32 molecular orbitals and uses PySCF for orbitals, integrals, MP2 amplitudes, and coupled-cluster reference energies.SLSQP from SciPy is used for UCCSD optimization, with STO-3G, cc-pVDZ, and cc-pCVDZ basis sets.Source: §IV · p. 5
- The molecular geometries are experimental and were taken from the Computational Chemistry Comparison and Benchmark DataBase.Source: §IV · p. 6