arXiv subjects

Pieter Kok

Publications and source records attributed to Pieter Kok.

At least 73 records · Page 4Linked to original sources

arXiv2009

Cluster state generation with atomic ensembles via the dipole blockade mechanism

We present a new scheme for cluster states generation based on atomic ensembles and the dipole blockade mechanism. The protocol requires identical single photon sources, one ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates Q-qubit GHZ states with probability p ~ eta^{Q/2}, where eta is the combined detection and source efficiency. This is significantly more efficient than any known robust probabilistic entangling operation. The GHZ states form the basic building block for universal cluster states - a resource for the one-way quantum computer.

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arXiv2007

Effects of self-phase modulation on weak nonlinear optical quantum gates

A possible two-qubit gate for optical quantum computing is the parity gate based on the weak Kerr effect. Two photonic qubits modulate the phase of a coherent state, and a quadrature measurement of the coherent state reveals the parity of the two qubits without destroying the photons. This can be used to create so-called cluster states, a universal resource for quantum computing. Here, the effect of self-phase modulation on the parity gate is studied, introducing generating functions for the Wigner function of a modulated coherent state. For materials with non-EIT-based Kerr nonlinearities, there is typically a self-phase modulation that is half the magnitude of the cross-phase modulation. Therefore, this effect cannot be ignored. It is shown that for a large class of physical implementations of the phase modulation, the quadrature measurement cannot distinguish between odd and even parity. Consequently, weak nonlinear parity gates must be implemented with physical systems where the self-phase modulation is negligable.

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arXiv2007

Lecture notes on Optical Quantum Computing

A quantum computer is a machine that can perform certain calculations much faster than a classical computer by using the laws of quantum mechanics. Quantum computers do not exist yet, because it is extremely difficult to control quantum mechanical systems to the necessary degree. What is more, we do at this moment not know which physical system is the best suited for making a quantum computer (although we have some ideas). It is likely that a mature quantum information processing technology will use (among others) light, because photons are ideal carriers for quantum information. These notes are an expanded version of the five lectures I gave on the possibility of making a quantum computer using light, at the Summer School in Theoretical Physics in Durban, 14-24 January, 2007. There are quite a few proposals using light for quantum computing, and I can highlight only a few here. I will focus on photonic qubits, and leave out continuous variables completely. I assume that the reader is familiar with basic quantum mechanics and introductory quantum computing.

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arXiv2007

Efficient growth of complex graph states via imperfect path erasure

Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok [Phys. Rev. A 71, 060310 (2005)]. Compared to straightforward postselection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states.

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arXiv2007

Adaptive strategies for graph state growth in the presence of monitored errors

Graph states (or cluster states) are the entanglement resource that enables one-way quantum computing. They can be grown by projective measurements on the component qubits. Such measurements typically carry a significant failure probability. Moreover, they may generate imperfect entanglement. Here we describe strategies to adapt growth operations in order to cancel incurred errors. Nascent states that initially deviate from the ideal graph states evolve toward the desired high fidelity resource without impractical overheads. Our analysis extends the diagrammatic language of graph states to include characteristics such as tilted vertices, weighted edges, and partial fusion, which arise from experimental imperfections. The strategies we present are relevant to parity projection schemes such as optical `path erasure' with distributed matter qubits.

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arXiv2006

Creating large noon states with imperfect phase control

Optical noon states (|N,0> + |0,N>) are an important resource for Heisenberg-limited metrology and quantum lithography. The only known methods for creating noon states with arbitrary $N$ via linear optics and projective measurments seem to have a limited range of application due to imperfect phase control. Here, we show that bootstrapping techniques can be used to create high-fidelity noon states of arbitrary size.

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arXiv2006

Review article: Linear optical quantum computing

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. We review the original theory and its improvements, and we give a few examples of experimental two-qubit gates. We discuss the use of realistic components, the errors they induce in the computation, and how these errors can be corrected.

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arXiv2005

Repeat-Until-Success quantum computing using stationary and flying qubits

We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g. single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g. photons). Our scheme solves some of the most pressing problems in existing non-hybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the efficient photon-loss tolerant build up of cluster states by Barrett and Kok [Phys. Rev. A 71, 060310(R) (2005)] with the idea of Repeat-Until-Success (RUS) quantum computing by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)]. This idea can be used to perform eventually deterministic two-qubit logic gates on spatially separated stationary qubits via photon pair measurements. Under non-ideal conditions, where photon loss is a possibility, the resulting gates can still be used to build graph states for one-way quantum computing. In this paper, we describe the RUS method, present possible experimental realizations, and analyse the generation of graph states.

