arXiv:1905.12250 · Physical Review A

Control limit on quantum state preparation under decoherence

K. Kobayashi, Naoki Yamamoto

Published May 28, 2019• 4 citations

Abstract

Quantum information technologies require careful control for generating and preserving a desired target quantum state. The biggest practical obstacle is of course decoherence. Therefore, the reachability analysis, which in our scenario aims to estimate the distance between the controlled state under decoherence and the target state, is of great importance to evaluate the realistic performance of those technologies. This paper presents a lower bound of the fidelity-based distance for a general open Markovian quantum system driven by the decoherence process and several types of control including feedback. The lower bound is straightforward to calculate and can be used as a guide for choosing the target state, as demonstrated in some examples. Moreover, the lower bound is applied to derive a theoretical limit in some quantum metrology problems based on a large-size atomic ensemble under control and decoherence.

DOI: 10.1103/physreva.99.052347

Related papers

Bound on the distance between controlled quantum state and target state under decoherence

Kohei Kobayashi

Abstract To implement quantum information technologies, carefully designed control for preparing a desired state plays a key role. However, in realistic situation, the actual performance of those methodologies is severely limited by decoherence. Therefore, it is important to evaluate how close we can steer the controlled state to a desired target state under decoherence. In this paper, we provide an upper bound of the distance between the two controlled quantum systems in the presence and absence of decoherence. The bound quantifies the degree of achievement of the control for a given target state under decoherence, and can be straightforwardly calculated without solving any equation. Moreover, the upper bound is applied to derive a theoretical limit of the probability for obtaining the target state under decoherence.

arXiv:2303.06466Journal of Physics CommunicationsJan 1, 20240 citations

Control limit for the quantum state preparation under stochastic control errors

Kohei Kobayashi

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 situations, 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:2211.14862Proceedings of the Royal Society A Mathematical Physical and Engineering SciencesSep 1, 20230 citations

Distance and time limit on quantum control under decoherence (本文)

幸平小林

To realize quantum information technologies, a technique of quantum control for preparing a desired quantum state used for an information resource plays an important role.For example, the measurement-based feedback control is a powerful method and many notable experiments have been demonstrated in superconducting qubit.However, in spite of the large impacts and development of those technologies, decoherence, which is the loss of quantum properties, is the fundamental and biggest obstacle.Due to it, the quantum state collapses to the classical state and the actual control performance is sometimes far away from the ideal one.Therefore, in considering the practical quantum

Jan 1, 20200 citations

Approximation of reachable sets for coherently controlled open quantum systems: Application to quantum state engineering

Jun Li, Dawei Lu, Zhihuang Luo +3 more

Precisely characterizing and controlling realistic quantum systems under noises is a challenging frontier in quantum sciences and technologies. In developing reliable controls for open quantum systems, one is often confronted with the problem of the lack of knowledge on the system controllability. The purpose of this paper is to give a numerical approach to this problem, that is, to approximately compute the reachable set of states for coherently controlled quantum Markovian systems. The approximation consists of setting both upper and lower bounds for system's reachable region of states. Furthermore, we apply our reachability analysis to the control of the relaxation dynamics of a two-qubit nuclear magnetic resonance spin system. We implement some experimental tasks of quantum state engineering in this open system at a near optimal performance in view of purity: e.g., increasing polarization and preparing pseudopure states. These results demonstrate the usefulness of our theory and show interesting and promising applications of environment-assisted quantum dynamics.

arXiv:1412.4146Physical Review AJul 7, 201618 citations

Bounding fidelity in quantum feedback control: theory and applications to Dicke state preparation

Eoin O’Connor, Hailan Ma, Marco G. Genoni

Abstract Achieving unit fidelity in quantum state preparation is often impossible in the presence of environmental decoherence. While continuous monitoring and feedback control can improve fidelity, perfect state preparation remains elusive in many scenarios. Inspired by quantum speed limits, we derive a fundamental bound on the steady-state average fidelity achievable via continuous monitoring and feedback control. This bound depends only on the unconditional Lindblad dynamics, the Hamiltonian variance, and the target state. We also adapt the bound to the case of Markovian feedback strategies. We then focus on preparing Dicke states in an atomic ensemble subject to collective damping and dispersive coupling. By imposing additional constraints on control Hamiltonians and monitoring strategies, we derive tighter fidelity bounds. Finally, we propose specific control strategies and validate them using reinforcement learning. Benchmarking their performance against our theoretical bounds highlights the relevance and usefulness of these bounds in characterizing quantum feedback control strategies.

arXiv:2503.19151Quantum Science and TechnologyJun 17, 20250 citations

A Quantum Optimal Control Problem with State Constrained Preserving Coherence

Nahid Binandeh Dehaghani, Фернандо Лобо Перейра, A. Pedro Aguiar

In this work, we address the problem of maximizing fidelity in a quantum state transformation process controlled in such a way as to keep decoherence within given bounds. We consider a three-level Λ-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We introduce fidelity as the performance index for the quantum state transformation process since the goal is to maximize the similarity of the final state density operator with the one of the desired target state. We formulate the quantum optimal control problem with state constraints where the latter reflect the fact that the decoherence level remains within a pre-defined bound. Optimality conditions of Pontryagin’s Maximum Principle in Gamkrelidze’s form are given. These provide a complete set of relations enabling the computation of the optimal control strategy. This is a novel approach in the context of quantum systems.

arXiv:2203.15727IEEE Conference on Decision and Control (CDC)Dec 6, 20226 citations