Approximate Compilation with Error Mitigation

Error mitigation by post selection and optimized quantum compilation are two seemingly distinct approaches of addressing errors in quantum computers. This work explores integrating error detection and post selection as an essential way to aid compilation. By initially compiling quantum circuits approximately and then using light-weight post-selection circuitry to detect approximation errors, the computational resources required for computation can be significantly reduced. When approximate circuits are significantly smaller and introduce errors that can be made detectable for the most part through simple circuits, the computational results thus efficiently obtained can be sufficiently error free to render them useful. While this method is broadly applicable, this work specifically demonstrates its effectiveness by optimizing CNOT gate counts in water molecule simulations based on unitary coupled-cluster theory. This enables a direct comparison with state-of-the-art results in circuit optimization. We report a nearly 50% reduction in CNOT gate counts over the state of the art. Combining approximation with post-selection proves effective at mitigating errors but does not reduce overall gate counts for the target accuracies we specifically considered herein, leaving room for further research.