arXiv subjects

Alastair Kay

Publications and source records attributed to Alastair Kay.

At least 55 records · Page 3Linked to original sources

arXiv2011

The Basics of Perfect Communication through Quantum Networks

Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer, but to design a suitable one. We are particularly interested in being able to design, or understand the limitations imposed upon, Hamiltonians subject to various naturally arising constraints such as a limited coupling topology with low connectivity (specified by a graph) and type of interaction. In this paper, we characterise the necessary and sufficient conditions for transfer through a network, and describe some natural consequences such as the impossibility of routing between many different recipients for a large class of Hamiltonians, and the limitations on transfer rate. We also consider some of the trade-offs that arise in uniformly coupled networks (both Heisenberg and XX models) between transfer distance and the size of the network as a consequence of the derived conditions.

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arXiv2010

Local Realism of Macroscopic Correlations

We show that for macroscopic measurements which cannot reveal full information about microscopic states of the system, the monogamy of Bell inequality violations present in quantum mechanics implies that practically all correlations between macroscopic measurements can be described by local realistic models. Our results hold for sharp measurement and arbitrary closed quantum systems.

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arXiv2010

Quantum Control Theory for State Transformations: Dark States and their Enlightenment

For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an upper bound on the achievable fidelity of a transformation between a pair of states based on the symmetries of the system. A large class of spin networks is presented for which this bound can be saturated. In this context, we show how the inaccessible dark states for a given excitation-preserving evolution can be calculated, and illustrate how some of these can be accessed using extra catalytic excitations. This emphasises that it is not sufficient for analyses of state transfer in spin networks to restrict to the single excitation subspace. One class of symmetries in these spin networks is exactly characterised in terms of the underlying graph properties.

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arXiv2010

Arboreal Bound Entanglement

In this paper, we discuss the entanglement properties of graph-diagonal states, with particular emphasis on calculating the threshold for the transition between the presence and absence of entanglement (i.e. the separability point). Special consideration is made of the thermal states of trees, including the linear cluster state. We characterise the type of entanglement present, and describe the optimal entanglement witnesses and their implementation on a quantum computer, up to an additive approximation. In the case of general graphs, we invoke a relation with the partition function of the classical Ising model, thereby intimating a connection to computational complexity theoretic tasks. Finally, we show that the entanglement is robust to some classes of local perturbations.

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arXiv2010

Perfect Quantum Routing in Regular Spin Networks

Regular families of coupled quantum networks are described such the unknown state of a qubit can be perfectly routed from any node to any other node in a time linear in the distance. Unlike previous constructions, the transfer can be achieved perfectly on a network that is local on any specified number of spatial dimensions. The ability to route the state, and the regularity of the networks, vastly improve the utility of this scheme in comparison to perfect state transfer schemes. The structures can also be used for entanglement generation.

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arXiv2010

Optimal Detection of Entanglement in GHZ States

We present a broad class of states which are diagonal in the basis of N-qubit GHZ states such that non-positivity under the partial transpose operation is necessary and sufficient for the presence of entanglement. This class includes many naturally arising instances such as dephased or depolarised GHZ states. Furthermore, our proof directly leads to an entanglement witness which saturates this bound. The witness is applied to thermal GHZ states to prove that the entanglement can be extremely robust to system imperfections.

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arXiv2010

A Review of Perfect State Transfer and its Application as a Constructive Tool

We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.

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arXiv2010

Computation on Spin Chains with Limited Access

We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a single site and its interaction with its neighbor. Control of an array of sites yields sufficient parallelism for the implementation of fault-tolerant circuits. The framework exposes contradictions between the control theoretic concept of controllability with the ability of a system to perform quantum computation.

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arXiv2009

Limitations of Passive Protection of Quantum Information

The ability to protect quantum information from the effect of noise is one of the major goals of quantum information processing. In this article, we study limitations on the asymptotic stability of quantum information stored in passive N-qubit systems. We consider the effect of small imperfections in the implementation of the protecting Hamiltonian in the form of perturbations or weak coupling to a ground state environment. We prove that, regardless of the protecting Hamiltonian, there exists a perturbed evolution that necessitates a final error correcting step when the state of the memory is read. Such an error correction step is shown to require a finite error threshold, the lack thereof being exemplified by the 3D compass model. We go on to present explicit weak Hamiltonian perturbations which destroy the logical information stored in the 2D toric code in a time O(log(N)).

