1,405 research outputs found
Optimal ancilla-free Clifford+T approximation of z-rotations
We consider the problem of approximating arbitrary single-qubit z-rotations
by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new
probabilistic algorithm for solving this problem optimally, i.e., for finding
the shortest possible circuit whatsoever for the given problem instance. The
algorithm requires a factoring oracle (such as a quantum computer). Even in the
absence of a factoring oracle, the algorithm is still near-optimal under a mild
number-theoretic hypothesis. In this case, the algorithm finds a solution of
T-count m + O(log(log(1/epsilon))), where m is the T-count of the
second-to-optimal solution. In the typical case, this yields circuit
approximations of T-count 3log_2(1/epsilon) + O(log(log(1/epsilon))). Our
algorithm is efficient in practice, and provably efficient under the
above-mentioned number-theoretic hypothesis, in the sense that its expected
runtime is O(polylog(1/epsilon)).Comment: 40 pages. New in v3: added a section on worst-case behavio
Graphical Methods in Device-Independent Quantum Cryptography
We introduce a framework for graphical security proofs in device-independent
quantum cryptography using the methods of categorical quantum mechanics. We are
optimistic that this approach will make some of the highly complex proofs in
quantum cryptography more accessible, facilitate the discovery of new proofs,
and enable automated proof verification. As an example of our framework, we
reprove a previous result from device-independent quantum cryptography: any
linear randomness expansion protocol can be converted into an unbounded
randomness expansion protocol. We give a graphical proof of this result, and
implement part of it in the Globular proof assistant.Comment: Publishable version. Diagrams have been polished, minor revisions to
the text, and an appendix added with supplementary proof
An Intelligent Fuse-box for use with Renewable Energy Sources integrated within a Domestic Environment
This paper outlines a proposal for an intelligent fuse-box that can replace existing fuse-boxes in a domestic context such that a number of renewable energy sources can easily be integrated into the domestic power supply network, without the necessity for complex islanding and network protection. The approach allows intelligent control of both the generation of power and its supply to single or groups of electrical appliances. Energy storage can be implemented in such a scheme to even out the power supplied and simplify the control scheme required, and environmental monitoring and load analysis can help in automatically controlling the supply and demand profiles for optimum electrical and economic efficiency. Simulations of typical scenarios are carried out to illustrate the concept in operation
A Biset-Enriched Categorical Model for Proto-Quipper with Dynamic Lifting
Quipper and Proto-Quipper are a family of quantum programming languages that,
by their nature as circuit description languages, involve two runtimes: one at
which the program generates a circuit and one at which the circuit is executed,
normally with probabilistic results due to measurements. Accordingly, the
language distinguishes two kinds of data: parameters, which are known at
circuit generation time, and states, which are known at circuit execution time.
Sometimes, it is desirable for the results of measurements to control the
generation of the next part of the circuit. Therefore, the language needs to
turn states, such as measurement outcomes, into parameters, an operation we
call dynamic lifting. The goal of this paper is to model this interaction
between the runtimes by providing a general categorical structure enriched in
what we call "bisets". We demonstrate that the biset-enriched structure
achieves a proper semantics of the two runtimes and their interaction, by
showing that it models a variant of Proto-Quipper with dynamic lifting. The
present paper deals with the concrete categorical semantics of this language,
whereas a companion paper deals with the syntax, type system, operational
semantics, and abstract categorical semantics.Comment: In Proceedings QPL 2022, arXiv:2311.0837
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