15 research outputs found
Tight Bounds on the Synthesis of 3-bit Reversible Circuits: NFT Library
The reversible circuit synthesis problem can be reduced to permutation group.
This allows Schreier-Sims Algorithm for the strong generating set-finding
problem to be used to find tight bounds on the synthesis of 3-bit reversible
circuits using the NFT library. The tight bounds include the maximum and
minimum length of 3-bit reversible circuits, the maximum and minimum cost of
3-bit reversible circuits. The analysis shows better results than that found in
the literature for the lower bound of the cost. The analysis also shows that
there are 1960 universal reversible sub-libraries from the main NFT library.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1101.438
A Library-Based Synthesis Methodology for Reversible Logic
In this paper, a library-based synthesis methodology for reversible circuits
is proposed where a reversible specification is considered as a permutation
comprising a set of cycles. To this end, a pre-synthesis optimization step is
introduced to construct a reversible specification from an irreversible
function. In addition, a cycle-based representation model is presented to be
used as an intermediate format in the proposed synthesis methodology. The
selected intermediate format serves as a focal point for all potential
representation models. In order to synthesize a given function, a library
containing seven building blocks is used where each building block is a cycle
of length less than 6. To synthesize large cycles, we also propose a
decomposition algorithm which produces all possible minimal and inequivalent
factorizations for a given cycle of length greater than 5. All decompositions
contain the maximum number of disjoint cycles. The generated decompositions are
used in conjunction with a novel cycle assignment algorithm which is proposed
based on the graph matching problem to select the best possible cycle pairs.
Then, each pair is synthesized by using the available components of the
library. The decomposition algorithm together with the cycle assignment method
are considered as a binding method which selects a building block from the
library for each cycle. Finally, a post-synthesis optimization step is
introduced to optimize the synthesis results in terms of different costs.Comment: 24 pages, 8 figures, Microelectronics Journal, Elsevie
Improving Quantum Circuit Synthesis with Machine Learning
In the Noisy Intermediate Scale Quantum (NISQ) era, finding implementations
of quantum algorithms that minimize the number of expensive and error prone
multi-qubit gates is vital to ensure computations produce meaningful outputs.
Unitary synthesis, the process of finding a quantum circuit that implements
some target unitary matrix, is able to solve this problem optimally in many
cases. However, current bottom-up unitary synthesis algorithms are limited by
their exponentially growing run times. We show how applying machine learning to
unitary datasets permits drastic speedups for synthesis algorithms. This paper
presents QSeed, a seeded synthesis algorithm that employs a learned model to
quickly propose resource efficient circuit implementations of unitaries. QSeed
maintains low gate counts and offers a speedup of in synthesis time
over the state of the art for a 64 qubit modular exponentiation circuit, a core
component in Shor's factoring algorithm. QSeed's performance improvements also
generalize to families of circuits not seen during the training process.Comment: 11 pages, 10 figure
Exact and practical pattern matching for quantum circuit optimization
Quantum computations are typically compiled into a circuit of basic quantum
gates. Just like for classical circuits, a quantum compiler should optimize the
quantum circuit, e.g. by minimizing the number of required gates. Optimizing
quantum circuits is not only relevant for improving the runtime of quantum
algorithms in the long term, but is also particularly important for near-term
quantum devices that can only implement a small number of quantum gates before
noise renders the computation useless. An important building block for many
quantum circuit optimization techniques is pattern matching, where given a
large and a small quantum circuit, we are interested in finding all maximal
matches of the small circuit, called pattern, in the large circuit, considering
pairwise commutation of quantum gates.
In this work, we present a classical algorithm for pattern matching that
provably finds all maximal matches in time polynomial in the circuit size (for
a fixed pattern size). Our algorithm works for both quantum and reversible
classical circuits. We demonstrate numerically that our algorithm, implemented
in the open-source library Qiskit, scales considerably better than suggested by
the theoretical worst-case complexity and is practical to use for circuit sizes
typical for near-term quantum devices. Using our pattern matching algorithm as
the basis for known circuit optimization techniques such as template matching
and peephole optimization, we demonstrate a significant (~30%) reduction in
gate count for random quantum circuits, and are able to further improve
practically relevant quantum circuits that were already optimized with
state-of-the-art techniques.Comment: Raban Iten and Romain Moyard contributed equally to this work. Major
updates: Added numerical analysis of the pattern matching algorithm; fixed
two special cases that were missed by our algorithm and updated the
worst-case complexity analysis. 10 pages summary + 23 pages main text + 7
pages appendi
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