Avoiding Quantum Chaos in Quantum Computation

We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supportingComment: RevTex, 5 pages including 3 eps-figure

Quantum Bit Regeneration

Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error caused by loss (amplitude damping to a reservoir at T=0), based on using a dual-rail representation of a quantum bit. This is possible because (1) balanced loss does not perform a ``which-path'' measurement in an interferometer, and (2) balanced quantum nondemolition measurement of the ``total'' photon number can be used to detect loss-induced quantum jumps without disturbing the quantum coherence essential to the quantum bit. Our results are immediately applicable to optical quantum computers using single photonics devices.Comment: 4 pages, postscript only, figures available at http://feynman.stanford.edu/qcom

Defect Formation in Quench-Cooled Superfluid Phase Transition

We use neutron absorption in rotating 3He-B to heat locally a 10 micrometer-size volume into normal phase. When the heated region cools back in microseconds, vortex lines are formed. We record with NMR the number of lines as a function of superflow velocity and compare to the Kibble-Zurek theory of vortex-loop freeze-out from a random network of defects. The measurements confirm the calculated loop-size distribution and show that also the superfluid state itself forms as a patchwork of competing A and B phase blobs. This explains the A to B transition in supercooled neutron-irradiated 3He-A.Comment: RevTex file, 4 pages, 3 figures, resubmitted to Phys. Rev. Let

Polarization state of a biphoton: quantum ternary logic

Polarization state of biphoton light generated via collinear frequency-degenerate spontaneous parametric down-conversion is considered. A biphoton is described by a three-component polarization vector, its arbitrary transformations relating to the SU(3) group. A subset of such transformations, available with retardation plates, is realized experimentally. In particular, two independent orthogonally polarized beams of type-I biphotons are transformed into a beam of type-II biphotons. Polarized biphotons are suggested as ternary analogs of two-state quantum systems (qubits)

Quantum Process Tomography: Resource Analysis of Different Strategies

Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum information science. Several methods are known which achieve this goal, namely Standard Quantum Process Tomography (SQPT), Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of Direct Characterization of Quantum Dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known QPT schemes in terms of the total number of required elementary quantum operations.Comment: 15 pages, 5 figures, published versio

Density of Bloch Waves after a Quench

Production of Bloch waves during a rapid quench is studied by analytical and numerical methods. The density of Bloch waves decays exponentially with the quench time. It also strongly depends on temperature. Very few textures are produced for temperatures lower than a characteristic temperature proportional to the square of the magnetic field.Comment: 4 pages in RevTex + 3 .ps files; improved presentation; version to appear in PR

Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow

We report the observation of vortex formation upon the absorption of a thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the superfluid into the normal phase. The subsequent cooling of this region back through the superfluid transition results in the nucleation of quantized vortices. Depending on the superflow velocity, sufficiently large vortex rings grow under the influence of the Magnus force and escape into the container volume where they are detected individually with nuclear magnetic resonance. The larger the superflow velocity the smaller the rings which can expand. Thus it is possible to obtain information about the morphology of the initial defect network. We suggest that the nucleation of vortices during the rapid cool-down into the superfluid phase is similar to the formation of defects during cosmological phase transitions in the early universe.Comment: 4 pages, LaTeX file, 4 figures are available at ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-95009.p

Factoring in a Dissipative Quantum Computer

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.Comment: plain tex, 18 pages, 8 postscript figure

Density of kinks just after a quench in an overdamped system

A quench in an overdamped one dimensional $\phi^4$ model is studied by analytical and numerical methods. For an infinite system or a finite system with free boundary conditions, the density of kinks after the transition is proportional to the eighth root of the rate of the quench. For a system with periodic boundary conditions, it is proportional to the fourth root of the rate. The critical exponent predicted in Zurek scenario is put in question.Comment: 4 pages in RevTex + 1 .ps fil

Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping

We show how macroscopically distinct quantum superposition states (Schroedinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors. Spontaneous emission causes a bit flip error which is easily corrected by a standard error correction circuit. The method works arbitrarily well as the distance between the amplitudes of the superposed coherent states increases.Comment: 4 pages, 2 postscript figures, LaTeX2e, RevTeX, minor changes, 1 reference adde