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Quantum Chemistry as a Benchmark for Near-Term Quantum Computers
Alexander J. McCaskey, Zachary P. Parks, Jacek Jakowski, Shirley V. Moore, T. Morris, Travis S. Humble, Raphael C. Pooser
TL;DR
The paper develops a quantum chemistry benchmark for evaluating near-term quantum computers on electronic-structure calculations. It combines VQE with active-space and ansatz reductions plus error mitigation, finding classical-comparable energies and chemical accuracy for certain settings while remaining constrained by hardware operation limits.
Problem
Application-specific benchmarks for comparing quantum-computing performance across scalable scientific problem instances were absent, despite hardware-property metrics not directly measuring task performance.
Method
The benchmark combines VQE, active-space reduction, reduced and extended UCC ansätze, and error-mitigation strategies for molecular electronic-structure calculations.
Results
Computed ground-state energies were comparable with classical simulations, and certain configurations achieved chemical accuracy on certain quantum computers.
Takeaways & Limitations
The benchmark provides a litmus test and possible pass/fail metric for quantum-computer utility in this specific quantum-chemistry task, with complexity adjustable as hardware improves.
Takeaways & Limitations
Near-term devices are constrained by total operations and two-qubit-gate counts, while usable classically comparable results require classical post-processing.
Abstract
from arXiv · showhide
We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark on the 20 qubit IBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH),with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.
I. INTRODUCTION
The paper addresses the lack of application-specific benchmarks that can compare quantum computers on scalable scientific tasks. It proposes a quantum chemistry benchmark combining VQE, resource reductions, and error mitigation for current hardware.
- Application-specific metrics are needed to evaluate quantum-computing performance on scientific tasks across computational paradigms.
- The benchmark defines electronic-structure instances realizable on current hardware and varies choices that influence computational performance.
- Active-space reduction and density-matrix purification accommodate limited noisy-qubit counts and circuit depth.
- For alkali metal hydrides, the calculation can be reduced to two valence electrons and the equivalent of minimal-basis hydrogen, with approximations gradually lifted as devices improve.
- The benchmark uses VQE with UCC or hardware-efficient state-preparation circuits and evaluates recovery of molecular ground-state energies.
II. RELATED WORK
Prior work established VQE applications on small molecular systems, but trial-circuit choices create a trade-off between physical constraints, parameter count, and circuit depth. Active-space and amplitude-screening approaches reduce UCC resources.
- VQE has been applied to small molecules on multiple QPUs using varied trial circuits, with classical-search complexity depending strongly on circuit form.
- Current platforms contain extensive noise, motivating application-specific evaluation beyond hardware-property measurements.
- UCC conserves electron number but produces relatively deep circuits, whereas HWE is shorter yet permits variable electron numbers and unphysical states.
- Pre-screening cluster amplitudes reduces UCC parameters and circuit depth by discarding excitation operators below a chosen perturbative threshold.
III. CHEMISTRY ON QUANTUM COMPUTERS
The chemistry workflow transforms an electronic-structure problem into a qubit Hamiltonian, reduces orbital and electron spaces, prepares a parameterized trial state, and estimates its energy through Pauli measurements.
- Electronic-structure accuracy and resource cost depend on the selected basis set and simulation method within a hierarchy spanning HF, DFT, perturbation, CI, and coupled-cluster methods.
- The workflow specifies the molecule, generates integrals and a Hartree–Fock reference, maps the Hamiltonian to qubits, builds a trial circuit, and targets hardware.
- The molecular Hamiltonian contains nuclear-repulsion, one-electron, and two-electron terms expressed with creation and annihilation operators and electron-repulsion integrals.
- Frozen-core reduction neglects correlation from lowest-energy core electrons while treating their interaction with correlated electrons in an average mean-field manner.
- The orbital space is partitioned into frozen-core, active, and inactive-virtual regions, with Hamiltonian indices restricted accordingly.
- VQE initializes a reference state, applies U(θ), measures Pauli terms, contracts their expectations into Ē(θ), and classically updates parameters until convergence.
- The single-parameter UCC circuit for four qubits and two electrons controls a double-excitation amplitude and serves as a recurring primitive benchmark.
IV. BENCHMARKING APPROACH
The benchmark varies Hamiltonian complexity, trial-unitary class, and error-mitigation post-processing. It first reduces circuit width through frozen-core and discrete Z2-symmetry reductions.
- Benchmark performance depends on the spin-Hamiltonian complexity, parameterized trial circuit U(θ), and error-mitigation strategy.
- The approach reduces Hamiltonian complexity with frozen-core approximation and discrete Z2 symmetries before selecting a trial-unitary class.
- Benchmarking results are evaluated as a function of multiple error-mitigation post-processing techniques.
A. Trial Circuits
The benchmark compares trial-circuit choices that trade circuit depth and optimization cost against physical validity and orbital coverage. Reduced UCC variants use symmetry reduction to make chemistry circuits feasible on current hardware, while hardware-efficient circuits shorten depth but enlarge parameter spaces.
- Ansatz choice sets both program depth and noise exposure, while parameter count controls classical optimization difficulty and QPU-call requirements.
- UCC uses particle excitations from a reference state, and UCCSD truncates the excitation operator to single and double excitations.
- UCCSD can represent exact FCI solutions for two-electron systems under frozen-core approximation, but its depth reaches about 100 for four qubits and two electrons.
- For hydrogenic four-orbital, two-fermion systems, symmetry reduction approximates eight equivalent four-site terms with one term, yielding a reduced parameterized unitary.
