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OSA Workshop on Entanglement and Quantum Decoherence

What is decoherence and how to control it?

Gershon Kurizki, G. Gordon, N. Erez

Published Jan 1, 2008• 0 citations
Publisher

Abstract

A physical picture -is presented of decoherence and its dynamical control on non-Markovian time scales. The Nakajima-Zwanzig master-equation formalism , combined with optimal-control theory , is used to obtain universal recipes for driving fields capable of optimally suppressing decoherence or maximizing fidelity in multipartite quantum computing or storage .This approach also allows ultrafast control of thermodynamic properties.

DOI
10.1364/weqd.2008.edd2

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A physical picture -is presented of decoherence and its dynamical control on non-Markovian time scales. The Nakajima-Zwanzig master-equation formalism , combined with optimal-control theory , is used to obtain universal recipes for driving fields capable of optimally suppressing decoherence or maximizing fidelity in multipartite quantum computing or storage .This approach also allows ultrafast control of thermodynamic properties.
A unified theory is given of dynamically modified decay and decoherence of field-driven multipartite systems. When this universal framework is applied to two-level systems or qubits experiencing either amplitude or phase noise due to their coupling to a thermal bath, it results in completely analogous formulae for the modified decoherence rates in both cases. The spectral representation of the modified decoherence rates underscores the main insight derived from this approach, namely, that the decoherence rate is the spectral overlap of the noise and modulation spectra. This allows us to come up with general recipes for modulation schemes for the optimal reduction of decoherence under realistic constraints. An extension of the treatment to multilevel and multipartite systems exploits intra-system symmetries to dynamically protect multipartite entangled states. Another corollary of this treatment is that entanglement, which is very susceptible to noise and can die, i.e., vanish at finite times, can be resuscitated by appropriate modulations prescribed by our universal formalism. This dynamical decoherence control is also shown to be advantageous in quantum computation setups, where control fields are applied concurrently with the gate operations to increase the gate fidelity.
An efficient optimal-control theory based on the Krotov method is introduced for a non-Markovian open quantum system with a time-nonlocal master equation in which the control parameter and the bath correlation function are correlated. This optimal-control method is developed via a quantum dissipation formulation that transforms the time-nonlocal master equation to a set of coupled linear time-local equations of motion in an extended auxiliary Liouville space. As an illustration, the optimal-control method is applied to find the control sequences for high-fidelity ZZZ gates and identity gates of a qubit embedded in a non-Markovian bath. ZZZ gates and identity gates with errors less than ${10}^{\ensuremath{-}5}$ for a wide range of bath decoherence parameters can be achieved for the non-Markovian open qubit system with control over only the ${\ensuremath{\sigma}}_{z}$ term. The control-dissipation correlation and the memory effect of the bath are crucial in achieving the high-fidelity gates.
The irreversible time evolution of a quantum system interacting with a large environmental system can be described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian mater equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effects of the external field. It is shown that, when the external field is a sequence of phase-modulation pulses, the decoherence of the quantum system can be suppressed under certain conditions. To see the effects of phase-modulation pulses, the irreversible time evolutions of qubit and photon systems are investigated in detail.
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of motion for the dynamics itself, rather than the state. Here we develop a Markovian master equation for the process matrix of an open system interacting with a reservoir, which resembles the Lindblad Markovian master equation. We employ this equation to introduce a scheme for optimal local coherent process control at target times and extend the Krotov technique to obtain optimal control. We illustrate utility of this framework through several quantum coherent-control scenarios, such as optimal decoherence suppression, gate simulation, and passive and indirect control of the reservoir, in all of which we aim to simulate a given terminal process at a given final time.
The driven two-level system is a useful model to describe many quantum objects, particularly in quantum information processing. However, the exact master equation for such a system has barely been explored. Making use of the Feynman-Vernon influence functional theory, we derive an exact non-Markovian master equation for the driven two-level system and show the lost feature in the perturbative treatment for this system. The perturbative treatment leads to the time-convolutionless (TCL) and Nakajima-Zwanzig (NZ) master equations. So to this end we derive the TCL and NZ master equations for the system and compare the dynamics given by the three master equations. We find the validity condition for the TCL and NZ master equations. Based on the exact non-Markovian master equation, we analyze the regime of validity for the secular approximation in the time-convolutionless master equation and discuss the leading corrections of the nonsecular terms to the quantum dynamics. Significant effects are found in the dynamics of the driven system.