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Concatenating bang-bang control with decoherence-free subspaces for quantum computation

Yong Zhang, Zheng-Wei Zhou, Bo Yu, Guang‐Can Guo

Published Nov 11, 2003• 0 citations
OpenAlex

Abstract

A scheme to implement a quantum computer subjected to decoherence and governed by un-tunable qubit-qubit interaction is presented. By concatenating bang-bang (BB) control and decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced docoherence that result in quantum information dissipating into the environment. For the un-tunable qubit-qubit interaction in the quantum system, BB control plus DFSs encoding will stabilize encoded quantum states. We show how this quantum system to implement universal quantum computation.

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A scheme to implement a quantum computer subjected to decoherence and governed by un-tunable qubit-qubit interaction is presented. By concatenating bang-bang (BB) control and decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced docoherence that result in quantum information dissipating into the environment. For the un-tunable qubit-qubit interaction in the quantum system, BB control plus DFSs encoding will stabilize encoded quantum states. We show how this quantum system to implement universal quantum computation.
A scheme to implement a quantum computer subjected to decoherence and governed by an untunable qubit-qubit interaction is presented. By concatenating dynamical decoupling through bang-bang (BB) pulse with decoherence-free subspaces (DFSs) encoding, we protect the quantum computer from environment-induced decoherence that results in quantum information dissipating into the environment. For the inherent qubit-qubit interaction that is untunable in the quantum system, BB control plus DFSs encoding will eliminate its undesired effect which spoils quantum information in qubits. We show how this quantum system can be used to implement universal quantum computation.
A decoherence-free subspace (DFS) isolates quantum information from deleterious environmental interactions. We give explicit sequences of strong and fast ["bang-bang" (BB)] pulses that create the conditions allowing for the existence of DFSs that support scalable, universal quantum computation. One such example is the creation of the conditions for collective decoherence, wherein all system particles are coupled in an identical manner to their environment. The BB pulses needed for this are generated using only the Heisenberg exchange interaction. In conjunction with previous results, this shows that Heisenberg exchange is by itself an enabler of universal fault-tolerant quantum computation on DFSs.
A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented. At most two-qubit interactions are required, and the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under spatially symmetric (collective) decoherence. Our results have immediate relevance to quantum computer implementations in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled quantum dot arrays and donor-atom arrays.
Decoherence-free subspaces (DFSs) shield quantum information from errors induced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of the Pauli group (the group of tensor products of Pauli matrices). Unlike previous studies of DFSs, this type of error does not involve any spatial symmetry assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class of DFSs. We do so by introducing a hybrid DFS quantum error-correcting-code approach, where errors that arise due to departure of the codewords from the DFS are corrected actively.
Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural fault-tolerant computation) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one- or two-body interactions must leave the code space during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.
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.