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arXiv:1101.5496 · New Journal of Physics

Coherent state topological cluster state production

Casey R. Myers, Timothy C. Ralph

Published Nov 30, 2011• 25 citations
arXivHTMLPDF

Abstract

We present results illustrating the construction of three-dimensional (3D) topological cluster states with coherent state logic. Such a construction would be ideally suited for wave-guide implementations of optical quantum information processing. We investigate the use of a deterministic controlled- Z gate, showing that given large enough initial cat states, it is possible to build large 3D cluster states. We model X and Z basis measurements by displaced photon number detections and x -quadrature homodyne detections, respectively. We investigate whether teleportation can aid in cluster state construction and whether this introduction of located loss errors fits within the topological cluster state framework.

DOI
10.1088/1367-2630/13/11/115015

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We present results illustrating the construction of three-dimensional (3D) topological cluster states with coherent state logic. Such a construction would be ideally suited for wave-guide implementations of optical quantum information processing. We investigate the use of a deterministic controlled- Z gate, showing that given large enough initial cat states, it is possible to build large 3D cluster states. We model X and Z basis measurements by displaced photon number detections and x -quadrature homodyne detections, respectively. We investigate whether teleportation can aid in cluster state construction and whether this introduction of located loss errors fits within the topological cluster state framework.
Entanglement is one of the most mysterious and fleeting properties of nature. It is also a powerful resource for quantum information processing. Efforts to design and build a quantum computer are severely constrained by the difficulties of preserving useful qubit entanglement against the environment. Concatenated fault-tolerant error correction provides a framework to perform scalable computation, but is extremely expensive in terms of resources. Direct topological implementations promise robust entanglement and control, but require physical systems with as yet unobserved controllable topological phases. Here we present the first practical scheme for constructing a topological quantum computer based on a 3D cluster state lattice of photons on chip. In contrast to the resource requirements of other schemes, a target error rate of 10^(-16) requires approximately 3000 components per logical qubit. This constitutes a significant advance towards practical quantum computing and leads the way for topological architectures in other implementations.
Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α|⪢d/2π, as a qudit — a d-level quantum system — that is an even (meaning same size of amplitudes) superposition of d pseudo-number basis states. A pair of such coherent-state qudits can be maximally entangled by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.
Introduction Cluster states were introduced in Chapter 18, along with some of the approaches to achieving fault tolerance in measurement-based quantum computing. In this chapter, we describe an extremely promising fault-tolerant cluster state quantum computing scheme [RH07, RHG07] with a threshold error rate of 7.46 × 10 −3 , low overhead arbitrarily long-range logical gates and novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only. Detailed proposed implementations of this scheme exist for ion traps [SJ09] and single photons with cavity mediated interactions [DGI+07]. The discussion is organized as follows. In Section 20.2, we describe the topological cluster state, which is a specific three-dimensional (3D) cluster state, and give a brief overview of what topological cluster state quantum computing involves. Section 20.3 describes logical qubits in more detail and how to initialize them to ∣0 L 〉 and ∣+ L 〉 and measure them in the Z L and X L bases. State injection, the non-fault-tolerant construction of arbitrary logical states, is covered in Section 20.4. Logical gates, namely the logical identity gate and the logical CNOT gate, are discussed in Section 20.5 along with their byproduct operators. Section 20.6 describes the errorcorrection procedure. In Section 20.7, we calculate an estimate for the threshold of this scheme. Section 20.8 presents an analysis of the overhead as a function of both the circuit size and the error rate.
Large-scale quantum information processing and distributed quantum computation require the ability to perform entangling operations on a large number of qubits. We describe a new photonic module which prepares, deterministically, photonic cluster states using an atom in a cavity as an ancilla. Based on this module, we design a network for constructing 2D cluster states and then we extend the architecture to 3D topological cluster states. Advantages of our design include a passive switching mechanism and the possibility of using global control pulses for the atoms in the cavity. The architecture described here is well-suited for integrated photonic circuits on a chip and could be used as a basis of a future quantum optical processor or in a quantum repeater node.
Optical quantum computation has represented one of the most successful testbed systems for quantum information processing. Along with ion-traps and nuclear magnetic resonance (NMR), experimentalists have demonstrated control of qubits, multi-gubit gates and small quantum algorithms. However, photonic based qubits suffer from a problematic lack of a large scale architecture for fault-tolerant computation which could conceivably be built in the near future. While optical systems are, in some regards, ideal for quantum computing due to their high mobility and low susceptibility to environmental decoherence, these same properties make the construction of compact, chip based architectures difficult. Here we discuss many of the important issues related to scalable fault-tolerant quantum computation and introduce a feasible architecture design for an optics based computer. We combine the recent development of topological cluster state computation with the photonic module, simple chip based devices which can be utilized to deterministically entangle photons. The integration of this operational unit with one of the most exciting computational models solves many of the existing problems with other optics based architectures and leads to a feasible large scale design which can continuously generate a 3D cluster state with a photonic module resource cost linear in the cross sectional size of the cluster.
Photons are excellent carriers of quantum information; their polarization remains coherent for long times and it is easy to measure and precisely rotate. The fundamental hurdle with photon-based quantum information processing is the lack of direct photon-photon interactions to provide entanglement between pairs of photons. Recent proposals show the ability to build large cluster states from small entangled states using non-deterministic operations, but the generation of deterministic high-fidelity small entangled states remains a challenge. In this talk, we will show how the necessary cluster-state building blocks for large-scale quantum computation can be created from coupled solid-state quantum emitters without the need for any two-qubit gates and regardless of whether the emitters are identical. We provide a recipe for the generation of two-dimensional, ‘cluster-state’ entangled photons that can be carried out with existing experimental capabilities.