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arXiv:1305.0212 · New Journal of Physics

Experimental characterization of universal one-way quantum computing

B A Bell, Mark Tame, A S Clark, R W Nock, W J Wadsworth, J G Rarity

Published May 20, 2013• 26 citations

Abstract

We report the characterization of a universal set of logic gates for one-way quantum computing using a four-photon ‘star’ cluster state generated by fusing photons from two independent photonic crystal fibre sources. We obtain a fidelity for the cluster state of 0.66 ± 0.01 with respect to the ideal case. We perform quantum process tomography to completely characterize a controlled-NOT, Hadamard and T gate all on the same compact entangled resource. Together, these operations make up a universal set of gates such that arbitrary quantum logic can be efficiently constructed from combinations of them. We find process fidelities with respect to the ideal cases of 0.64 ± 0.01 for the CNOT, 0.67 ± 0.03 for the Hadamard and 0.76 ± 0.04 for the T gate. The characterization of these gates enables the simulation of larger protocols and algorithms. As a basic example, we simulate a Swap gate consisting of three concatenated CNOT gates. Our work provides some pragmatic insights into the prospects for building up to a fully scalable and fault-tolerant one-way quantum computer with photons in realistic conditions.

DOI: 10.1088/1367-2630/15/5/053030

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We report the characterization of a universal set of logic gates for one-way quantum computing using a four-photon ‘star’ cluster state generated by fusing photons from two independent photonic crystal fibre sources. We obtain a fidelity for the cluster state of 0.66 ± 0.01 with respect to the ideal case. We perform quantum process tomography to completely characterize a controlled-NOT, Hadamard and T gate all on the same compact entangled resource. Together, these operations make up a universal set of gates such that arbitrary quantum logic can be efficiently constructed from combinations of them. We find process fidelities with respect to the ideal cases of 0.64 ± 0.01 for the CNOT, 0.67 ± 0.03 for the Hadamard and 0.76 ± 0.04 for the T gate. The characterization of these gates enables the simulation of larger protocols and algorithms. As a basic example, we simulate a Swap gate consisting of three concatenated CNOT gates. Our work provides some pragmatic insights into the prospects for building up to a fully scalable and fault-tolerant one-way quantum computer with photons in realistic conditions.

We describe the application of four-qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic operations of one-way quantum computation. These consist of arbitrary single-qubit rotations, either probabilistic or deterministic, and simple two-qubit gates, such as a controlled-NOT (CNOT) gate for equatorial qubits and a universal controlled-phase gate (controlled-

Z

or CZ) gate acting on arbitrary target qubits. Other basic computation operations, such as the Grover's search and the Deutsch's algorithms, have been realized by using these states. In all the cases we obtained a high value of the operation fidelities. These results demonstrate that cluster states of two photons entangled in many degrees of freedom are good candidates for the realization of more complex quantum computation operations based on a larger number of qubits.

In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.

We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then, by performing single-qubit measurements, the CNOT gate is applied to arbitrary single input qubits. To characterize the performance of the gate, we estimate its quantum process fidelity and prove its entangling capability. In addition, our results show that the gate cannot be reproduced by local operations and classical communication. Our experiment shows that such hyper-entangled cluster states are promising candidates for efficient optical quantum computation.

The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.