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arXiv2009

The Role of Rotational Invariance in the Properties of Hamiltonians

Is it possible to prove that the properties of Hamiltonians, such as the ground state energy, results of dynamical evolution, or thermal state expectation values, can be efficiently calculated when the Hamiltonians have physically motivated constraints such as translational or rotational invariance? We report that rotational invariance does not reduce the difficulty of finding the ground state energy of the system. Crucially, the construction it preserves the translational invariance of a Hamiltonian. The failure of the construction for the properties of thermal states at finite temperatures is discussed.

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arXiv2009

How long can a quantum memory withstand depolarizing noise?

We investigate the possibilities and limitations of passive Hamiltonian protection of a quantum memory against depolarizing noise. Without protection, the lifetime of a single qubit is independent of N, the number of qubits composing the memory. In the presence of a protecting Hamiltonian, the lifetime increases at most logarithmically with N. We construct an explicit time-independent Hamiltonian which saturates this bound, exploiting the noise itself to achieve the protection.

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arXiv2009

Optimal Cloning and Singlet Monogamy

The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be generated between spins (known as monogamy), and how well an unknown state can be cloned. This situation is remedied by giving a set of sufficient conditions such that the optimal Completely Positive map can be implemented as a teleportation operation into a standard, reference, state. The case of arbitrary 1 to N asymmetric cloning of d-dimensional spins can then be solved exactly, yielding the concept of `singlet monogamy'. The utility of this relation is demonstrated by calculating properties of Heisenberg systems, and contrasting them with the results from standard monogamy arguments.

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arXiv2009

The Non-Equilibrium Reliability of Quantum Memories

The ability to store quantum information without recourse to constant feedback processes would yield a significant advantage for future implementations of quantum information processing. In this paper, limitations of the prototypical model, the Toric code in two dimensions, are elucidated along with a sufficient condition for overcoming these limitations. Specifically, the interplay between Hamiltonian perturbations and dynamically occurring noise is considered as a system in its ground state is brought into contact with a thermal reservoir. This proves that when utilizing the Toric code on N^2 qubits in a 2D lattice as a quantum memory, the information cannot be stored for a time O(N). In contrast, the 2D Ising model protects classical information against the described noise model for exponentially long times. The results also have implications for the robustness of braiding operations in topological quantum computation.

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arXiv2008

Quantum Self-Correcting Stabilizer Codes

In this paper, we explicitly construct (Abelian) anyonic excitations of arbitrary stabilizer Hamiltonians which are local on a 2D lattice of qubits. This leads directly to the conclusion that, in the presence of local thermal noise, such systems cannot be used for the fault-tolerant storage of quantum information by self-correction i.e. they are ruled out as candidates for a `quantum hard drive'. We suggest that in 3D, the same construction leads to an argument that self-correction is impossible.

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arXiv2008

Reproducing spin lattice models in strongly coupled atom-cavity systems

In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing phenomena in condensed matter physics, such as the spin-1/2 Ising, XX, Heisenberg, and XXZ models. The ability to construct networks of arbitrary geometry also allows for the simulation of topological effects. By tuning the number of excitations present, the dimension of the spin to be simulated can be controlled, and mixtures of different spin types produced. The facility of single-site addressing, the use of only the natural hopping photon dynamics without external fields, and the recent experimental advances towards strong coupling, makes the prospect of using these arrays as efficient quantum simulators promising.

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arXiv2008

Interfacing with Hamiltonian Dynamics

Simple constructions and protocols are demonstrated to allow the implementation of universal quantum computation on an arbitrarily large quantum system by controlling a fixed number of spins, vastly reducing the engineering requirements in comparison to a direct implementation of the circuit model. Analytic pulse sequences are derived for deterministic gate operation and system cooling which only require pulse strengths that are comparable to the intrinsic Hamiltonian of the system.

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arXiv2008

Bounding Fault-Tolerant Thresholds for Purification and Quantum Computation

In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be subject to less than 5.3% error. An existing proof that purification is equivalent to error correction is used to show that this bound can also be applied to concatenated error correcting codes in the presence of noisy gates, and hence gives a limit to the tolerable error rate for a fault-tolerant quantum computer formed by concatenation. This is shown to apply also to the case where error detection and post-selection, as proposed by Knill, is used to enhance the threshold. We demonstrate the trade-off between gate/environmentally induced faulty rotations and qubit loss errors.

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arXiv2008

The Computational Power of Symmetric Hamiltonians

The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still BQP complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a Universal Quantum Interface, a device which enables control of an entire computation through the control of a fixed number of spins, and using it as a building-block to entirely remove the need for control, except in the system initialisation. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a QMA-complete problem.

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