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ABSTRACT: The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just {\em three} if one of the three quantum systems has a third state that is accessible during the computation, i.e. is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (eg. atoms, photonic polarization and spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success.
06/2008;
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ABSTRACT: Quantum computation offers the potential to solve fundamental yet otherwise
intractable problems across a range of active fields of research. Recently,
universal quantum-logic gate sets - the building blocks for a quantum computer
- have been demonstrated in several physical architectures. A serious obstacle
to a full-scale implementation is the sheer number of these gates required to
implement even small quantum algorithms. Here we present and demonstrate a
general technique that harnesses higher dimensions of quantum systems to
significantly reduce this number, allowing the construction of key quantum
circuits with existing technology. We are thereby able to present the first
implementation of two key quantum circuits: the three-qubit Toffoli and the
two-qubit controlled-unitary. The gates are realised in a linear optical
architecture, which would otherwise be absolutely infeasible with current
technology.
04/2008;
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ABSTRACT: Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits-three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.
Physical Review Letters 03/2008; 100(6):060504. · 7.37 Impact Factor
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ABSTRACT: Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation. Here, we implement a compiled version in a photonic system. For the first time, we demonstrate the core processes, coherent control, and resultant entangled states required in a full-scale implementation. These are necessary steps on the path towards scalable quantum computing. Our results highlight that the algorithm performance is not the same as that of the underlying quantum circuit and stress the importance of developing techniques for characterizing quantum algorithms.
Physical Review Letters 01/2008; 99(25):250505. · 7.37 Impact Factor
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ABSTRACT: A heavy focus for optical quantum computing is the introduction of error-correction, and the minimisation of resource requirements. We detail a complete encoding and manipulation scheme designed for linear optics quantum computing, incorporating scalable operations and loss-tolerant architecture. Comment: 8 pages, 6 figures
07/2007;
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ABSTRACT: We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to measure, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution.
Physical Review Letters 07/2007; 98(22):223601. · 7.37 Impact Factor
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ABSTRACT: The realisation of a triggered entangled photon source will be of great importance in quantum information, including for quantum key distribution and quantum computation. We show here that: 1) the source reported in ``A semiconductor source of triggered entangled photon pairs''[1. Stevenson et al., Nature 439, 179 (2006)]} is not entangled; 2) the entanglement indicators used in Ref. 1 are inappropriate, relying on assumptions invalidated by their own data; and 3) even after simulating subtraction of the significant quantity of background noise, their source has insignificant entanglement.
03/2006;
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ABSTRACT: We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realizations, using partially polarizing beam splitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-z gate in both continuous-wave and pulsed regimes of operation, fully characterizing it in each case using quantum process tomography. We also demonstrate a fully resolving, nondeterministic optical Bell-state analyzer based on this controlled-z gate. This new architecture is ideally suited to guided optics implementations of optical gates.
Physical Review Letters 12/2005; 95(21):210504. · 7.37 Impact Factor
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ABSTRACT: We present a linear optics quantum computation scheme that employs an incremental parity encoding approach. The scheme uses techniques from cluster state computation and achieves comparable resource usage with increased tolerance to photon loss.
Quantum Electronics and Laser Science Conference, 2005. QELS '05; 06/2005
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ABSTRACT: We demonstrate complete characterization of a two-qubit entangling process--a linear optics controlled-NOT gate operating with coincident detection--by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.
Physical Review Letters 09/2004; 93(8):080502. · 7.37 Impact Factor
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ABSTRACT: We present a scheme which offers a significant reduction in the resources required to implement linear optics quantum computing. The scheme is a variation of the proposal of Knill, Laflamme, and Milburn, and makes use of an incremental approach to the error encoding to boost probability of success.
08/2004;
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ABSTRACT: 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 characterization 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.
Physical Review Letters 08/2004; 93(5):053601. · 7.37 Impact Factor
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ABSTRACT: We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrödinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.
Journal of Optics B Quantum and Semiclassical Optics 07/2004; 6(8):S828. · 1.81 Impact Factor
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ABSTRACT: We show that quantum computation circuits using coherent states as the logical qubits can be constructed from simple linear networks, conditional photon measurements and "small" coherent superposition resource states.
06/2003;
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ABSTRACT: We examine three possible implementations of non-deterministic linear optical cnot gates with a view to an in-principle demonstration in the near future. To this end we consider demonstrating the gates using currently available sources such as spontaneous parametric down conversion and coherent states, and current detectors only able to distinguish between zero or many photons. The demonstration is possible in the co-incidence basis and the errors introduced by the non-optimal input states and detectors are analysed.
01/2003;
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A. Gilchrist
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ABSTRACT: We present some applications of high-efficiency quantum interrogation (“interaction-free measurement”) for the creation of entangled states of separate atoms and of separate photons. The quantum interrogation of a quantum object in a superposition of object-in and object-out leaves the object and probe in an entangled state. The probe can then be further entangled with other objects in subsequent quantum interrogations. By then projecting out those cases in which the probe is left in a particular final state, the quantum objects can themselves be left in various entangled states. In this way, we show how to generate two-, three-, and higher-qubit entanglement between atoms and between photons. The effect of finite efficiency for the quantum interrogation is delineated for the various schemes.
Phys. Rev. A. 07/2002; 66(1).
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ABSTRACT: We explore in detail the possibility of generating a pair-coherent state in the non-degenerate parametric oscillator when decoherence is included. Such states are predicted in the transient regime in parametric oscillation where the pump mode is adiabatically eliminated. Two specific signatures are examined to indicate whether the state of interest has been generated, the Schrodinger cat state - like signatures, and the fidelity. Solutions in a transient regime reveal interference fringes which are indicative of the formation of a Schrodinger cat state. The fidelity indicates the purity of our prepared state compared to the ideal pair-coherent state.
03/2001;
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[show abstract]
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ABSTRACT: We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realizations, using partially polarizing beam splitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-Z gate in both continuous-wave and pulsed regimes of operation, fully characterizing it in each case using quantum process tomography. We also demonstrate a fully resolving, nondeterministic optical Bell-state analyzer based on this controlled-Z gate. This new architecture is ideally suited to guided optics implementations of optical gates. Yes Yes
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[show abstract]
[hide abstract]
ABSTRACT: We demonstrate complete characterization of a two-qubit entangling process—a linear optics controlled-NOT gate operating with coincident detection—by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively. Yes Yes
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[show abstract]
[hide abstract]
ABSTRACT: We demonstrate phase super-resolution in the absence of entangled states. The key insight is to use the inherent time-reversal symmetry of quantum mechanics: our theory shows that it is possible to measure, as opposed to prepare, entangled states. Our approach is robust, requiring only photons that exhibit classical interference: we experimentally demonstrate high-visibility phase super-resolution with three, four, and six photons using a standard laser and photon counters. Our six-photon experiment demonstrates the best phase super-resolution yet reported with high visibility and resolution. Yes Yes
