Schemes for Parallel Quantum Computation Without Local Control of Qubits

Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating 'types' of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state 1 minus the number in state 2. Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions are suitable: we highlight two potential implementations.Comment: 12 pages + 3 figures. Several small corrections mad

Scalability of Shor's algorithm with a limited set of rotation gates

Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $\pi/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing fault-tolerant techniques. Approximating a given controlled $\pi/2^{d}$ rotation gate to within $\delta=O(1/2^{d})$ currently requires both a number of qubits and number of fault-tolerant gates that grows polynomially with $d$. In this paper we show that this additional growth in space and time complexity would severely limit the applicability of Shor's algorithm to large integers. Consequently, we study in detail the effect of using only controlled rotation gates with $d$ less than or equal to some $d_{\rm max}$. It is found that integers up to length $L_{\rm max} = O(4^{d_{\rm max}})$ can be factored without significant performance penalty implying that the cumbersome techniques of fault-tolerant computation only need to be used to create controlled rotation gates of magnitude $\pi/64$ if integers thousands of bits long are desired factored. Explicit fault-tolerant constructions of such gates are also discussed.Comment: Substantially revised version, twice as long as original. Two tables converted into one 8-part figure, new section added on the construction of arbitrary single-qubit rotations using only the fault-tolerant gate set. Substantial additional discussion and explanatory figures added throughout. (8 pages, 6 figures

Superfast Cooling

Currently laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong coupling regime which then allows cooling rates that are faster than the trap frequency with state of the art experimental parameters. The scheme we present can work for trapped atoms or ions as well as mechanical oscillators. It can also cool medium size ions chains close to the ground state.Comment: 5 pages 4 figure

Security of Quantum Key Distribution with Coherent States and Homodyne Detection

We assess the security of a quantum key distribution protocol relying on the transmission of Gaussian-modulated coherent states and homodyne detection. This protocol is shown to be equivalent to a squeezed state protocol based on a CSS code construction, and is thus provably secure against any eavesdropping strategy. We also briefly show how this protocol can be generalized in order to improve the net key rate.Comment: 7 page

Decoherence of geometric phase gates

We consider the effects of certain forms of decoherence applied to both adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit we illustrate path-dependent sensitivity to anisotropic noise and for two qubits we quantify the loss of entanglement as a function of decoherence.Comment: 4 pages, 3 figure

Quantum Convolutional Error Correction Codes

I report two general methods to construct quantum convolutional codes for quantum registers with internal $N$ states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general quantum error for every eight consecutive quantum registers.Comment: To be reported in the 1st NASA Conf. on Quantum Comp., uses llncs.sty, 12 page

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.Comment: 5 pages, 4 figures, RevTe

Determination of the phase of an electromagnetic field via incoherent detection of fluorescence

We show that the phase of a field can be determined by incoherent detection of the population of one state of a two-level system if the Rabi frequency is comparable to the Bohr frequency so that the rotating wave approximation is inappropriate. This implies that a process employing the measurement of population is not a square-law detector in this limit. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-frequency transitions. We present a scheme for observing this effect in an atomic beam, despite the spread in the interaction time.Comment: 4 pages, 2 fig

Scalable simultaneous multi-qubit readout with 99.99% single-shot fidelity

We describe single-shot readout of a trapped-ion multi-qubit register using space and time-resolved camera detection. For a single qubit we measure 0.9(3)x10^{-4} readout error in 400us exposure time, limited by the qubit's decay lifetime. For a four-qubit register (a "qunybble") we measure an additional error of only 0.1(1)x10^{-4} per qubit, despite the presence of 4% optical cross-talk between neighbouring qubits. A study of the cross-talk indicates that the method would scale with negligible loss of fidelity to ~10000 qubits at a density <~1 qubit/um^2, with a readout time ~1us/qubit.Comment: 4 pages, 3 figures; simulations added to fig.3, with some further text and figure revisions. Main results unchanged

Atomic density and temperature distributions in magneto-optical traps

A theoretical investigation into density, pressure, and temperature distributions in magneto-optical traps is presented. After a brief overview of the forces that arise from reradiation and absorption, a condition that the absorptive force be conservative is used to show that, if the temperature is uniform throughout the trap, any. density solutions to the force equations will not be physical. Further, consistent density solutions are unlikely to exist at all. In contrast, with a varying temperature reasonable solutions are demonstrated, with some restrictions. Doppler forces involved in ring-shaped trap structures are used to calculate orbit radii in racetrack geometry traps, and corrections to the present discrepancy between theoretical and experimental studies are discussed in the context of reradiation and diffusion