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Proceedings of the ... American Control Conference/Proceedings of the American Control Conference

A direct method for analysis and synthesis of a decoherence-free mode in quantum linear systems

Yu Pan, Daoyi Dong, Ian R. Petersen

Published Jul 1, 2016• 1 citation
Publisher

Abstract

A decoherence-free mode lies at the heart of the preservation of quantum information against external noise. In this paper we propose a direct method for the analysis and synthesis of a decoherence-free mode in quantum linear systems. First, we derive a necessary condition for the existence of a decoherence-free mode. Then, the synthesis of the decoherence-free mode via Hamiltonian control is discussed.

DOI
10.1109/acc.2016.7526106

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A decoherence-free mode lies at the heart of the preservation of quantum information against external noise. In this paper we propose a direct method for the analysis and synthesis of a decoherence-free mode in quantum linear systems. First, we derive a necessary condition for the existence of a decoherence-free mode. Then, the synthesis of the decoherence-free mode via Hamiltonian control is discussed.
Abstract In this paper, the synthesis of robust memory modes for linear quantum passive systems in the presence of unknown inputs has been studied, aimed at facilitating secure storage and communication of quantum information. In particular, we can switch on decoherence-free (DF) modes in the storage stage by placing the poles on the imaginary axis via a coherent feedback control scheme, and these memory modes can further be simultaneously made robust against perturbations to the system parameters by minimizing the condition number associated with imaginary poles. The DF modes can also be switched off by tuning the controller parameters to place the poles in the left half of the complex plane in the writing/reading stage. We develop explicit algebraic conditions guiding the design of such a coherent quantum controller, which involves employing an augmented system model to counter the influence of unknown inputs. Examples are provided to illustrate the procedure of synthesizing robust memory modes for linear optical quantum systems.
Since there are many examples in which no decoherence-free subsystems exist (among them all cases where the error generators act irreducibly on the system Hilbert space), it is of interest to search for novel mechanisms which suppress decoherence in these more general cases. Drawing on recent work (quant-ph/0502153) we present three results which indicate decoherence suppression without the need for noiseless subsystems. There is a certain trade-off; our results do not necessarily apply to an arbitrary initial density matrix or for completely generic noise parameters. On the other hand, our computational methods are novel and the result---suppression of decoherence in the error-algebra approach without noiseless subsystems---is an interesting new direction.
Decoherence-free subspaces protect quantum information from the effects of noise that is correlated across the physical qubits used to implement them. Given the ability to impose suitable Hamiltonians upon such a multi-qubit system, one can also implement a set of logical gates which enables universal computation on this information without compromising this protection. Real physical systems, however, seldom come with the correct Hamiltonians built-in, let alone the ability to turn them off and on at will. In the course of our development of quantum information processing devices based on liquid-state NMR, we have found the task of operating on quantum information encoded in decoherence-free subspaces rather more challenging than is commonly assumed. This contribution presents an overview of these challenges and the methods we have developed for overcoming them in practice. These methods promise to be broadly applicable to many of the physical systems proposed for the implementation of quantum information processing devices.
This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather than the commonly-taken Schrödinger picture, the notions of controllability and observability in control theory are employed to characterize a DF subsystem. A particularly useful result is a general if and only if condition for a linear system to have a DF component; this condition is used to demonstrate how to actually construct a DF dynamics in some specific examples. It is also shown that, as in the finite dimensional case, we are able to do coherent manipulation and preservation of a state of a DF subsystem.
In this paper we extend our previous research on coherent observer-based pole placement approach to study the synthesis of robust decoherence-free (DF) modes for linear quantum passive systems, which is aimed at preservation of quantum information. In particular, DF modes can be generated by placing the poles on the imaginary axis via a coherent feedback design scheme, and these modes can further be simultaneously made robust against perturbations to the system parameters by minimizing the condition number associated with imaginary poles. We develop explicit algebraic conditions for the existence of such a coherent quantum controller, with the corresponding deign procedure provided. Examples are given to illustrate the process of tuning the DF modes towards perfect robustness via the proposed pole placement technique.