3,091 research outputs found
Generating reversible circuits from higher-order functional programs
Boolean reversible circuits are boolean circuits made of reversible
elementary gates. Despite their constrained form, they can simulate any boolean
function. The synthesis and validation of a reversible circuit simulating a
given function is a difficult problem. In 1973, Bennett proposed to generate
reversible circuits from traces of execution of Turing machines. In this paper,
we propose a novel presentation of this approach, adapted to higher-order
programs. Starting with a PCF-like language, we use a monadic representation of
the trace of execution to turn a regular boolean program into a
circuit-generating code. We show that a circuit traced out of a program
computes the same boolean function as the original program. This technique has
been successfully applied to generate large oracles with the quantum
programming language Quipper.Comment: 21 pages. A shorter preprint has been accepted for publication in the
Proceedings of Reversible Computation 2016. The final publication is
available at http://link.springer.co
Quantum Computing with Very Noisy Devices
In theory, quantum computers can efficiently simulate quantum physics, factor
large numbers and estimate integrals, thus solving otherwise intractable
computational problems. In practice, quantum computers must operate with noisy
devices called ``gates'' that tend to destroy the fragile quantum states needed
for computation. The goal of fault-tolerant quantum computing is to compute
accurately even when gates have a high probability of error each time they are
used. Here we give evidence that accurate quantum computing is possible with
error probabilities above 3% per gate, which is significantly higher than what
was previously thought possible. However, the resources required for computing
at such high error probabilities are excessive. Fortunately, they decrease
rapidly with decreasing error probabilities. If we had quantum resources
comparable to the considerable resources available in today's digital
computers, we could implement non-trivial quantum computations at error
probabilities as high as 1% per gate.Comment: 47 page
The Significance of the -Numerical Range and the Local -Numerical Range in Quantum Control and Quantum Information
This paper shows how C-numerical-range related new strucures may arise from
practical problems in quantum control--and vice versa, how an understanding of
these structures helps to tackle hot topics in quantum information.
We start out with an overview on the role of C-numerical ranges in current
research problems in quantum theory: the quantum mechanical task of maximising
the projection of a point on the unitary orbit of an initial state onto a
target state C relates to the C-numerical radius of A via maximising the trace
function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one
may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii)
in restricting the dynamics to {\em local} operations on each qubit, i.e. to
the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2).
Interestingly, the latter then leads to a novel entity, the {\em local}
C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither
star-shaped nor simply connected in contrast to the conventional C-numerical
range. This is shown in the accompanying paper (math-ph/0702005).
We present novel applications of the C-numerical range in quantum control
assisted by gradient flows on the local unitary group: (1) they serve as
powerful tools for deciding whether a quantum interaction can be inverted in
time (in a sense generalising Hahn's famous spin echo); (2) they allow for
optimising witnesses of quantum entanglement. We conclude by relating the
relative C-numerical range to problems of constrained quantum optimisation, for
which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200
Realisation of a programmable two-qubit quantum processor
The universal quantum computer is a device capable of simulating any physical
system and represents a major goal for the field of quantum information
science. Algorithms performed on such a device are predicted to offer
significant gains for some important computational tasks. In the context of
quantum information, "universal" refers to the ability to perform arbitrary
unitary transformations in the system's computational space. The combination of
arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate is
a gate set capable of achieving universal control of any number of qubits,
provided that these gates can be performed repeatedly and between arbitrary
pairs of qubits. Although gate sets have been demonstrated in several
technologies, they have as yet been tailored toward specific tasks, forming a
small subset of all unitary operators. Here we demonstrate a programmable
quantum processor that realises arbitrary unitary transformations on two
qubits, which are stored in trapped atomic ions. Using quantum state and
process tomography, we characterise the fidelity of our implementation for 160
randomly chosen operations. This universal control is equivalent to simulating
any pairwise interaction between spin-1/2 systems. A programmable multi-qubit
register could form a core component of a large-scale quantum processor, and
the methods used here are suitable for such a device.Comment: 7 pages, 4 figure
Recognition of Face Identity and Emotion in Expressive Specific Language Impairment
Objective: To study face and emotion recognition in children with mostly expressive specific language impairment (SLI-E). Subjects and Methods: A test movie to study perception and recognition of faces and mimic-gestural expression was applied to 24 children diagnosed as suffering from SLI-E and an age-matched control group of normally developing children. Results: Compared to a normal control group, the SLI-E children scored significantly worse in both the face and expression recognition tasks with a preponderant effect on emotion recognition. The performance of the SLI-E group could not be explained by reduced attention during the test session. Conclusion: We conclude that SLI-E is associated with a deficiency in decoding non-verbal emotional facial and gestural information, which might lead to profound and persistent problems in social interaction and development. Copyright (C) 2012 S. Karger AG, Base
