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arXiv:1311.6330 · Nature Communications

Implementing a strand of a scalable fault-tolerant quantum computing fabric

Jerry M. Chow, Jay Gambetta, Easwar Magesan, David W. Abraham, Andrew W. Cross, Blake Johnson, Nicholas A. Masluk, Colm A. Ryan, John A. Smolin, Srikanth J. Srinivasan, Matthias Steffen

Published Jun 24, 2014• 280 citations
arXivHTMLPDF
DOI
10.1038/ncomms5015

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We investigate how to concatenate different decoherence-free subspaces to realize scalable universal fault-tolerant quantum computation. Based on tunable XXZXXZXXZ interactions, we present an architecture for scalable quantum computers which can fault-tolerantly perform universal quantum computation by manipulating only a single type of parameter. By using the concept of interaction-free subspaces, we eliminate the need to tune the couplings between logical qubits, which further reduces the technical difficulties for implementing quantum computation.
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal gate set fault-tolerantly is an expensive task in terms of physical operations, and any possible shortcut to save operations is potentially beneficial and might lead to a reduction in overhead for fault-tolerant computations. We show how the automorphism group of a quantum code can be used to implement some operators on the encoded quantum states in a fault-tolerant way by merely permuting the physical qubits. We derive conditions that a code has to satisfy in order to have a large group of operations that can be implemented transversally when combining transversal CNOT with automorphisms. We give several examples for quantum codes with large groups, including codes with parameters [8, 3, 3], [15, 7, 3], [22, 8, 4], and [31, 11, 5].