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.

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 Synthesis Strategy of Reversible Circuits on DNA Computers

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1242
Author(s):  
Mirna Rofail ◽  
Ahmed Younes
Keyword(s):  
Average Length ◽  
Logic Gates ◽  
Building Blocks ◽  
Quantum Cost ◽  
Reversible Circuits ◽  
Synthesis Strategy ◽  
Reversible Gate ◽  
Displacement Reactions ◽  
Reversible Logic Gates ◽  
Dna Computers

DNA computers and quantum computers are gaining attention as alternatives to classical digital computers. DNA is a biological material that can be reprogrammed to perform computing functions. Quantum computing performs reversible computations by nature based on the laws of quantum mechanics. In this paper, DNA computing and reversible computing are combined to propose novel theoretical methods to implement reversible gates and circuits in DNA computers based on strand displacement reactions, since the advantages of reversible logic gates can be exploited to improve the capabilities and functionalities of DNA computers. This paper also proposes a novel universal reversible gate library (URGL) for synthesizing n-bit reversible circuits using DNA to reduce the average length and cost of the constructed circuits when compared with previous methods. Each n-bit URGL contains building blocks to generate all possible permutations of a symmetric group of degree n. Our proposed group (URGL) in the paper is a permutation group. The proposed implementation methods will improve the efficiency of DNA computer computations as the results of DNA implementations are better in terms of quantum cost, DNA cost, and circuit length.

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 Decoherence dynamics estimation for superconducting gate-model quantum computers

2020 ◽  
Vol 19 (10) ◽  
Author(s):  
Laszlo Gyongyosi
Keyword(s):  
Gaussian Noise ◽  
Quantum Computer ◽  
Computer Architectures ◽  
Quantum Circuits ◽  
Optimal Placement ◽  
Quantum Computers ◽  
Intermediate Scale ◽  
Layout Generation ◽  
Quantum Technology ◽  
Physical Layout

Abstract Superconducting gate-model quantum computer architectures provide an implementable model for practical quantum computations in the NISQ (noisy intermediate scale quantum) technology era. Due to hardware restrictions and decoherence, generating the physical layout of the quantum circuits of a gate-model quantum computer is a challenge. Here, we define a method for layout generation with a decoherence dynamics estimation in superconducting gate-model quantum computers. We propose an algorithm for the optimal placement of the quantum computational blocks of gate-model quantum circuits. We study the effects of capacitance interference on the distribution of the Gaussian noise in the Josephson energy.

Towards Compact Modeling of Noisy Quantum Computers: A Molecular-Spin-Qubit Case of Study

2022 ◽  
Vol 18 (1) ◽  
pp. 1-26
Author(s):  
Mario Simoni ◽  
Giovanni Amedeo Cirillo ◽  
Giovanna Turvani ◽  
Mariagrazia Graziano ◽  
Maurizio Zamboni
Keyword(s):  
Physical Simulation ◽  
Quantum Circuits ◽  
Compact Modeling ◽  
Quantum Computers ◽  
Expected Performance ◽  
Classical Simulation ◽  
Spin Qubit ◽  
Compact Models ◽  
Standard Formalism ◽  
Definition Of

Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.

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 A Character Condition for Quadruple Transitivity

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
S. Aldhafeeri ◽  
R. T. Curtis
Keyword(s):  
Symmetric Group ◽  
Permutation Group ◽  
Irreducible Character

Let be a permutation group of degree viewed as a subgroup of the symmetric group . We show that if the irreducible character of corresponding to the partition of into subsets of sizes and 2, that is, to say the character often denoted by , remains irreducible when restricted to , then = 4, 5 or 9 and , A5, or PΣL2(8), respectively, or is 4-transitive.

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.

scholarly journals Option Pricing using Quantum Computers

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 291 ◽  
Author(s):  
Nikitas Stamatopoulos ◽  
Daniel J. Egger ◽  
Yue Sun ◽  
Christa Zoufal ◽  
Raban Iten ◽  
...  
Keyword(s):  
Option Pricing ◽  
Quantum Computer ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Barrier Options ◽  
Error Mitigation ◽  
Quantum Device ◽  
Amplitude Estimation ◽  
Simulation Results ◽  
Path Dependent

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

A FRAMEWORK FOR REPRESENTING AND PRODUCING MOVIES ON QUANTUM COMPUTERS

2011 ◽  
Vol 09 (06) ◽  
pp. 1459-1497 ◽  
Author(s):  
ABDULLAH M. ILIYASU ◽  
PHUC Q. LE ◽  
FANGYAN DONG ◽  
KAORU HIROTA
Keyword(s):  
Quantum Circuits ◽  
Quantum Computers ◽  
Transition Rates ◽  
Projective Measurement ◽  
Physical Realization ◽  
Quantum Devices ◽  
Frame Transition ◽  
Key Frames ◽  
Movie Script ◽  
The Physical Realization

Adopting a generalization of the DiVincenzo criteria for the physical realization of quantum devices, a standalone component each, is proposed to prepare, manipulate, and measure the various content required to represent and produce movies on quantum computers. The quantum CD encodes, prepares, and initializes the broad content or key frames conveying the movie script. The quantum player uses the simple motion operations to manipulate the contents of the key frames in order to interpolate the missing viewing frames required to effectively depict the shots and scenes of the movie. The movie reader combines the projective measurement technique and the ancilla-driven quantum computation to retrieve the classical movie sequence comprising of both the key and viewing frames for each shot. At appropriate frame transition rates, this sequence creates the impression of continuity in order to depict the various movements and actions in the movie. Two well-thought-out examples demonstrate the feasibility of the proposed framework. Concatenated, these components together facilitate the proposed framework for quantum movie representation and production, thus, opening the door towards manipulating quantum circuits aimed at applications for information representation and processing.

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