A Depolarizing Noise-aware Transpiler for Optimal Amplitude Amplification

Abstract: Amplitude amplification provides a quadratic speed-up for an array of quantum algorithms when run on a quantum machine perfectly isolated from its environment. However, the advantage is substantially diminished as the NISQ-era quantum machines lack the large number of qubits necessary to provide error correction. Noise in the computation grows with the number of gate counts in the circuit with each iteration of amplitude amplification. After a certain number of amplifications, the loss in accuracy from the gate noise starts to overshadow the gain in accuracy due to amplification, forming an inflection point. Beyond this point, accuracy continues to deteriorate until the machine reaches a maximally mixed state where the result is uniformly random. Hence, quantum transpilers should take the noise parameters of the underlying quantum machine into consideration such that the circuit can be optimized to attain the maximal accuracy possible for that machine. In this work, we propose an extension to the transpiler that predicts the accuracy of the result at every amplification with high fidelity by applying pure Bayesian analysis to individual gate noise rates. Using this information, it finds the inflection point and optimizes the circuit by halting amplification at that point. The prediction is made without needing to execute the circuit either on a quantum simulator or an actual quantum machine.