Quantum Analogue Computing

We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data is encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data is encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous variable quantum computers (CVQC) becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.Comment: 10 pages, to appear in the Visions 2010 issue of Phil. Trans. Roy. Soc.

On the error statistics of Viterbi decoding and the performance of concatenated codes

Computer simulation results are presented on the performance of convolutional codes of constraint lengths 7 and 10 concatenated with the (255, 223) Reed-Solomon code (a proposed NASA standard). These results indicate that as much as 0.8 dB can be gained by concatenating this Reed-Solomon code with a (10, 1/3) convolutional code, instead of the (7, 1/2) code currently used by the DSN. A mathematical model of Viterbi decoder burst-error statistics is developed and is validated through additional computer simulations

Single Shot Quantum State Estimation via a Continuous Measurement in the Strong Backaction Regime

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a nonnegligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem -- state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal POVM. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.Comment: 10 pages, 5 epic figure

Clifford algebras and universal sets of quantum gates

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR

Mechanism for nonequilibrium symmetry breaking and pattern formation in magnetic films

Magnetic thin films exhibit a strong variation in properties depending on their degree of disorder. Recent coherent x-ray speckle experiments on magnetic films have measured the loss of correlation between configurations at opposite fields and at the same field, upon repeated field cycling. We perform finite temperature numerical simulations on these systems that provide a comprehensive explanation for the experimental results. The simulations demonstrate, in accordance with experiments, that the memory of configurations increases with film disorder. We find that non-trivial microscopic differences exist between the zero field spin configuration obtained by starting from a large positive field and the zero field configuration starting at a large negative field. This seemingly paradoxical beahvior is due to the nature of the vector spin dynamics and is also seen in the experiments. For low disorder, there is an instability which causes the spontaneous growth of line-like domains at a critical field, also in accord with experiments. It is this unstable growth, which is highly sensitive to thermal noise, that is responsible for the small correlation between patterns under repeated cycling. The domain patterns, hysteresis loops, and memory properties of our simulated systems match remarkably well with the real experimental systems.Comment: 12 pages, 10 figures Added comparison of results with cond-mat/0412461 and some more discussio

Efficient Scheme for Initializing a Quantum Register with an Arbitrary Superposed State

Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as |i_1 i_2 ... i_n\ket with $i_j$ being either 0 or 1, but is a non-trivial task to construct an {\it arbitrary} superposed quantum state. In this Paper, we present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires $O(Nn^2)$ standard 1- and 2-bit gate operations, {\it without introducing additional quantum bits}. Application of the scheme in some special cases is discussed.Comment: 4 pages, 4 figures, accepted by Phys. Rev.

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates

Unsolvability of the Halting Problem in Quantum Dynamics

It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider the case when the observer's reference frame is the system that is to be evolved in both pictures. We then show that in order to include the evolution of observer's reference frame in a physically sensible way, the Heisenberg picture with time going backwards yields a correct description.Comment: 4 pages, 3 figure

Time-Resolved Ultraviolet Observations of the Globular Cluster X-ray Source in NGC 6624: The Shortest Known Period Binary System

Using the Faint Object Spectrograph (FOS) aboard the Hubble Space Telescope, we have obtained the first time-resolved spectra of the King et al. ultraviolet-bright counterpart to the 11-minute binary X-ray source in the core of the globular cluster NGC 6624. This object cannot be readily observed in the visible, even from HST, due to a much brighter star superposed <0.1'' distant. Our FOS data show a highly statistically significant UV flux modulation with a period of 11.46+-0.04 min, very similar to the 685 sec period of the known X-ray modulation, definitively confirming the association between the King et al. UV counterpart and the intense X-ray source. The UV amplitude is very large compared with the observed X-ray oscillations: X-ray variations are generally reported as 2-3% peak-to-peak, whereas our data show an amplitude of about 16% in the 126-251 nm range. A model for the system by Arons & King predicts periodic UV fluctuations in this shortest-known period binary system, due to the cyclically changing aspect of the X-ray heated face of the secondary star (perhaps a very low mass helium degenerate). However, prior to our observations, this predicted modulation has not been detected. Employing the Arons & King formalism, which invokes a number of different physical assumptions, we infer a system orbital inclination 35deg<i<50 deg. Amongst the three best-studied UV/optical counterparts to the intense globular cluster X-ray sources, two are now thought to consist of exotic double-degenerate ultrashort period binary systems.Comment: 10 pages including 2 figures in Latex (AASTeX 4.0). Accepted for publication in vol. 482 (1997 June 10 issue) of The Astrophysical Journal (Letters

Rapid solution of problems by nuclear-magnetic-resonance quantum computation

We offer an improved method for using a nuclear-magnetic-resonance quantum computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the application of the NMRQC are exponential diminishment of density-matrix elements with the number of bits, threatening weak signal levels, and the high cost of preparing a suitable starting state. A third obstacle is a heretofore unnoticed restriction on measurement operators available for use by an NMRQC. Variations on the function classes of the Deutsch-Jozsa problem are introduced, both to extend the range of problems advantageous for quantum computation and to escape all three obstacles to use of an NMRQC. By adapting it to one such function class, the Deutsch-Jozsa problem is made solvable without exponential loss of signal. The method involves an extra work bit and a polynomially more involved Oracle; it uses the thermal-equilibrium density matrix systematically for an arbitrary number of spins, thereby avoiding both the preparation of a pseudopure state and temporal averaging.Comment: 19 page