scholarly journals Using negated control signals in quantum computing circuits

2011 ◽  
Vol 24 (3) ◽  
pp. 423-435 ◽  
Author(s):  
Claudio Moraga
Keyword(s):  
Quantum Computing ◽  
Control Variable ◽  
Quantum Circuits ◽  
Quantum Cost ◽  
Schematic Representation ◽  
Control Signals ◽  
Reversible Circuits ◽  
Mixed Polarity

White dots have been used in the schematic representation of reversible circuits to indicate that a control variable has to be inverted to become active. The present paper argues that the use of negated control signals may also offer advantages for the realization, by reducing the number of elementary components. In the case of quantum circuits, this contributes to reduce the quantum cost. It is shown that mixed polarity Reed Muller expressions, possibly extended with Boolean disjunctions, are very helpful to design quantum computing circuits including negated control signals.

scholarly journals Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1025
Author(s):  
Mariam Gado ◽  
Ahmed Younes
Keyword(s):  
Symmetric Group ◽  
Permutation Group ◽  
Building Blocks ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Cost ◽  
Reversible Circuits ◽  
Negative Controls ◽  
Target Qubit

The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which is a subset of the symmetric group, where the NCT library is considered as the generators of the permutation group.

scholarly journals Efficient Quantum Circuits for One-Way Quantum Computing

2009 ◽  
Vol 102 (10) ◽  
Author(s):  
Tetsufumi Tanamoto ◽  
Yu-xi Liu ◽  
Xuedong Hu ◽  
Franco Nori
Keyword(s):  
Quantum Computing ◽  
Quantum Circuits

Quantum circuits for simple periodic functions

2014 ◽  
Vol 14 (9&10) ◽  
pp. 763-776
Author(s):  
Omar Gamel ◽  
Daniel F.V. James
Keyword(s):  
Quantum Computing ◽  
Periodic Function ◽  
Quantum Circuits ◽  
Special Importance ◽  
Periodic Functions ◽  
Single Period ◽  
Shor's Algorithm ◽  
Toffoli Gates ◽  
One To One

Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for a simple monoperiodic function, that is one-to-one within a single period, of a given period $p$. We conjecture that to create a simple periodic function of period $p$, where $p$ is an $n$-bit number, one needs at most $n$ Toffoli gates.

Efficient reversible quantum design of sig-magnitude to two's complement converters

2020 ◽  
Vol 20 (9&10) ◽  
pp. 747-765
Author(s):  
F. Orts ◽  
G. Ortega ◽  
E.M. E.M. Garzon
Keyword(s):  
Quantum Computing ◽  
Scientific Community ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
State Of The Art ◽  
The Other ◽  
Quantum Computers ◽  
Binary Number ◽  
Quantum Cost ◽  
The One

Despite the great interest that the scientific community has in quantum computing, the scarcity and high cost of resources prevent to advance in this field. Specifically, qubits are very expensive to build, causing the few available quantum computers are tremendously limited in their number of qubits and delaying their progress. This work presents new reversible circuits that optimize the necessary resources for the conversion of a sign binary number into two's complement of N digits. The benefits of our work are two: on the one hand, the proposed two's complement converters are fault tolerant circuits and also are more efficient in terms of resources (essentially, quantum cost, number of qubits, and T-count) than the described in the literature. On the other hand, valuable information about available converters and, what is more, quantum adders, is summarized in tables for interested researchers. The converters have been measured using robust metrics and have been compared with the state-of-the-art circuits. The code to build them in a real quantum computer is given.

scholarly journals Gaussian Elimination versus Greedy Methods for the Synthesis of Linear Reversible Circuits

2021 ◽  
Vol 2 (3) ◽  
pp. 1-26
Author(s):  
Timothée Goubault De Brugière ◽  
Marc Baboulin ◽  
Benoît Valiron ◽  
Simon Martiel ◽  
Cyril Allouche
Keyword(s):  
Quantum Computing ◽  
State Of The Art ◽  
Gaussian Elimination ◽  
Random Operators ◽  
Lu Factorization ◽  
Large Problem ◽  
Computational Costs ◽  
Elimination Algorithm ◽  
Reversible Circuits ◽  
Greedy Methods

Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of qubits, making them a good candidate to deploy efficient methods to reduce computational costs. We propose a new algorithm for synthesizing any linear reversible operator by using an optimized version of the Gaussian elimination algorithm coupled with a tuned LU factorization. We also improve the scalability of purely greedy methods. Overall, on random operators, our algorithms improve the state-of-the-art methods for specific ranges of problem sizes: The custom Gaussian elimination algorithm provides the best results for large problem sizes (n > 150), while the purely greedy methods provide quasi optimal results when n < 30. On a benchmark of reversible functions, we manage to significantly reduce the CNOT count and the depth of the circuit while keeping other metrics of importance (T-count, T-depth) as low as possible.

scholarly journals Fast equivalence -- checking for quantum circuits

2010 ◽  
Vol 10 (9&10) ◽  
pp. 721-734
Author(s):  
Shigeru Yamashita ◽  
Igor L. Markov
Keyword(s):  
Formal Verification ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Equivalence Checking ◽  
Sat Solvers ◽  
Reversible Circuits ◽  
Verification Tools ◽  
Verification Methodology ◽  
Verification Techniques ◽  
Factoring Algorithm

We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage existing techniques for simplification of quantum circuits. For reversible circuits which arise as runtime bottlenecks of key quantum algorithms, we develop several verification techniques and empirically compare them. We also combine existing quantum verification tools with the use of SAT-solvers. Experiments with circuits for Shor's number-factoring algorithm, containing thousands of gates, show improvements in efficiency by four orders of magnitude.

General Method to Design Reversible Universal n-Bit Up/Down Counters

2020 ◽  
Vol 29 (10) ◽  
pp. 2050165
Author(s):  
Zeinab Kalantari ◽  
Mohammad Eshghi ◽  
Majid Mohammadi ◽  
Somayeh Jassbi
Keyword(s):  
Power Consumption ◽  
Electronic Devices ◽  
Reducing Power ◽  
Sequential Circuits ◽  
Quantum Cost ◽  
Multiple Outputs ◽  
Reversible Circuits ◽  
Direct Design ◽  
The Common ◽  
General Method

With the growing trend towards reducing the size of electronic devices, reducing power consumption has become one of the major concerns of circuit designers, and designing reversible circuits is one of the approaches proposed for reducing power consumption. Although several studies have been done in the field of synthesizing combinational reversible circuits, little work has been done for designing reversible sequential circuits. Furthermore, many researches in this context use traditional designs which replace latches, flip-flops and associated combinational gates with their reversible counterparts. This traditional technique is not very promising, because it leads to high quantum cost (QC) and garbage outputs. Recently, researchers have proposed direct design of reversible sequential circuits using Reed Muller expressions to obtain next state output. Since most sequential circuits have multiple outputs, using common product terms between multiple outputs might decrease QC significantly. In this paper, a modular and low QC design for a synchronous reversible [Formula: see text]-bit up/down counter with parallel load capability is presented. In this design, the common terms among multiple outputs are used efficiently, which leads to a low QC for the counter. A general formula to evaluate the QC of our proposed reversible counter is presented. This result shows that in our proposed design by increasing the number of bits of counter ([Formula: see text], the QC increases linearly, while in previous works by increasing the number of bits of counter, the QC increases exponentially.

REDUCING QUANTUM COST OF REVERSIBLE CIRCUITS FOR HOMOGENEOUS BOOLEAN FUNCTIONS

2010 ◽  
Vol 19 (07) ◽  
pp. 1423-1434 ◽  
Author(s):  
AHMED YOUNES
Keyword(s):  
Low Power ◽  
Boolean Functions ◽  
Quantum Computers ◽  
Quantum Cost ◽  
Power Devices ◽  
Computing Systems ◽  
Factorization Algorithm ◽  
Reversible Circuits

Homogeneous Boolean functions have many applications in computing systems, e.g., cryptography. This paper presents a factorization algorithm for reducing the quantum cost of the reversible circuits for that class of Boolean functions. The algorithm reduces the multi-calculation of any common parts of the circuit. This allows Homogeneous Boolean related applications to be implemented efficiently on novel computing paradigms such as quantum computers and low power devices.

scholarly journals Human-Competitive Evolution of Quantum Computing Artefacts by Genetic Programming

2006 ◽  
Vol 14 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Paul Massey ◽  
John A. Clark ◽  
Susan Stepney
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Genetic Programming ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Quantum Fourier Transform ◽  
Competitive Evolution ◽  
Specific Quantum

We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

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