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AIP conference proceedings

Deterministic linear-optics quantum computing based on a hybrid approach

Seung-Woo Lee, Hyunseok Jeong

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We suggest a scheme for all-optical quantum computation using hybrid qubits.It enables one to efficiently perform universal linear-optical gate operations in a simple and near-deterministic way using hybrid entanglement as off-line resources.
DOI
10.1063/1.4903151

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We suggest an efficient scheme for quantum computation with linear optical elements, where the qubits are encoded in single photon states. The scheme reduces the resources required per logical gate by several orders of magnitude, compared to an earlier proposal of Knill, Laflamme, and Milburn, while the resource overhead per gate is independent of the length of the computation. A central feature of the scheme, enabling these improvements, is the prior construction of a "linked" photon state designed according to the particular quantum circuit one wishes to process. Once this state has been successfully prepared, the computation is pursued deterministically by a sequence of teleportation steps.
Quantum gates are the essential block for quantum computer. High-dimensional quantum gates exhibit remarkable advantages over their two-dimensional counterparts for some quantum information processing tasks. Here we present a family of entanglement-based optical controlled-SWAP gates on C2⊗Cd⊗Cd\mathbb{C}^{2}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}C2⊗Cd⊗Cd. With the hybrid encoding, we encode the control qubits and target qudits in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only (2+3d)(2+3d)(2+3d) (d≥2d\geq 2d≥2) linear optics, beating an earlier result of 14 linear optics with d=2d=2d=2. The circuit depth 5 is much lower than an earlier result of 11 with d=2d=2d=2. Besides, the fidelity of the presented circuit can reach 99.4\%, and it is higher than the previous counterpart with d=2d=2d=2. Our scheme are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Moreover, our approach allows d>2d>2d>2.
By employing displacement operations, single-photon subtractions, and weak cross-Kerr nonlinearity, we propose an alternative way of implementing several universal quantum logical gates for all-optical hybrid qubits encoded in both single-photon polarization state and coherent state. Since these schemes can be straightforwardly implemented only using local operations without teleportation procedure, therefore, less physical resources and simpler operations are required than the existing schemes. With the help of displacement operations, a large phase shift of the coherent state can be obtained via currently available tiny cross-Kerr nonlinearity. Thus, all of these schemes are nearly deterministic and feasible under current technology conditions, which makes them suitable for large-scale quantum computing.
In this paper, we look at the possibility of realizing one-way quantum computing through a hybrid quantum computing architecture based on stationary qubits inside an optical cavity and flying qubits (photons). It has been shown that direct qubit-qubit interactions for two-qubit gate implementations can be replaced by the experimentally less demanding generation of single photons on demand and linear optics photon pair measurements. The outcomes of these measurements indicate either the completion of the gate or the presence of the original qubits, such that the operation can be repeated until success.
Summary form only given. We discuss an efficient scheme which is elegant in its simplicity. By encoding the quantum information in multi-photon coherent states, rather than single photon states, simple optical manipulations acquire unexpected power. The required resource, which may be produced non-deterministically, is a superposition of the vacuum and a coherent state. Given this, the scheme is deterministic and requires only simple linear optics and photon counting. Qubit readout uses homodyne detection.