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arXiv2005

Quantum Interferometric Sensors

Quantum entanglement has the potential to revolutionize the entire field of interferometric sensing by providing many orders of magnitude improvement in interferometer sensitivity. The quantum-entangled particle interferometer approach is very general and applies to many types of interferometers. In particular, without nonlocal entanglement, a generic classical interferometer has a statistical-sampling shot-noise limited sensitivity that scales like $1/\sqrt{N}$, where $N$ is the number of particles passing through the interferometer per unit time. However, if carefully prepared quantum correlations are engineered between the particles, then the interferometer sensitivity improves by a factor of $\sqrt{N}$ to scale like 1/N, which is the limit imposed by the Heisenberg Uncertainty Principle. For optical interferometers operating at milliwatts of optical power, this quantum sensitivity boost corresponds to an eight-order-of-magnitude improvement of signal to noise. This effect can translate into a tremendous science pay-off for space missions. For example, one application of this new effect is to fiber optical gyroscopes for deep-space inertial guidance and tests of General Relativity (Gravity Probe B). Another application is to ground and orbiting optical interferometers for gravity wave detection, Laser Interferometer Gravity Observatory (LIGO) and the European Laser Interferometer Space Antenna (LISA), respectively. Other applications are to Satellite-to-Satellite laser Interferometry (SSI) proposed for the next generation Gravity Recovery And Climate Experiment (GRACE II).

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arXiv2005

Efficient optical quantum information processing

Quantum information offers the promise of being able to perform certain communication and computation tasks that cannot be done with conventional information technology (IT). Optical Quantum Information Processing (QIP) holds particular appeal, since it offers the prospect of communicating and computing with the same type of qubit. Linear optical techniques have been shown to be scalable, but the corresponding quantum computing circuits need many auxiliary resources. Here we present an alternative approach to optical QIP, based on the use of weak cross-Kerr nonlinearities and homodyne measurements. We show how this approach provides the fundamental building blocks for highly efficient non-absorbing single photon number resolving detectors, two qubit parity detectors, Bell state measurements and finally near deterministic control-not (CNOT) gates. These are essential QIP devices

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arXiv2005

Preparing multi-partite entanglement of photons and matter qubits

We show how to make event-ready multi-partite entanglement between qubits which may be encoded on photons or matter systems. Entangled states of matter systems, which can also act as single photon sources, can be generated using the entangling operation presented in quant-ph/0408040. We show how to entangle such sources with photon qubits, which may be encoded in the dual rail, polarization or time-bin degrees of freedom. We subsequently demonstrate how projective measurements of the matter qubits can be used to create entangled states of the photons alone. The state of the matter qubits is inherited by the generated photons. Since the entangling operation can be used to generate cluster states of matter qubits for quantum computing, our procedure enables us to create any (entangled) photonic quantum state that can be written as the outcome of a quantum computer.

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arXiv2005

Relativistic quantum communication with bosonic and fermionic interferometers

We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.

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arXiv2005

Efficient high-fidelity quantum computation using matter qubits and linear optics

We propose a practical, scalable, and efficient scheme for quantum computation using spatially separated matter qubits and single photon interference effects. The qubit systems can be NV-centers in diamond, Pauli-blockade quantum dots with an excess electron or trapped ions with optical transitions, which are each placed in a cavity and subsequently entangled using a double-heralded single-photon detection scheme. The fidelity of the resulting entanglement is extremely robust against the most important errors such as detector loss, spontaneous emission, and mismatch of cavity parameters. We demonstrate how this entangling operation can be used to efficiently generate cluster states of many qubits, which, together with single qubit operations and readout, can be used to implement universal quantum computation. Existing experimental parameters indicate that high fidelity clusters can be generated with a moderate constant overhead.

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arXiv2004

Communicating continuous quantum variables between different Lorentz frames

We show how to communicate Heisenberg-limited continuous (quantum) variables between Alice and Bob in the case where they occupy two inertial reference frames that differ by an unknown Lorentz boost. There are two effects that need to be overcome: the Doppler shift and the absence of synchronized clocks. Furthermore, we show how Alice and Bob can share Doppler-invariant entanglement, and we demonstrate that the protocol is robust under photon loss.

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arXiv2004

Comment on: "Measuring a Photonic Qubit without Destroying It"

Recently, Pryde et al reported the demonstration of a quantum non-demolition scheme for single-photon polarization states with linear optics and projective measurements [Phys. Rev. Lett. 92, 190402 (2004)]. Here, we argue that their interpretation of the experiment is inconsistent with the fidelity measure they use.

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arXiv2004

From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.

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arXiv2004

Quantum lithography, entanglement and Heisenberg-limited parameter estimation

We explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased resolution in quantum lithography follow from the use of entanglement. Mathematically, the hyperresolution of quantum lithography appears naturally in the derivation of Heisenberg-limited parameter estimation. We also review recent experiments offering a proof of principle of quantum lithography, and we address the question of state preparation and the fabrication of suitable photoresists.

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arXiv2003

Towards photostatistics from photon-number discriminating detectors

We study the properties of a photodetector that has a number-resolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a {\em non-photon} number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.

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