arXiv subjects

Alastair Kay

Publications and source records attributed to Alastair Kay.

At least 37 records · Page 2Linked to original sources

arXiv2018

Co-Processors for Quantum Devices

Quantum devices, from simple fixed-function tools to the ultimate goal of a universal quantum computer, will require high quality, frequent repetition of a small set of core operations, such as the preparation of entangled states. These tasks are perfectly suited to realisation by a co-processor or supplementary instruction set, as is common practice in modern CPUs. In this paper, we present two quintessentially quantum co-processor functions: production of a GHZ state, and implementation of optimal universal (asymmetric) quantum cloning. Both are based on the evolution of a fixed Hamiltonian. We introduce a new technique for deriving the parameters of these Hamiltonians based on the numerical integration of Toda-like flows.

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arXiv2018

Perfect Coding for Dephased Quantum State Transfer

We develop a family of perfect quantum error correcting codes that correct for phase errors that arise on any qubit, at any time, during a perfect state transfer experiment. These ensure that we find the optimal operating regime for corrected state transfer. For a specific class of system, we further show that while dephasing noise can be corrected, depolarising noise cannot.

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arXiv2017

Tailoring Spin Chain Dynamics for Fractional Revivals

The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites. We concentrate in particular on cases where the excitation is superposed over a small subset of the qubits on the spin chain, known as fractional revivals, demonstrating that spin chains are capable of producing a far greater range of fractional revivals than previously known, at high speed. We also provide a numerical technique for generating chains that produce arbitrary single-excitation states, such as the W state.

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arXiv2016

The Topological Properties of Fault-Tolerant Circuits

The design of time-independent local Hamiltonians that realise quantum algorithms is derived from the study of perfect state transfer. The novel features of this evolution are the perfect realisation of the computation, and the ability to implement operations in parallel rather than sequentially. This is applied to a quantum circuit for concatenated error correcting codes, and the properties of the eigenstates are compared to those of topological memories. An erroneous implementation of the algorithm (one where a single error could lead to a fault in the output) is found not to be topological, whereas a true fault-tolerant algorithm possesses self-correcting properties, suggesting the existence of a unifying structure for fault-tolerant memories.

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arXiv2016

Generating Quantum States through Spin Chain Dynamics

Spin chains can realise perfect quantum state transfer between the two ends via judicious choice of coupling strengths. In this paper, we study what other states can be created by engineering a spin chain. We conclude that, up to local phases, all single excitation quantum states with support on every site of the chain can be created. We pay particular attention to the generation of W-states that are superposed over every site of the chain.

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arXiv2016

Optimal Universal Quantum Cloning: Asymmetries and Fidelity Measures

We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.

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arXiv2016

Quantum Error Correction for State Transfer in Noisy Spin Chains

Can robustness against experimental imperfections and noise be embedded into a quantum simulation? In this paper, we report on a special case in which this is possible. A spin chain can be engineered such that, in the absence of imperfections and noise, an unknown quantum state is transported from one end of the chain to the other, due only to the intrinsic dynamics of the system. We show that an encoding into a standard error correcting code (a Calderbank-Shor-Steane code) can be embedded into this simulation task such that a modified error correction procedure on read-out can recover from sufficiently low rates of noise during transport.

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arXiv2015

The Degree of Quantum Correlation Required to Speed-Up a Computation

The one clean qubit model of quantum computation (DQC1) efficiently implements a computational task that is not known to have a classical alternative. During the computation, there is never more than a small but finite amount of entanglement present, and it is typically vanishingly small in the system size. In this paper, we demonstrate that there is nothing unexpected hidden within the DQC1 model -- Grover's Search, when acting on a mixed state, provably exhibits a speed-up over classical with guarantees as to the presence of only vanishingly small amounts of quantum correlations (entanglement and quantum discord) -- while arguing that this is not an artefact of the oracle-based construction. We also present some important refinements in the evaluation of how much entanglement may be present in DQC1, and how the typical entanglement of the system must be evaluated.

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arXiv2014

Characterising the Performance of XOR Games and the Shannon Capacity of Graphs

In this paper we give a set of necessary and sufficient conditions such that quantum players of a two-party {\sc xor} game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrisation of new families of games which have no quantum advantage, for arbitrary input probability distributions up to certain symmetries. In the future, these might be used in information-theoretic studies on reproducing the set of quantum non-local correlations.

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arXiv2014

The Implications of Ignorance for Quantum Error Correction Thresholds

Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for the likes of the Toric code require them to work well beyond this limit. We argue that without the assumption of being below the distance limit, the success of error correction is not only contingent on the noise model, but what the noise model is believed to be. Any discrepancy must adversely affect the threshold rate, and risks invalidating existing threshold theorems. We prove that for the 2D Toric code, suitable thresholds still exist by utilising a mapping to the 2D random bond Ising model.