- The reduced one-term circuit is a recurring CX-ladder primitive that supports cross-platform energy metrics and mapping larger molecules through frozen-core approximation.
- The extended UCC ansatz adds parameters for additional two-qubit spin subspaces, spreading excitations across all active orbitals and addressing the reduced ansatz's inability to reach FCI energy.
- Hardware-efficient circuits alternate single-qubit rotations with hardware-connectivity entanglers, reducing depth but increasing parameter count and susceptibility to barren plateaus.
B. Error Mitigation Strategies
The benchmark evaluates readout correction, zero-noise extrapolation, and McWeeny purification as distinct responses to measurement and gate noise. Purification operates on the two-body reduced density matrix to improve energy estimates from noisy mixed states.
- NISQ execution introduces systematic noise and readout errors, so benchmark results require explicit error-mitigation variants.
- Readout correction models independent per-qubit bit flips using pi(1|0) and pi(0|1) probabilities to adjust measured expectation values.
- Zero-noise extrapolation emulates stronger two-qubit white noise by inserting CNOT pairs, then extrapolates measured energies to zero inserted noise.
- McWeeny purification iteratively transforms the noisy two-body reduced density matrix as ρ_pqrs ← 3(ρ_pqrs)^2 − 2(ρ_pqrs)^3 until the change falls below ϵ.
- The two-body reduced density matrix is sufficient for computing total energy because an appropriate trace yields the one-body reduced density matrix.
C. Software Implementation
The software implementation makes the benchmark hardware-independent and configurable through input files specifying algorithms, circuits, molecules, mitigation, and target QPUs. The implementation supports execution across available quantum processors.
- The framework abstracts hardware and application domains through an extensible benchmark design with configurable benchmark parameters.
- XACC extensions provide Python interfaces and runtime services for application-centric and algorithmic-primitive benchmarking across major QPUs.
- An INI input file specifies the VQE algorithm, trial circuit, optimizer, molecular-integral routine, mitigation strategies, and target QPU.
- The NaH example uses the STO-3G basis, readout-error correction, Richardson extrapolation, frozen spin orbitals, and active spin orbitals [5].
- Figure 4 compares exact, raw, readout-corrected, and Richardson-extrapolated energies versus the variational parameter for NaH, KH, and RbH on IBM Tokyo.
V. RESULTS
The benchmark evaluates reduced quantum-chemistry calculations on IBM Tokyo and Rigetti Aspen using multiple ansätze and error-mitigation strategies, with ground-state energy compared against classical references. Reduced UCC circuits and post-processing can substantially improve accuracy, reaching chemical-accuracy-scale agreement in selected settings.
- Benchmark setup: The benchmark covers NaH, KH, and RbH using frozen-core active spaces with four active orbitals and two fermionic degrees of freedom on IBM Tokyo and Rigetti Aspen.All fermionic Hamiltonians were mapped to spin Hamiltonians using Jordan-Wigner transformation.
- Ansatz comparison: The 20-parameter hardware-efficient ansatz failed to match classical FCI energies, while symmetry reduction improved accuracy but remained above the Hartree-Fock energy.These experiments used COBYLA optimization with 30 iterations and nearest-neighbor entanglement.
- Ansatz comparison: The single-parameter UCC ansatz outperformed the hardware-efficient ansatz despite three additional CNOT gates in an otherwise similar-depth circuit.This comparison highlights the differing performance of chemistry-informed and hardware-efficient trial circuits under noise.
- RDM purification: For the ucc-3 ansatz, optimization plots compare purified and unpurified energies across iterations on IBM Tokyo and Rigetti Aspen, with FCI distance shown against the chemical-accuracy threshold.The NaH energy-surface calculation additionally evaluated four Na–H distances, repeating each distance five times with errors around 0.01.
- Error mitigation: With readout-error correction and quadratic Richardson extrapolation, benchmark energies were comparable to classical FCI results within error bars for all reduced 4-qubit Hamiltonians.The extrapolation estimates the theoretical zero-noise point from circuits with increasing numbers of noisy CNOT identity pairs.
- RDM purification: RDM purification produced chemical accuracy at the optimal angle for NaH on the Rigetti QPU using the ucc-1 ansatz.Chemical accuracy is identified as 0.0016 Ha; Figure 5 compares purified and unpurified energies on IBM Tokyo and Rigetti Aspen.
VI. DISCUSSION
The benchmark accounts for near-term hardware limits and uses ground-state energy to compare quantum chemistry performance. Certain configurations achieve chemical accuracy, while error-mitigation methods improve raw circuit results.
- VI. DISCUSSION: Near-term quantum computation is constrained by limited operation counts, two-qubit gate depth, and the need for classical post-processing.These constraints motivate a benchmark that supports cross-platform comparison of scientific use cases.
- VI. DISCUSSION: The benchmark combines VQE, active-space reduction, reduced and extended UCC ansätze, and error-mitigation strategies on IBM Tokyo and Rigetti Aspen.Ground-state energy is used as the benchmark metric, with results comparable to classical simulation.
- VI. DISCUSSION: Certain benchmark configurations return chemically accurate results on certain machines.The active orbital space and ansatz complexity can increase as hardware improves.
- VI. DISCUSSION: RDM purification and ansatz subspace extension both improve results over raw circuit execution.Ansatz extension corrects algorithmic error, while purification indicates systematic hardware error and the register’s mixed-state character.
VII. CONCLUSION
The paper proposes a novel benchmark for near-term quantum computers.
- VII. CONCLUSION: The paper proposes a novel benchmark of near-term quantum computers.