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arXiv:quant-ph/0311067 · Physical Review A

Concatenating dynamical decoupling with decoherence-free subspaces for quantum computation

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

Published Apr 20, 2004• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.69.042315

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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 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 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.
Decoherence-free subsystems (DFSs) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem theoretically exist, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFSs. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two physical qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.
We present a scheme to implement a universal set of quantum gates based on achievable interactions, and the gates can be protected against decoherence through a dynamical-decoupling approach without encoding. By properly designing system evolution, the desired system interactions commute with the elements forming dynamical decoupling pulses. Thus, the effect of decoherence can be eliminated by repeatedly applying the pulses, without noticeably affecting the system evolution governed by the desired system interactions given a small enough time interval between pulses. Moreover, due to the commutation between the elements forming the pulses and the desired system interactions, our scheme is resistant to different types of decoherence, and so not limited to specific decoherence. Our scheme also works well in the case that the desired system interactions cannot be achieved ideally due to imperfect control of system parameters, through the action of dynamical-decoupling pulses.
We present a scheme to implement a universal set of quantum gates based on achievable interactions, and the gates can be protected against decoherences through dynamical-decoupling approach without encoding. By properly designing system evolutions, the desired system interactions commute with the elements forming dynamical decoupling pulses. Thus, the effect of decoherences can be eliminated by repeatedly applying the pulses, without noticeably affecting the system evolutions governed by the desired system interactions given small enough time interval between pulses. Moreover, due to the commutation between the elements forming the pulses and the desired system interactions, our scheme is resistant to different types of decoherences, and so not limited to specific decoherences. Our scheme also works well in the case that the desired system interactions cannot be achieved ideally due to imperfect control of system parameters, through the action of dynamical-decoupling pulses.
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.