arXiv subjects
Publications and source records attributed to J. Twamley.
We develop the work of Christandl et al. [M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Phys. Rev. A 71, 032312 (2005)], to show how a d-hypercube homogenous network can be dressed by additional links to perfectly route quantum information between any given input and output nodes in a duration which is independent of the routing chosen and, surprisingly, size of the network.
We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_η$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_η$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.
Coherent coupling between single quantum objects is at the heart of modern quantum physics. When coupling is strong enough to prevail over decoherence, it can be used for the engineering of correlated quantum states. Especially for solid-state systems, control of quantum correlations has attracted widespread attention because of applications in quantum computing. Such coherent coupling has been demonstrated in a variety of systems at low temperature1, 2. Of all quantum systems, spins are potentially the most important, because they offer very long phase memories, sometimes even at room temperature. Although precise control of spins is well established in conventional magnetic resonance3, 4, existing techniques usually do not allow the readout of single spins because of limited sensitivity. In this paper, we explore dipolar magnetic coupling between two single defects in diamond (nitrogen-vacancy and nitrogen) using optical readout of the single nitrogen-vacancy spin states. Long phase memory combined with a defect separation of a few lattice spacings allow us to explore the strong magnetic coupling regime. As the two-defect system was well-isolated from other defects, the long phase memory times of the single spins was not diminished, despite the fact that dipolar interactions are usually seen as undesirable sources of decoherence. A coherent superposition of spin pair quantum states was achieved. The dipolar coupling was used to transfer spin polarisation from a nitrogen-vacancy centre spin to a nitrogen spin, with optical pumping of a nitrogen-vacancy centre leading to efficient initialisation. At the level anticrossing efficient nuclear spin polarisation was achieved. Our results demonstrate an important step towards controlled spin coupling and multi-particle entanglement in the solid state.
We present an example of quantum process tomography (QPT) performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the chi matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted. The results of QPT performed after three different decoherence times are used to find the error generators, or Lindblad operators, for the system, using the technique introduced by Boulant et al. [N. Boulant, T.F. Havel, M.A. Pravia and D.G. Cory, Phys. Rev. A 67, 042322 (2003)].
We study the electrical transport of a harmonically-bound, single-molecule endohedral fullerene shuttle operating in the Coulomb blockade regime, i.e. single electron shuttling. In particular we examine the dependance of the tunnel current on an ultra-small stationary force exerted on the shuttle. We derive a quantum master equation for the full shuttle system which includes the metallic contacts, the spatially dependent tunnel couplings to the shuttle, the electronic and motional degrees of freedom of the shuttle itself and a coupling of the shuttle's motion to a phonon bath. We analyse the resulting quantum master equation and find that, due to the exponential dependance of the tunnel probability on the shuttle-contact separation, the current is highly sensitive to very small forces. In particular we predict that the spin state of the endohedral electrons of the endohedral fullerene in a large magnetic gradient field can be distinguished from the resulting current signals within a few tens of nanoseconds. This effect could prove useful for the detection of the endohedral spin-state of individual paramagnetic molecules such as N@C60 and P@C60, or the detection of very small static forces acting on a molecular shuttle.
We study the dynamics of a single excitation in an infinite XXZ spin chain, which is launched from the origin. We study the time evolution of the spread of entanglement in the spin chain and obtain an expression for the second order spatial moment of concurrence, about the origin, for both ordered and disordered chains. In this way, we show that a finite central disordered region can lead to sustained superballistic growth in the second order spatial moment of entanglement within the chain.
We present a qutrit quantum computer design using trapped ions in the presence of a magnetic field gradient. The magnetic field gradient induces a "spin-spin" type coupling, similar to the J-coupling observed in molecules, between the qutrits which allows conditional quantum logic to take place. We describe in some detail, how one can execute specific one and two qutrit quantum gates, required for universal qutrit quantum computing.
We present an example of quantum process tomography performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the $χ$ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted.
Composite pulse sequences designed for nuclear magnetic resonance experiments are currently being applied in many quantum information processing technologies.We present an analysis of a family of composite pulse sequences used to address systematic pulse-length errors in the execution of quantum gates. It has been demonstrated by Cummins et al. [Phys. Rev. A 67, 042308 (2003)] that for this family of composite pulse sequences, the fidelity of the resulting unitary operation compared with the ideal unitary operation is 1+C*epsilon^6, where epsilon is the fractional error in the length of the pulse. We derive an exact expression for the 6th order coefficient, C, and from this deduce conditions under which this 6th order dependance is observed. We also present new pulse sequences which achieve the same fidelity.
