arXiv subjects

Alexei Gilchrist

Publications and source records attributed to Alexei Gilchrist.

48 records · Page 3Linked to original sources

arXiv2008

Optimal tracking for pairs of qubit states

In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.

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arXiv2007

Choice of Measurement Sets in Qubit Tomography

Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements has been largely unexplored in the literature. In this work we develop theoretical asymptotic bounds for the average fidelity of pure qubit tomography using measurement sets whose axes correspond to vertices of Platonic solids. We also present complete simulations of maximum likelihood tomography for mixed qubit states using the Platonic solid measurements. We show that overcomplete measurement sets can be used to improve the accuracy of tomographic reconstructions.

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arXiv2006

A photon loss tolerant Zeno CSIGN gate

We model an optical implementation of a CSIGN gate that makes use of the Quantum Zeno effect [1,2] in the presence of photon loss. The raw operation of the gate is severely affected by this type of loss. However, we show that by using the same photon loss codes that have been proposed for linear optical quantum computation (LOQC), the performance is greatly enhanced and such gates can outperform LOQC equivalents. The technique can be applied to other types of nonlinearities, making the implementation of nonlinear optical gates much more attractive.

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arXiv2006

Quantum Control of a Single Qubit

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyse a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two non-orthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a non-projective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realises the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.

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arXiv2005

Efficient Parity Encoded Optical Quantum Computing

We present a linear optics quantum computation scheme with a greatly reduced cost in resources compared to KLM. The scheme makes use of elements from cluster state computation and achieves comparable resource usage to those schemes while retaining the circuit based approach of KLM.

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arXiv2005

Loss Tolerant Optical Qubits

We present a linear optics quantum computation scheme that employs a new encoding approach that incrementally adds qubits and is tolerant to photon loss errors. The scheme employs a circuit model but uses techniques from cluster state computation and achieves comparable resource usage. To illustrate our techniques we describe a quantum memory which is fault tolerant to photon loss.

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arXiv2004

Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment

We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterisation of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit-commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.

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arXiv2003

Measuring Controlled-NOT and two-qubit gate operation

Accurate characterisation of two-qubit gates will be critical for any realisation of quantum computation. We discuss a range of measurements aimed at characterising a two-qubit gate, specifically the CNOT gate. These measurements are architecture-independent, and range from simple truth table measurements, to single figure measures such as the fringe visibility, parity, fidelity, and entanglement witnesses, through to whole-state and whole-gate measures achieved respectively via quantum state and process tomography. In doing so, we examine critical differences between classical and quantum gate operation.

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arXiv2003

Photon Added Detection

The production of conditional quantum states and quantum operations based on the result of measurement is now seen as a key tool in quantum information and metrology. We propose a new type of photon number detector. It functions non-deterministically, but when successful, it has high fidelity. The detector, which makes use of an n-photon auxiliary Fock state and high efficiency Homodyne detection, allows a tunable tradeoff between fidelity and probability. By sacrificing probability of operation, an excellent approximation to a photon number detector is achieved.

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arXiv2003

Generating optical nonlinearity using trapped atoms

We describe a scheme for producing an optical nonlinearity using an interaction with one or more ancilla two-level atomic systems. The nonlinearity, which can be implemented using high efficiency fluorescence shelving measurements, together with general linear transformations is sufficient for simulating arbitrary Hamiltonian evolution on a Fock state qudit. We give two examples of the application of this nonlinearity, one for the creation of nonlinear phase shifts on optical fields as required in single photon quantum computation schemes, and the other for the preparation of optical Schrodinger cat states.

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arXiv2003

Quantum dynamics as a physical resource

How useful is a quantum dynamical operation for quantum information processing? Motivated by this question we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of such strength measures, based on axiomatic considerations independent of state-based resources. The power of this theory is demonstrated with applications to quantum communication complexity, quantum computational complexity, and entanglement generation by unitary operations.

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arXiv2002

A practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].

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