Threshold theorem in isolated quantum dynamics with stochastic control errors
arXiv:2009.11151 · doi:10.1098/rsta.2021.0412
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.
9 pages, 0 figure
References in corpus (8)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Simple proof of equivalence between adiabatic quantum computation and the circuit model
- Towards Fault Tolerant Adiabatic Quantum Computation
- Noise resistance of adiabatic quantum computation using random matrix theory
- Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field
- High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
- Experimentally verifying anti-Kibble-Zurek behavior in a quantum system under noisy control field
- Sensitivity of quantum speedup by quantum annealing to a noisy oracle