We provide an analysis of basic quantum-information processing protocols under the effect of intrinsic nonidealities in cluster states. These nonidealities are based on the introduction of randomness in the entangling steps that create the cluster state and are motivated by the unavoidable imperfections faced in creating entanglement using condensed-matter systems. Aided by the use of an alternative and very efficient method to construct cluster-state configurations, which relies on the concatenation of fundamental cluster structures, we address quantum-state transfer and various fundamental gate simulations through noisy cluster states. We find that a winning strategy to limit the effects of noise is the management of small clusters processed via just a few measurements. Our study also reinforces recent ideas related to the optical implementation of a one-way quantum computer.
We provide an analysis of basic quantum-information processing protocols under the effect of intrinsic nonidealities in cluster states. These nonidealities are based on the introduction of randomness in the entangling steps that create the cluster state and are motivated by the unavoidable imperfections faced in creating entanglement using condensed-matter systems. Aided by the use of an alternative and very efficient method to construct cluster-state configurations, which relies on the concatenation of fundamental cluster structures, we address quantum-state transfer and various fundamental gate simulations through noisy cluster states. We find that a winning strategy to limit the effects of noise is the management of small clusters processed via just a few measurements. Our study also reinforces recent ideas related to the optical implementation of a one-way quantum computer.
We assess the effects of a realistic intrinsic model for imperfections in cluster states by introducing noisy cluster states and characterizing their role in the one-way computational model. A suitable strategy to counter-affect these non-idealities is represented by the use of small clusters, stripped of any redundancy, which leads to the search for compact schemes for one-way quantum computation. In light of this, we quantitatively address the behavior of a simple four-qubit cluster which simulates a controlled-NOT under the influences of our model for decoherence. Our scheme can be particularly useful in an all-optical setup and the strategy we address can be directly applied in those experimental situations where small cluster states can be constucted.
Quantum information processing is the coherent manipulation of a quantum state for the purpose of performing an information processing task. It is known that certain tasks can in principle be performed much more efficiently using quantum information processing rather than ordinary classical processing. Examples include factoring, secure key distribution, and the simulation of quantum systems. However, significant theoretical and technological obstacles stand in the road to achieving these promised benefits. It is exceedingly difficult to construct devices that are able to achieve an extensive level of control of a quantum state while keeping that state well isolated from the effects of noise. Although there is considerable experimental effort underway to build devices that are less noisy and more controllable, there is also a significant theoretical program aimed at finding schemes that make such physical limitations have less effect on the overall reliability of a device. The crowning achievement is the theory of fault-tolerant quantum error-correction, which shows that a noisy quantum device can be efficiently made to behave as though it were noise free, so long as the amount of noise present is below the “noise threshold”. A central result of this thesis is the calculation of the noise threshold for optical cluster-state quantum computing. Optical cluster-state quantum computing is one of the most promising proposals for the physical implementation of a quantum computer (i.e., a generic quantum information processing device). Previous studies of the value of the threshold, that considered other physical implementations, do not apply to optical quantum computing due to the unusual features of the optical proposal such as nondeterministic gates and photon loss. We present the first detailed analysis of the value of the noise threshold for this proposal. Our analysis involves a number of innovations, including a method for error-correction known as telecorrection, whereby repeated error-syndrome measurements are guaranteed to agree due to the use of teleportation during the correction process. This thesis also considers how to overcome limits to the amount of physical control able to be applied to a quantum device. We ask, if a quantum device can only control limited parts of its quantum state, can that device still be used to achieve a useful information processing task? We consider simple networks of interacting quantum spins where only a few of the spins are controllable, and consider the problem of using this system for high-fidelity quantum communication (i.e., using the system as a simple “quantum wire”). Without control, such systems generally yield a very poor communication fidelity. We show that a very simple scheme that involves controlling a small number of the spins can be used to greatly increase the fidelity across the entire network. The scheme is designed using techniques of state encoding. The thesis also considers the problem of engineering the interactions in a quantum device so that the ground state is a quantum error-correcting code. Such a problem is an important part of the proposal for naturally fault-tolerant systems, which have the ability to resist noise whilst using little or no external control. Our results prove that a certain important class of quantum error-correcting codes, the so called nondegenerate codes, cannot be the eigenstate of any physically-plausible quantum system. This result places significant restrictions on the design of naturally fault-tolerant devices, and sheds light on why current proposals for natural fault tolerance use codes that are degenerate.
We study the effects of amplitude and phase damping decoherence in d-dimensional one-way quantum computation. We focus our attention on low dimensions and elementary unidimensional cluster state resources. Our investigation shows how information transfer and entangling gate simulations are affected for $d\ensuremath{\geqslant}2$. To understand motivations for extending the one-way model to higher dimensions, we describe how basic qudit cluster states deteriorate under environmental noise of experimental interest. In order to protect quantum information from the environment, we consider encoding logical qubits into qudits and compare entangled pairs of linear qubit-cluster states to single qudit clusters of equal length and total dimension. A significant reduction in the performance of cluster state resources for d>2 is found when Markovian-type decoherence models are present.
Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how quantum networking, embodied by the generation of a special class of multipartite states called cluster states, can be used to achieve a powerful paradigm for quantum information processing. Here we analyze randomly generated cluster states in order to address the emergence of correlations as a function of the density of edges in a given underlying graph. We find that the most widespread multipartite entanglement does not correspond to the highest amount of edges in the cluster. We extend the analysis to higher dimensions, finding similar results, which suggest the establishment of small world structures in the entanglement sharing of randomised cluster states, which can be exploited in engineering more efficient quantum information carriers.
In this thesis, we investigate how protocols in quantum communication theory are influenced by noise. Specifically, we take into account noise during the transmission of quantum information and noise during the processing of quantum information. We describe three novel quantum communication protocols which can be accomplished efficiently in a noisy environment: (1) Factorization of Eve: We show that it is possible to disentangle transmitted qubits a posteriori from the quantum channel's degrees of freedom. (2) Cluster state purification: We give multi-partite entanglement purification protocols for a large class of entangled quantum states. (3) Entanglement purification protocols from quantum codes: We describe a constructive method to create bipartite entanglement purification protocols form quantum error correcting codes, and investigate the properties of these protocols, which can be operated in two different modes, which are related to quantum communication and quantum computation protocols, respectively.
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.