Digestibility in selected rainbow trout families and modelling of growth from the specific intake of digestible protein
The experiments aimed to clarify variations in digestibility of dietary nutrients in rainbow trout. Furthermore, the objective was to study how differences in digestibility might be related to growth and feed utilisation at various growth rates. When comparing the results from the experiments it appeared that particularly protein digestibility was closely related to specific growth rate and feed conversion ratio at high growth rates. As a tool to visualise the relationship between protein digestibility and growth of rainbow trout a growth model was developed based on the specific intake of digestible protein, and general assumptions on protein content and protein retention efficiency in rainbow trout. The model indicated that increased protein digestibility only partly explained growth increase and that additional factors were important for growth increment
Experimental realisation of Shor's quantum factoring algorithm using qubit recycling
Quantum computational algorithms exploit quantum mechanics to solve problems
exponentially faster than the best classical algorithms. Shor's quantum
algorithm for fast number factoring is a key example and the prime motivator in
the international effort to realise a quantum computer. However, due to the
substantial resource requirement, to date, there have been only four
small-scale demonstrations. Here we address this resource demand and
demonstrate a scalable version of Shor's algorithm in which the n qubit control
register is replaced by a single qubit that is recycled n times: the total
number of qubits is one third of that required in the standard protocol.
Encoding the work register in higher-dimensional states, we implement a
two-photon compiled algorithm to factor N=21. The algorithmic output is
distinguishable from noise, in contrast to previous demonstrations. These
results point to larger-scale implementations of Shor's algorithm by harnessing
scalable resource reductions applicable to all physical architectures.Comment: 7 pages, 3 figure
Adding control to arbitrary unknown quantum operations
While quantum computers promise significant advantages, the complexity of
quantum algorithms remains a major technological obstacle. We have developed
and demonstrated an architecture-independent technique that simplifies adding
control qubits to arbitrary quantum operations-a requirement in many quantum
algorithms, simulations and metrology. The technique is independent of how the
operation is done, does not require knowledge of what the operation is, and
largely separates the problems of how to implement a quantum operation in the
laboratory and how to add a control. We demonstrate an entanglement-based
version in a photonic system, realizing a range of different two-qubit gates
with high fidelity.Comment: 9 pages, 8 figure
Quantum Computation with Coherent Spin States and the Close Hadamard Problem
We study a model of quantum computation based on the
continuously-parameterized yet finite-dimensional Hilbert space of a spin
system. We explore the computational powers of this model by analyzing a pilot
problem we refer to as the close Hadamard problem. We prove that the close
Hadamard problem can be solved in the spin system model with arbitrarily small
error probability in a constant number of oracle queries. We conclude that this
model of quantum computation is suitable for solving certain types of problems.
The model is effective for problems where symmetries between the structure of
the information associated with the problem and the structure of the unitary
operators employed in the quantum algorithm can be exploited.Comment: RevTeX4, 13 pages with 8 figures. Accepted for publication in Quantum
Information Processing. Article number: s11128-015-1229-
On the experimental verification of quantum complexity in linear optics
The first quantum technologies to solve computational problems that are
beyond the capabilities of classical computers are likely to be devices that
exploit characteristics inherent to a particular physical system, to tackle a
bespoke problem suited to those characteristics. Evidence implies that the
detection of ensembles of photons, which have propagated through a linear
optical circuit, is equivalent to sampling from a probability distribution that
is intractable to classical simulation. However, it is probable that the
complexity of this type of sampling problem means that its solution is
classically unverifiable within a feasible number of trials, and the task of
establishing correct operation becomes one of gathering sufficiently convincing
circumstantial evidence. Here, we develop scalable methods to experimentally
establish correct operation for this class of sampling algorithm, which we
implement with two different types of optical circuits for 3, 4, and 5 photons,
on Hilbert spaces of up to 50,000 dimensions. With only a small number of
trials, we establish a confidence >99% that we are not sampling from a uniform
distribution or a classical distribution, and we demonstrate a unitary specific
witness that functions robustly for small amounts of data. Like the algorithmic
operations they endorse, our methods exploit the characteristics native to the
quantum system in question. Here we observe and make an application of a
"bosonic clouding" phenomenon, interesting in its own right, where photons are
found in local groups of modes superposed across two locations. Our broad
approach is likely to be practical for all architectures for quantum
technologies where formal verification methods for quantum algorithms are
either intractable or unknown.Comment: Comments welcom
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