Corpus ID: 18050599

Efficient Synthesis of Linear Reversible Circuits

@article{Patel2003EfficientSO,
  title={Efficient Synthesis of Linear Reversible Circuits},
  author={Ketan N. Patel and Igor L. Markov and John Patrick Hayes},
  journal={arXiv: Quantum Physics},
  year={2003}
}
In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with O(n^2) gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O(n^2/log n) gates. We present an algorithm that is… Expand

Figures from this paper

Scalable Simplification of Reversible Circuits
Reversible logic circuit synthesis has applications in various modern computational problems, low power design, and quantum circuit synthesis. Several algorithms for synthesis and simplification ofExpand
Efficient reversible and quantum implementations of symmetric Boolean functions
It is a well-known fact in logic design that synthesis of some special classes of Boolean functions is often easier than the synthesis of a general unrestricted specification. In reversible logic,Expand
Using Reed-Muller Expansions in the Synthesis and Optimization of Boolean Quantum Circuits
TLDR
The chapter shows that there is a direct correspondence between Boolean quantum operations and the classical Reed-Muller expansions, which makes it possible for the problem of synthesis and optimization of Boolean quantum circuits to be tackled within the domain of Reed-muller logic under manufacturing constraints. Expand
Tight Bounds on the Synthesis of 3-Bit Reversible Circuits: Nffr Library
  • A. Younes
  • Mathematics, Computer Science
  • J. Circuits Syst. Comput.
  • 2014
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 theExpand
Analysis and Improvement of Transformation-Based Reversible Logic Synthesis
TLDR
Two novel techniques to the transformation-based synthesis flow for improving synthesis outcome are suggested, based on properties of Boolean functions and generalized Fredkin gates during synthesis flow. Expand
SAT-based {CNOT, T} Quantum Circuit Synthesis
TLDR
This work has developed an exact SAT-based algorithm for quantum circuit rewriting that aims at reducing CNOT gates without increasing the number of T gates and finds the minimum {CNOT, T} circuit for a given phase polynomial description of a unitary transformation. Expand
Detection and Elimination of Non-Trivial Reversible Identities
AbstractNon-Trivial Reversible Identities (NTRIs) are reversible circuits that have equal inputs and outputs.NTRIs cannot be detected using optimization algorithms in the literature. Existence ofExpand
Resource optimization for fault-tolerant quantum computing
TLDR
This thesis shows how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems and finds that by using a special class of non-deterministic circuits, the cost of decomposition can be reduced by as much as a factor of four over state-of-the-art techniques, which typically use deterministic circuits. Expand
A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits
We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute forceExpand
An arbitrary twoqubit computation In 23 elementary gates or less
TLDR
This work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits, and constructively proves a worstcase upper bound of 23 elementary gates, of which at most 4 (CNOTs) entail multi-qubit interactions. Expand
...
1
2
3
...

References

SHOWING 1-10 OF 11 REFERENCES
Reversible logic circuit synthesis
TLDR
In an application important to quantum computing, oracle circuits for Grover's search algorithm are synthesized, and a significant improvement over a previously proposed synthesis algorithm is shown. Expand
A General Decomposition for Reversible Logic
Logic synthesis for reversible logic differs considerably from standard logic synthesis. The gates are multi-output and the unutilized outputs from these gates are called “garbage”. One of theExpand
Elementary gates for quantum computation.
TLDR
U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits. Expand
Two-bit gates are universal for quantum computation.
  • DiVincenzo
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
  • 1995
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. TheExpand
Quantum Algorithms: Applicable Algebra and Quantum Physics
Classical computer science relies on the concept of Turing machines as a unifying model of universal computation. According to the modern Church-Turing Thesis, this concept is interpreted in the formExpand
Reducing quantum computations to elementary unitary operations
  • G. Cybenko
  • Mathematics, Computer Science
  • Comput. Sci. Eng.
  • 2001
TLDR
Standard techniques from numerical linear algebra can be used to represent quantum computations as sequences of simple quantum operations, called quantum Givens operators, on single quantum bits. Expand
Numerical recipes in C
TLDR
The Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08. Expand
Elementary gates for quantum c o putation.Physical
  • 1995
Faradˇ zev. On economical construction of the transitive closure of an oriented graph
  • Soviet Mathematics Doklady,
  • 1970
On economical construction of the transitive closure of an oriented graph
  • Soviet Mathematics Doklady
  • 1970
...
1
2
...