Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources

Proposals for experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation allows one to treat more difficult problems using fewer qubits and lower gate depths than would otherwise be possible. However, while this approximation captures many important qualitative features, it may leave the results wanting in terms of absolute accuracy (basis error) of the representation. In traditional approaches, increasing this accuracy requires increasing the number of qubits and an appropriate increase in circuit depth as well. Here we explore two techniques requiring no additional qubits or circuit depth that are able to remove much of this approximation in favor of additional measurements. The techniques are constructed and analyzed theoretically, and some numerical proof-of-concept calculations are shown. As an example, we show how to achieve the accuracy of a 20-qubit representation using only four qubits and a modest number of additional measurements for a hydrogen molecule. We close with an outlook on the impact such techniques may have on both near-term and fault-tolerant quantum simulations.