Threshold theorem in isolated quantum dynamics with stochastic control errors

TL;DR

This paper establishes a threshold theorem for isolated quantum systems under stochastic control errors, linking noise strength and measurement count to successfully achieve target states in quantum computations.

Contribution

It introduces a threshold theorem that quantifies the conditions under which target states can be reliably obtained despite stochastic control errors in quantum dynamics.

Findings

If noise sum is below inverse of time, target state is achievable with constant measurements.

Exceeding this noise level causes exponential increase in measurements needed.

The theorem applies broadly to quantum annealing and adiabatic quantum computing.

Abstract

We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrodinger equation. For a class of stochastic control errors, we establish a threshold theorem that provides a sufficient condition to obtain the target state, which should be determined in noiseless isolated quantum dynamics, as a relation between the number of measurements and noise strength. The theorem guarantees that if the sum of the noise strengths is less than the inverse of computational time, the target state can be obtained through a constant-order number of measurements. If the opposite is true, the number of measurements to guarantee obtaining the target state increases exponentially with computational time. Our threshold theorem can be applied to any isolated quantum dynamics such as quantum annealing and adiabatic quantum computation.