Quantum-classical auxiliary field quantum Monte Carlo with matchgate shadows on trapped ion quantum computers

We demonstrate an end-to-end workflow to model chemical reaction barriers with the quantum-classical auxiliary field quantum Monte Carlo (QC-AFQMC) algorithm with quantum tomography using matchgate shadows. The workflow operates within an accelerated quantum supercomputing environment with the IonQ Forte quantum computer and NVIDIA graphic processing units (GPUs) on Amazon Web Services. We present several algorithmic innovations and an efficient GPU-accelerated execution that achieves a several orders of magnitude speedup over the state-of-the-art implementation of QC-AFQMC. We apply the algorithm to simulate the oxidative addition step of the nickel-catalyzed Suzuki-Miyaura reaction using 24 qubits of IonQ Forte with 16 qubits used to represent the trial state, plus 8 additional ancilla qubits for error mitigation, resulting in the largest QC-AFQMC with matchgate shadow experiments ever performed on quantum hardware. We achieve a 9 × speedup in collecting matchgate circuit measurements, and our distributed-parallel postprocessing implementation attains a 656 × time-to-solution improvement over the prior state of the art. Chemical reaction barriers for the model reaction evaluated with active-space QC-AFQMC are within the uncertainty interval of ± 4 kcal/mol from the reference CCSD(T) (coupled cluster singles and doubles with perturbative triples) result when matchgates are sampled on the ideal simulator and within 10 kcal/mol from reference when measured on quantum processing unit. This work marks a step toward practical quantum chemistry simulations on quantum devices while identifying several opportunities for further development.