Quantum measurement data compressed into a machine-learning model: quantum-classical Monte Carlo reaches chemical accuracy on 40 qubits of Willow
Synopsis
Hybrid quantum-classical Monte Carlo had been limited by the large classical cost of repeatedly processing quantum measurement data, with hardware demonstrations reaching only 16 qubits. Compressing those measurements into a differentiable machine-learning surrogate that supplies the wavefunction overlaps and derivatives Monte Carlo needs accelerates the end-to-end calculation by orders of magnitude on Google's Willow processor, bringing hydrogen chains and iron-sulfur clusters to chemical accuracy on up to 40 qubits, more than doubling the scale of earlier hardware demonstrations.
Interpretation
A reusable machine-learning surrogate bypasses the classical postprocessing bottleneck of hybrid quantum-classical Monte Carlo, extending the end-to-end calculation to 40 qubits on Google's Willow processor. Earlier hardware demonstrations reached only 16 qubits, with a single calculation consuming over 13,000 GPU hours, while a 40-qubit calculation was estimated to require millions of CPU hours. At 8 and 16 qubits, with the same measurement data, the surrogate reduces total quantum-classical Monte Carlo cost by 190-fold and 4,100-fold respectively, a comparison that includes labeling, training and the full Monte Carlo run.
The approach learns only the overlaps between the quantum state and the many-body configurations encountered in Monte Carlo, rather than reconstructing the full quantum state. The conventional path repeats classical postprocessing for every snapshot, every walker and every imaginary-time step, so cost grows with the product of snapshots, walkers and steps. A differentiable surrogate is trained on overlap labels for a small set of training determinants, after which propagation queries only the surrogate, whose evaluation cost is independent of the snapshot count; hydrogen chains use a neural quantum state surrogate and the iron-sulfur cluster a nonorthogonal configuration interaction surrogate.
On the strongly correlated iron-sulfur cluster, a trial wavefunction trained on quantum data brings auxiliary-field Monte Carlo to chemical accuracy. A classical nonorthogonal configuration interaction trial with the same number of determinants has a lower variational energy yet yields an auxiliary-field Monte Carlo energy about 5 kcal/mol below the exact result, and classical trials with 2 to 8 determinants all miss chemical accuracy. The (18e, 14o) and (30e, 20o) active spaces of [Fe2S2(SCH3)4]2- map onto 28 and 40 qubits; the singlet ground-state error is within chemical accuracy, and the singlet-to-high-spin gap is 20.2(1) kcal/mol against an exact 19.3 kcal/mol.
Perspective
The demonstrated scope is hydrogen chains of up to 20 atoms (40 qubits, mean-field trial) and the 28- and 40-qubit active spaces of [Fe2S2(SCH3)4]2- on Google's Willow processor; the 40-qubit high-spin data come from classical circuit simulation rather than hardware measurement. The intended reader works at the intersection of quantum chemistry and quantum computing.
The statistical measurement cost of resolving overlaps decays exponentially with system size; the authors say this limitation has not prevented the present calculations but that its impact at larger scales remains to be understood, and the 40-qubit high-spin state used classically emulated data because the circuit was too deep to run.