Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Anharmonic effects on a phonon-number measurement of a quantum-mesoscopic-mechanical oscillator

We generalize a proposal for detecting single-phonon transitions in a single nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of each mechanical oscillator. In this scheme two NEMS oscillators are coupled via a term quadratic in the amplitude of oscillation for each oscillator. One NEMS oscillator is driven and strongly damped and becomes a transducer for phonon number in the other measured oscillator. We derive the conditions for this measurement scheme to be quantum limited and find a condition on the size of the anharmonicity. We also derive the relation between the phase diffusion back-action noise due to number measurement and the localization time for the measured system to enter a phonon-number eigenstate. We relate both these time scales to the strength of the measured signal, which is an induced current proportional to the position of the read-out oscillator.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Single-electron measurements with a micromechanical resonator

A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Quantum transport and integrability of the Anderson model for a quantum dot with multiple leads

We show that an Anderson Hamiltonian describing a quantum dot connected to multiple leads is integrable. A general expression for the nonlinear conductance is obtained by combining the Bethe ansatz exact solution with Landauer-Buttiker theory. In the Kondo regime, a closed form expression is given for the matrix conductance at zero temperature and when all the leads are close to the symmetric point. A bias-induced splitting of the Kondo resonance is possible for three or more leads. Specifically, for N leads, with each at a different chemical potential, there can be N-1 Kondo peaks in the conductance.

Experimental requirements for Grover's algorithm in optical quantum computation

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single nonscalable controlled- NOT (CNOT) gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature (London) 409, 46 (2001)].

Non-ideal monitoring of a qubit state using a quantum tunnelling device

We propose a model for non-ideal monitoring of the state of a coupled quantum dot qubit by a quantum tunnelling device. The non-ideality is modelled using an equivalent measurement circuit. This allows realistically available measurement results to be related to the state of the quantum system (qubit). We present a quantum trajectory that describes the stochastic evolution of the qubit state conditioned by tunnelling events (i.e. current) through the device. We calculate and compare the noise power spectra of the current in an ideal and a non-ideal measurement. The results show that when the two qubit dots are strongly coupled the non-ideal measurement cannot detect the qubit state precisely. The limitation of the ideal model for describing a realistic system maybe estimated from the noise spectra.

Progress in silicon-based quantum computation

We review progress at the Australian Centre for Quantum Computer Technology towards the fabrication and demonstration of spin qubits and charge qubits based on phosphorus donor atoms embedded in intrinsic silicon. Fabrication is being pursued via two complementary pathways: a 'top-down' approach for near-term production of few-qubit demonstration devices and a 'bottom-up' approach for large-scale qubit arrays with sub-nanometre precision. The 'top-down' approach employs a low-energy (keV) ion beam to implant the phosphorus atoms. Single-atom control during implantation is achieved by monitoring on-chip detector electrodes, integrated within the device structure. In contrast, the 'bottom-up' approach uses scanning tunnelling microscope lithography and epitaxial silicon overgrowth to construct devices at an atomic scale. In both cases, surface electrodes control the qubit using voltage pulses, and dual single-electron transistors operating near the quantum limit provide fast read-out with spurious-signal rejection.

Enhanced optical properties of the GaAsN/GaAs quantum-well structure by the insertion of InAs monolayers

Microstructural and optical properties of InAs-inserted and reference single GaAsN/GaAs quantum-well (QW) structures grown by metalorganic chemical vapor deposition were investigated using cross-sectional transmission electron microscopy and photoluminescence (PL). Significant enhancement of PL intensity and a blueshift of PL emission were observed from the InAs-inserted GaAsN/GaAs QW structure, compared with the single GaAsN/GaAs QW structure. Strain compensation and In-induced reduction of N incorporation are suggested to be two major factors affecting the optical properties. (C) 2004 American Institute of Physics.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

Schrodinger cats and their power for quantum information processing

We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrodinger 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.

Nonlinear quantum optical computing via measurement

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel ( 2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM ( 2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.