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Journal of Applied Physics

Using sequences of pulses to control coherence in an open quantum computing system

Bi Qiao, Harry E. Ruda, J. F. Chang

Published Jun 1, 2002• 9 citations
Publisher

Abstract

A method for quantum control of coherence in an open quantum computing system is presented. The approach was applied to finding a suitable control sequence for maintaining coherence in a silicon-based nuclear spin quantum computing system, subject to Bose-type environmental noise, and under the Born–Markovian and rotating wave approximations. It is shown that the evolution operator remains decoherence free while the three control pulses are being applied.

DOI
10.1063/1.1473678

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A method for quantum control of coherence in an open quantum computing system is presented. The approach was applied to finding a suitable control sequence for maintaining coherence in a silicon-based nuclear spin quantum computing system, subject to Bose-type environmental noise, and under the Born–Markovian and rotating wave approximations. It is shown that the evolution operator remains decoherence free while the three control pulses are being applied.
We design control setting that allows the implementation of an approximation of an unitary operation of a quantum system under decoherence using various quantum system layouts and numerical algorithms. We focus our attention on the possibility of adding ancillary qubits which help to achieve a desired quantum map on the initial system. Furthermore, we use three methods of optimizing the control pulses: genetic optimization, approximate evolution method and approximate gradient method. To model the noise in the system we use the Lindblad equation. We obtain results showing that applying the control pulses to the ancilla allows one to successfully implement unitary operation on a target system in the presence of noise, which is not possible which control field applied to the system qubits.
In this paper, based on the idea of reverse engineering, we propose a scheme to find analytical expressions of a laser pulse that allows for controlling the evolution of two-level systems as desired, regardless of the time-dependent phase of the system. The pulse relates to particular functions that predefine the evolution of a system. For illustration, we present concrete examples of driving the system from an arbitrary initial state to a final state along the user-prescribed particular way in both closed and open quantum systems. Simulation results indicate that the desired evolutionary path is accurately obtained when the rotating wave approximation (RWA) is satisfied. Most importantly, the scheme allows us to maintain system coherence and populations even in the presence of certain dephasing and thermal noises. Thus it may naturally find applications in quantum computing and quantum memories.
We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.
The external coherent control over the dynamics of quantum systems has been the aim of many studies in recent years, and several theoretical frameworks have been devised for that purpose. However, several of the proposed methods have been developed to control isolated quantum systems, disregarding the decoherence effects that impinge on the ubiquitous open quantum systems that exhibit a more complex dynamics than their isolated counterparts. In this paper, we investigate the effects of dissipation and decoherence for a quantum-control procedure based on sequences of reverse optimized electromagnetic pulses. Although the method performs well for pure quantum systems, moderate decoherence and dissipation hinders its accomplishment for ordinary conditions, irrespective of the pulse sequence rate. The method can be appropriate, nonetheless, for dynamical decoupling of the quantum subsystem from the environment.
In this paper, we design an optimal control law to suppress decoherence effects in Markovian open quantum systems. The optimal control law is subject to the tracking precision of the trajectory governed by the free system, which is ideally free from decoherence. We observe from numerical simulation that the undesired decohering dynamics can be partially squeezed out in most systems. Moreover, we observe the existence of sinusoidally oscillating resonant modes that play dominant roles in the controlled trajectory, which can be easily realized by continuous wave pulses. These key features are strictly demonstrated in subsequent analysis under proper assumptions. For systems in which the coherent control does not work, we suggest a feedback control strategy to extend the applicability of control to wider class of systems.
Coherent-optical-control schemes exploit the coherence of laser pulses to change the phases of interfering dynamical pathways and manipulate dynamical processes. These active control methods are closely related to dynamical decoupling techniques, popularized in the field of quantum information. Inspired by nuclear magnetic resonance spectroscopy, dynamical decoupling methods apply sequences of unitary operations to modify the interference phenomena responsible for the system dynamics thus also belonging to the general class of coherent-control techniques. This article reviews related developments in the fields of coherent optical control and dynamical decoupling, emphasizing the control of tunneling and decoherence in general model systems. Considering recent experimental breakthroughs in the demonstration of active control of a variety of systems, we anticipate that the reviewed coherent-control scenarios and dynamical-decoupling methods should raise significant experimental interest.