Proposals for near-term 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 introduce a technique requiring no additional qubits or circuit
depth that is able to remove much of this approximation in favor of additional
measurements. The technique is 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 4 qubits and a
modest number of additional measurements for a simple hydrogen molecule. We
close with an outlook on the impact this technique may have on both near-term
and fault-tolerant quantum simulations