Practical Quantum Simulations from Error Mitigation and Qubit Subspace Techniques

The goal of this work is to outline a path to practical quantum simulations on the noisy intermediate scale quantum hardware available to us today. Qubit subspace techniques such as tapering and the contextual subspace methodology allow us to reduce the quantum resource required to simulate a problem Hamiltonian by projecting into a reduced subspace where various symmetries (physical or artificial) have been exploited. Having alleviated some burden on the quantum device by removing classical redundancy in the target system, we turn to techniques of quantum error mitigation to extract some usable signal from such inherently noisy platforms. In particular, we investigate strategies based on measurement error mitigation, symmetry verification, zero-noise extrapolation and dual-state purification with numerical benchmarking to identify an effective hybrid scheme. We then apply these findings to model systems on superconducting hardware to validate our simulation framework. This includes an accurate characterisation of the electron correlation potential energy curve of molecular nitrogen and ground state preparation of the spin-frustrated Kagome lattice, a proposed quantum spin liquid; the latter achieved first-place in the IBM Quantum Open Science Prize 2022/23.