6,560 research outputs found
Minimization of Quantum Circuits using Quantum Operator Forms
In this paper we present a method for minimizing reversible quantum circuits
using the Quantum Operator Form (QOF); a new representation of quantum circuit
and of quantum-realized reversible circuits based on the CNOT, CV and
CV quantum gates. The proposed form is a quantum extension to the
well known Reed-Muller but unlike the Reed-Muller form, the QOF allows the
usage of different quantum gates. Therefore QOF permits minimization of quantum
circuits by using properties of different gates than only the multi-control
Toffoli gates. We introduce a set of minimization rules and a pseudo-algorithm
that can be used to design circuits with the CNOT, CV and CV quantum
gates. We show how the QOF can be used to minimize reversible quantum circuits
and how the rules allow to obtain exact realizations using the above mentioned
quantum gates.Comment: 11 pages, 14 figures, Proceedings of the ULSI Workshop 2012 (@ISMVL
2012
A Study of Optimal 4-bit Reversible Toffoli Circuits and Their Synthesis
Optimal synthesis of reversible functions is a non-trivial problem. One of
the major limiting factors in computing such circuits is the sheer number of
reversible functions. Even restricting synthesis to 4-bit reversible functions
results in a huge search space (16! {\approx} 2^{44} functions). The output of
such a search alone, counting only the space required to list Toffoli gates for
every function, would require over 100 terabytes of storage. In this paper, we
present two algorithms: one, that synthesizes an optimal circuit for any 4-bit
reversible specification, and another that synthesizes all optimal
implementations. We employ several techniques to make the problem tractable. We
report results from several experiments, including synthesis of all optimal
4-bit permutations, synthesis of random 4-bit permutations, optimal synthesis
of all 4-bit linear reversible circuits, synthesis of existing benchmark
functions; we compose a list of the hardest permutations to synthesize, and
show distribution of optimal circuits. We further illustrate that our proposed
approach may be extended to accommodate physical constraints via reporting
LNN-optimal reversible circuits. Our results have important implications in the
design and optimization of reversible and quantum circuits, testing circuit
synthesis heuristics, and performing experiments in the area of quantum
information processing.Comment: arXiv admin note: substantial text overlap with arXiv:1003.191
HDL-based Synthesis of Reversible Circuits : A Scalable Design Approach
Reversible computing is a promising research field due to its applications in several emerging technologies. Accordingly, several approaches for the design of reversible circuits have been introduced. Hardware Description Languages approach scales better than other methodologies, however, its main drawback is substantial amounts of additional circuit lines. This dissertation is an important step towards an elaborated scalable design flow of reversible circuits. In which, HDL-based design of reversible circuit is optimised, with line-awareness considered as the main objective. A line-aware programming style for a dedicated reversible hardware description language SyReC is proposed. Another contribution is a line-aware computation of HDL expressions. Reversible circuits' synthesis from a conventional hardware description language (VHDL) is examined. Finally, syntactical extensions to the dedicated hardware description language SyReC are suggested
Automated Synthesis of Quantum Subcircuits
The quantum computer has become contemporary reality, with the first
two-qubit machine of mere decades ago transforming into cloud-accessible
devices with tens, hundreds, or--in a few cases--even thousands of qubits.
While such hardware is noisy and still relatively small, the increasing number
of operable qubits raises another challenge: how to develop the now-sizeable
quantum circuits executable on these machines. Preparing circuits manually for
specifications of any meaningful size is at best tedious and at worst
impossible, creating a need for automation. This article describes an automated
quantum-software toolkit for synthesis, compilation, and optimization, which
transforms classically-specified, irreversible functions to both
technology-independent and technology-dependent quantum circuits. We also
describe and analyze the toolkit's application to three situations--quantum
read-only memories, quantum random number generators, and quantum oracles--and
illustrate the toolkit's start-to-finish features from the input of classical
functions to the output of quantum circuits ready-to-run on commercial
hardware. Furthermore, we illustrate how the toolkit enables research beyond
circuit synthesis, including comparison of synthesis and optimization methods
and deeper understanding of even well-studied quantum algorithms. As quantum
hardware continues to develop, such quantum circuit toolkits will play a
critical role in realizing its potential.Comment: 49 pages, 25 figures, 20 table
DDMF: An Efficient Decision Diagram Structure for Design Verification of Quantum Circuits under a Practical Restriction
Recently much attention has been paid to quantum circuit design to prepare
for the future "quantum computation era." Like the conventional logic
synthesis, it should be important to verify and analyze the functionalities of
generated quantum circuits. For that purpose, we propose an efficient
verification method for quantum circuits under a practical restriction. Thanks
to the restriction, we can introduce an efficient verification scheme based on
decision diagrams called
Decision Diagrams for Matrix Functions (DDMFs). Then, we show analytically
the advantages of our approach based on DDMFs over the previous verification
techniques. In order to introduce DDMFs, we also introduce new concepts,
quantum functions and matrix functions, which may also be interesting and
useful on their own for designing quantum circuits.Comment: 15 pages, 14 figures, to appear IEICE Trans. Fundamentals, Vol.
E91-A, No.1
Toward an architecture for quantum programming
It is becoming increasingly clear that, if a useful device for quantum
computation will ever be built, it will be embodied by a classical computing
machine with control over a truly quantum subsystem, this apparatus performing
a mixture of classical and quantum computation.
This paper investigates a possible approach to the problem of programming
such machines: a template high level quantum language is presented which
complements a generic general purpose classical language with a set of quantum
primitives. The underlying scheme involves a run-time environment which
calculates the byte-code for the quantum operations and pipes it to a quantum
device controller or to a simulator.
This language can compactly express existing quantum algorithms and reduce
them to sequences of elementary operations; it also easily lends itself to
automatic, hardware independent, circuit simplification. A publicly available
preliminary implementation of the proposed ideas has been realized using the
C++ language.Comment: 23 pages, 5 figures, A4paper. Final version accepted by EJPD ("swap"
replaced by "invert" for Qops). Preliminary implementation available at:
http://sra.itc.it/people/serafini/quantum-computing/qlang.htm
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