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arXiv:quant-ph/0005101 · Physical Review A

Optimal local implementation of nonlocal quantum gates

Jens Eisert, Kurt A. Jacobs, P. Papadopoulos, Martin Bodo Plenio

Published Oct 19, 2000• 417 citations
arXivHTMLPDF

Abstract

We investigate the minimal resources that are required in the local implementation of nonlocal quantum gates in a distributed quantum computer. Both classical communication requirements and entanglement consumption are investigated. We present general statements on the minimal resource requirements and present optimal procedures for a number of important gates, including controlled-NOT (CNOT) and Toffoli gates. We show that one bit of classical communication in each direction is both necessary and sufficient for the nonlocal implementation of the quantum CNOT, while in general two bits in each direction is required for the implementation of a general two-bit quantum gate. In particular, the state swapper requires this maximum classical communication overhead. Extensions of these ideas to multiparty gates are presented.

DOI
10.1103/physreva.62.052317

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Although a Toffoli gate can be equivalently implemented using several single-qubit and two-qubit gates, it will consume much resource, two of which are nonlocal controlled-NOT (CNOT) gates acting on two non-adjacent nodes, especially in distributed quantum computation (DQC). We, for the first time, employ an ancillary qubit to construct a nonlocal Toffoli gate for DQC in linear network topology. The ancillary-qubit-based scheme needs fewer qubits, quantum gates, and entanglement states than that based on quantum teleportation scheme and the entanglement swapping scheme. We also analyze the performance of the three proposed schemes under different application scenarios, and present their pros and cons. Our work will help to implement DQC in noisy intermediate-scale quantum (NISQ) era.