Fault-tolerant quantum computation with cluster states

By Morten Nielsen, Christopher M. Dawson. 2004

132 citations recorded by the source corpus.

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c64dbaa06446df904017225a61537f1a3ea16614

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Citations in the corpus

Multiphoton entanglement and interferometry (2008, background): “A threshold has been proved to exist (Nielsen and Dawson, 2005; Dawson et al., 2006a, 2006b; Aliferis and Leung, 2006); particularly, in the context of scalable optical cluster-state quantum computing, Nielsen and coworkers have shown that, for photon loss noise and depolarizing noise,…”
Universal Blind Quantum Computation (2008, background): “Step 8 converts the fault-tolerant circuit to a measurement pattern; it is known that this transformation retains the fault-tolerance property [26], [4].”
Measurement-based quantum computation (2009, background): “The existence of a non-zero threshold was first proven by reduction to the circuit mode”
Quantum accuracy threshold for concatenated distance-3 codes (2005, background): “ocations, and stochastic faults occur independently with probability ε<ε 0 at each location in the noisy circuit, the probability of failure can be bounded as P(k) fail ≤ Lε (k) ≤ ε 0L(ε/ε 0) 2k , (8) using eq. (6). By averaging over the fault locations in the level-kfault-tolerant circuit, we ﬁn”
Determinism in the one-way model (2005, background): “computing. 1 Introduction The recent one-way quantum computing model [1, 2, 3] has already drawn considerable attention, mainly because it suggests diﬀerent physical realisations of quantum computing [4, 5, 6, 7, 8, 9]. Computation consists of a ﬁrst phase of preparation and entanglement, followed b”
Experimental one-way quantum computing (2005, background): “Although a threshold has been proven to exist 18 , it is unknown whether cluster state quantum computation will be more or less sensitive to noise than the standard model.”
Fault-tolerant measurement-based quantum computing with continuous-variable cluster states. (2013, background): “Qubit cluster states admit a fault-tolerance threshold for measurement-based QC [34, 35], which can be made strikingly high (1.4”
Deterministic generation of all-photonic quantum repeaters from solid-state emitters (2016, background): “The standard process of generating graph states (or cluster states [12] for quantum computing)[15, 21, 23] begins with pairs of photons that are prepared in entangled (Bell) states through parametric down-conversion.”