Control limit for the quantum state preparation under stochastic control errors

Abstract

We investigate the effect of stochastic control errors on the Hamiltonian that controls a closed quantum system. Quantum information technologies require careful control for preparing a desired state used as an information resource. However, because the stochastic control errors inevitably appear in realistic situation, it is difficult to completely implement the control Hamiltonian. Under this error, the actual performance of quantum control is far away from the ideal one, and thus it is of great importance to evaluate the effect of the control errors. In this paper, we derive a lower bound of the fidelity between two closed quantum systems obeying the dynamics with and without errors. This bound reveals a reachable and unreachable set of the controlled quantum system under stochastic noises. Also, it is easily computable without considering the stochastic process and needing the full dynamics of the states. We demonstrate the actual performance of this bound via a simple control example. Furthermore, based on this result, we quantitatively evaluate the probability of obtaining the target state in the presence of control errors.

arXiv comment13 pages, 2 figures

References in corpus (14)

• Quantum Mechanics helps in searching for a needle in a haystack
• Quantum Annealing in the Transverse Ising Model
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Search by Local Adiabatic Evolution
• Quantum Computation by Adiabatic Evolution
• Berry phase for a spin 1/2 in a classical fluctuating field
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Tunable Quantum Tunneling of Magnetic Domain Walls
• 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
• Adiabatic quantum optimization in presence of discrete noise: Reducing the problem dimensionality
• Sensitivity of quantum speedup by quantum annealing to a noisy oracle
• Universal noise-precision relations in variational quantum algorithms
• Threshold theorem in isolated quantum dynamics with stochastic control errors