The readout of the quantum spin state is a challenge for any spin-based quantum computing implementation. We propose a scheme, based on the achieved technique of single electron transistor (SET), to implement the readout of electronic spin state inside a doped $C_{60}$ fullerene by means of the magnetic dipole-dipole coupling and spin filters. In the presence of an external magnetic field, we show how to perform the spin state detection by transforming the information contained in the spin state into the tunneling current. The robustness of our scheme against sources of error is discussed.
We propose two potentially practical schemes to carry out two-qubit quantum gates on endohedral fullerenes $N@C_{60}$ or $P@C_{60}$. The qubits are stored in electronic spin degrees of freedom of the doped atom $N$ or $P$. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate and the two-qubit conditional phase gate are performed by selective microwave pulses assisted by refocusing technique. We will discuss the necessary additional steps for the universality of our proposal. We will also show that our proposal is useful for both quantum gating and the readout of quantum information from the spin-based qubit state.
We propose a new design for a quantum information processor where qubits are encoded into Hyperfine states of ions held in a linear array of individually tailored microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single and multi-qubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the microtrap configurations we can tailor, in hardware, the qubit resonance frequencies and coupling strengths. We show the system possesses a side-band transition structure which does not scale with the size of the processor allowing scalable frequency discrimination between qubits. By using large magnetic field gradients, one can readout and reset the qubits in the ion chain via frequency selective optical pulses avoiding the need for many tightly focused laser beams for spatial qubit addressing.
We propose an efficient procedure for numerically evolving the Delta Kicked Harmonic Oscillator. The method allows for longer and more accurate simulations of the system as well as a simple procedure for calculating the systems Floquet eigenstates and quasi-energies. The method is used to examine the dynamical behaviour of the system in cases where the ratio of the kicking frequency to the systems natural frequency is both rational and irrational.
We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of Group V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a Hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state $S=3/2$. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automata is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum celluar automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automata operation and obtain a rough figure of merit for the the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes towards meeting the fifth criteria: qubit readout.
We examine the dynamics of a qubit stored in the motional degrees of freedom of an ultra-cold ion in an ion trap which is subject to the decoherence effects of a finite-temperature bath. We discover an encoding of the qubit, in two of the motional modes of the ion, which is stable against the occurrence of either none or one quantum jump. For the case of a zero-temperature bath we describe how to transfer only the information concerning the occurrence of quantum jumps and their types to a measuring apparatus, without affecting the ion's motional state significantly. We then describe how to generate a unitary restoration of the qubit given the jump information, through Raman processes generated by a series of laser pulses.
We describe how two vibrational degrees of freedom of a single trapped ion can be coupled through the action of suitably-chosen laser excitation. We concentrate on a two-dimensional ion trap with dissimilar vibrational frequencies in the x- and y-directions of motion, and derive from first principles a variety of quantized two-mode couplings, concentrating on a linear coupling which takes excitations from one mode to another. We demonstrate how this can result in a state rotation, in which it is possible to transfer the motional state of the ion from say the x-direction to the y-direction without prior knowledge of that motional state.
We quantise the centre of mass motion of a neutral Cs atom in the presence of a classical Gaussian-Laguerre$_{10}$ light field in the large detuning limit. This light field possesses orbital angular momentum which is transferred to the atom via spontaneous emissions. We use quantum trajectory and analytic methods to solve the master equation for the 2d centre of mass motion with recoil near the centre of the beam. For appropriate parameters, we observe heating in both the cartesian and polar observables within a few orbits of the atom in the beam. The angular momentum, $\hat{L}$, shows a rapid diffusion which results in $<\hat{L}>$ reaching a maximum and then decreasing to zero. We compare this with analytic results obtained for an atom illuminated by a superposition of Gaussian-Laguerre modes which possess no angular momentum, in the limit of no recoil.
For quantum systems with two dimensional configuration space we construct a physical radial momentum observable. Rescaling the radius we find the dilatonic degrees of freedom form a Weyl algebra. With this we construct the radial Wigner quasi-probability distribution function.