113,381 research outputs found
Monte Carlo sampling from the quantum state space. I
High-quality random samples of quantum states are needed for a variety of
tasks in quantum information and quantum computation. Searching the
high-dimensional quantum state space for a global maximum of an objective
function with many local maxima or evaluating an integral over a region in the
quantum state space are but two exemplary applications of many. These tasks can
only be performed reliably and efficiently with Monte Carlo methods, which
involve good samplings of the parameter space in accordance with the relevant
target distribution. We show how the standard strategies of rejection sampling,
importance sampling, and Markov-chain sampling can be adapted to this context,
where the samples must obey the constraints imposed by the positivity of the
statistical operator. For a comparison of these sampling methods, we generate
sample points in the probability space for two-qubit states probed with a
tomographically incomplete measurement, and then use the sample for the
calculation of the size and credibility of the recently-introduced optimal
error regions [see New J. Phys. 15 (2013) 123026]. Another illustration is the
computation of the fractional volume of separable two-qubit states.Comment: 13 pages, 5 figures, 1 table, 26 reference
Computational capacity of the universe
Merely by existing, all physical systems register information. And by
evolving dynamically in time, they transform and process that information. The
laws of physics determine the amount of information that a physical system can
register (number of bits) and the number of elementary logic operations that a
system can perform (number of ops). The universe is a physical system. This
paper quantifies the amount of information that the universe can register and
the number of elementary operations that it can have performed over its
history. The universe can have performed no more than ops on
bits.Comment: 17 pages, TeX. submitted to Natur
Climbing Mount Scalable: Physical-Resource Requirements for a Scalable Quantum Computer
The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the effective number of degrees of freedom
in the computer must grow nearly linearly with the number of qubits in an
equivalent qubit-based quantum computer.Comment: LATEX, 24 pages, 1 color .eps figure. This new version has been
accepted for publication in Foundations of Physic
Physical-resource demands for scalable quantum computation
The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the number of degrees of freedom in the
computer must grow nearly linearly with the number of qubits in an equivalent
qubit-based quantum computer.Comment: This paper will be published in the proceedings of the SPIE
Conference on Fluctuations and Noise in Photonics and Quantum Optics, Santa
Fe, New Mexico, June 1--4, 200
Synthesis of Topological Quantum Circuits
Topological quantum computing has recently proven itself to be a very
powerful model when considering large- scale, fully error corrected quantum
architectures. In addition to its robust nature under hardware errors, it is a
software driven method of error corrected computation, with the hardware
responsible for only creating a generic quantum resource (the topological
lattice). Computation in this scheme is achieved by the geometric manipulation
of holes (defects) within the lattice. Interactions between logical qubits
(quantum gate operations) are implemented by using particular arrangements of
the defects, such as braids and junctions. We demonstrate that junction-based
topological quantum gates allow highly regular and structured implementation of
large CNOT (controlled-not) gate networks, which ultimately form the basis of
the error corrected primitives that must be used for an error corrected
algorithm. We present a number of heuristics to optimise the area of the
resulting structures and therefore the number of the required hardware
resources.Comment: 7 Pages, 10 Figures, 1 Tabl
Quantum Bounded Query Complexity
We combine the classical notions and techniques for bounded query classes
with those developed in quantum computing. We give strong evidence that quantum
queries to an oracle in the class NP does indeed reduce the query complexity of
decision problems. Under traditional complexity assumptions, we obtain an
exponential speedup between the quantum and the classical query complexity of
function classes.
For decision problems and function classes we obtain the following results: o
P_||^NP[2k] is included in EQP_||^NP[k] o P_||^NP[2^(k+1)-2] is included in
EQP^NP[k] o FP_||^NP[2^(k+1)-2] is included in FEQP^NP[2k] o FP_||^NP is
included in FEQP^NP[O(log n)] For sets A that are many-one complete for PSPACE
or EXP we show that FP^A is included in FEQP^A[1]. Sets A that are many-one
complete for PP have the property that FP_||^A is included in FEQP^A[1]. In
general we prove that for any set A there is a set X such that FP^A is included
in FEQP^X[1], establishing that no set is superterse in the quantum setting.Comment: 11 pages LaTeX2e, no figures, accepted for CoCo'9
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