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arXiv2013

Limited measurement dependence in multiple runs of a Bell test

The assumption of free will - the ability of an experimentalist to make random choices - is central to proving the indeterminism of quantum resources, the primary tool in quantum cryptography. Relaxing the assumption in a Bell test allows violation of the usual classical threshold by correlating the random number generators used to select measurements with the devices that perform them. In this paper, we examine not only these correlations, but those across multiple runs of the experiment. This enables an explicit exposition of the optimal cheating strategy and how the correlations manifest themselves within this strategy. Similar to other recent results, we prove that there remain Bell violations for a sufficiently high, yet non-maximal degree of free will which cannot be simulated by a classical attack, regardless of how many runs of the experiment those choices are correlated over.

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arXiv2013

Comment on Partial Adiabatic Quantum Search

The partial adiabatic search algorithm was introduced in [A. Tulsi, Phys. Rev. A 80, 052328 (2009)] as a modification of the usual adiabatic algorithm for quantum search with the idea that most of the interesting computation only happens over a very short range of the adiabatic path. By focussing on that restricted range, one can potentially gain advantage by reducing the control requirements on the system, enabling a uniform rate of evolution. In this comment, we point out an oversight in the original work [1] that invalidates its proof. However, the argument can be corrected, and the calculations in [1] are then sufficient to show that the scheme still works. Nevertheless, subsequent works [2-6] cannot all be recovered in the same way.

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arXiv2013

Coherent Quantum Transport in Photonic Lattices

Transferring quantum states efficiently between distant nodes of an information processing circuit is of paramount importance for scalable quantum computing. We report on the first observation of a perfect state transfer protocol on a lattice, thereby demonstrating the general concept of trans- porting arbitrary quantum information with high fidelity. Coherent transfer over 19 sites is realized by utilizing judiciously designed optical structures consisting of evanescently coupled waveguide ele- ments. We provide unequivocal evidence that such an approach is applicable in the quantum regime, for both bosons and fermions, as well as in the classical limit. Our results illustrate the potential of the perfect state transfer protocol as a promising route towards integrated quantum computing on a chip.

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arXiv2012

Optimal Asymmetric Quantum Cloning

While the no-cloning theorem, which forbids the perfect copying of quantum states, is well-known as one of the defining features of quantum mechanics, the question of how well the theory allows a state to be cloned is yet to be completely solved. In this paper, rigorous solutions to the problem of M to N asymmetric cloning of qudits are obtained in a number of interesting cases. The central result is the solution to the 1 to N universal asymmetric qudit cloning problem for which the exact trade-off in the fidelities of the clones for every N and d is derived. Analogous results are proven for qubits when M=N-1. We also consider state-dependent 1 to N qubit cloning, providing a general parametrization in terms of a Heisenberg star Hamiltonian. In all instances, we determine the feasibility of implementing the cloning economically, i.e., without an ancilla, and determine the dimension of the ancilla when an economic implementation is not possible.

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arXiv2012

Using Separable Bell-Diagonal States to Distribute Entanglement

One of the many bizarre features of entanglement is that Alice, by sending a qubit to Bob in a separable state, can generate some entanglement between herself and Bob. This protocol is stripped down to the bare essentials to better elucidate the key properties of the initial resource state that enable this entanglement distribution. The necessary and sufficient conditions under which the correlations of a Bell-diagonal state serve as a useful resource are proven, giving upper and lower bounds on the entanglement that can be distributed when those conditions are met.

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arXiv2012

The effects of reduced "free will" on Bell-based randomness expansion

With the advent of quantum information, the violation of a Bell inequality is used as evidence of the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's Theorem is the existence of experimental "free will", meaning that measurement settings can be chosen at random and independently by each party. The relaxation of this assumption potentially shifts the balance of power towards an eavesdropper. We consider a no-signalling model with reduced "free will" and bound the adversary's capabilities in the task of randomness expansion.

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arXiv2012

How to Counteract Systematic Errors in Quantum State Transfer

In the absence of errors, the dynamics of a spin chain, with a suitably engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum state over large distances. Here, we propose encoding and decoding procedures to recover perfectly from low rates of systematic errors. The encoding and decoding regions, located at opposite ends of the chain, are small compared to the length of the chain, growing linearly with the size of the error. We also describe how these errors can be identified, again by only acting on the encoding and decoding regions.

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arXiv2011

The Capabilities of a Perturbed Toric Code as a Quantum Memory

We analyze the effect of typical, unknown perturbations on the 2D toric code when acting as a quantum memory, incorporating the effects of error correction on read-out. By transforming the system into a 1D transverse Ising model undergoing an instantaneous quench, and making extensive use of Lieb-Robinson bounds, we prove that for a large class of perturbations, the survival time of stored information grows at least logarithmically with the system size. A uniform magnetic field saturates this scaling behavior. We show that randomizing the stabilizer strengths gives a polynomial survival time with a degree that depends on the strength of the perturbation.

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