10,286 research outputs found
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Application of Permutation Group Theory in Reversible Logic Synthesis
The paper discusses various applications of permutation group theory in the
synthesis of reversible logic circuits consisting of Toffoli gates with
negative control lines. An asymptotically optimal synthesis algorithm for
circuits consisting of gates from the NCT library is described. An algorithm
for gate complexity reduction, based on equivalent replacements of gates
compositions, is introduced. A new approach for combining a group-theory-based
synthesis algorithm with a Reed-Muller-spectra-based synthesis algorithm is
described. Experimental results are presented to show that the proposed
synthesis techniques allow a reduction in input lines count, gate complexity or
quantum cost of reversible circuits for various benchmark functions.Comment: In English, 15 pages, 2 figures, 7 tables. Proceeding of the RC 2016
conferenc
Quantum resource estimates for computing elliptic curve discrete logarithms
We give precise quantum resource estimates for Shor's algorithm to compute
discrete logarithms on elliptic curves over prime fields. The estimates are
derived from a simulation of a Toffoli gate network for controlled elliptic
curve point addition, implemented within the framework of the quantum computing
software tool suite LIQ. We determine circuit implementations for
reversible modular arithmetic, including modular addition, multiplication and
inversion, as well as reversible elliptic curve point addition. We conclude
that elliptic curve discrete logarithms on an elliptic curve defined over an
-bit prime field can be computed on a quantum computer with at most qubits using a quantum circuit of at most Toffoli gates. We are able to classically simulate the
Toffoli networks corresponding to the controlled elliptic curve point addition
as the core piece of Shor's algorithm for the NIST standard curves P-192,
P-224, P-256, P-384 and P-521. Our approach allows gate-level comparisons to
recent resource estimates for Shor's factoring algorithm. The results also
support estimates given earlier by Proos and Zalka and indicate that, for
current parameters at comparable classical security levels, the number of
qubits required to tackle elliptic curves is less than for attacking RSA,
suggesting that indeed ECC is an easier target than RSA.Comment: 24 pages, 2 tables, 11 figures. v2: typos fixed and reference added.
ASIACRYPT 201
Programming Quantum Computers Using Design Automation
Recent developments in quantum hardware indicate that systems featuring more
than 50 physical qubits are within reach. At this scale, classical simulation
will no longer be feasible and there is a possibility that such quantum devices
may outperform even classical supercomputers at certain tasks. With the rapid
growth of qubit numbers and coherence times comes the increasingly difficult
challenge of quantum program compilation. This entails the translation of a
high-level description of a quantum algorithm to hardware-specific low-level
operations which can be carried out by the quantum device. Some parts of the
calculation may still be performed manually due to the lack of efficient
methods. This, in turn, may lead to a design gap, which will prevent the
programming of a quantum computer. In this paper, we discuss the challenges in
fully-automatic quantum compilation. We motivate directions for future research
to tackle these challenges. Yet, with the algorithms and approaches that exist
today, we demonstrate how to automatically perform the quantum programming flow
from algorithm to a physical quantum computer for a simple algorithmic
benchmark, namely the hidden shift problem. We present and use two tool flows
which invoke RevKit. One which is based on ProjectQ and which targets the IBM
Quantum Experience or a local simulator, and one which is based on Microsoft's
quantum programming language Q.Comment: 10 pages, 10 figures. To appear in: Proceedings of Design, Automation
and Test in Europe (DATE 2018
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