scholarly journals Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

2005 ◽  
Author(s):  
Guowu Yang ◽  
W.N.N. Hung ◽  
Xiaoyu Song ◽  
M. Perkowski
Keyword(s):  
Group Theory ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Multiple Valued Logic

scholarly journals Quantum Implementation of Powell’s Conjugate Direction Method

2019 ◽  
Vol 23 (4) ◽  
pp. 726-734
Author(s):  
Kehan Chen ◽  
Fei Yan ◽  
Kaoru Hirota ◽  
Jianping Zhao ◽  
◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Data Fitting ◽  
Quadratic Equation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Circuit Implementation ◽  
One Dimensional ◽  
Conjugate Direction ◽  
Conjugate Direction Method

A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.

scholarly journals Synthesis of quantum circuits in Linear Nearest neighbor Model using Positive Davio Lattices

2011 ◽  
Vol 24 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Marek Perkowski ◽  
Martin Lukac ◽  
Dipal Shah ◽  
Michitaka Kameyama
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Space ◽  
Synthesis Method ◽  
Logic Synthesis ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Synthesis Methods ◽  
Cost Models ◽  
Quantum Cost ◽  
One Dimensional

We present a logic synthesis method based on lattices that realize quantum arrays in One-Dimensional Ion Trap technology. This means that all gates are built from 2x2 quantum primitives that are located only on neighbor qubits in a one-dimensional space (called also vector of qubits or Linear Nearest Neighbor (LNN) architecture). The Logic circuits designed by the proposed method are realized only with 3*3 Toffoli, Feynman and NOT quantum gates and the usage of the commonly used multi-input Toffoli gates is avoided. This realization method of quantum circuits is different from most of reversible circuits synthesis methods from the literature that use only high level quantum cost based on the number of quantum gates. Our synthesis approach applies to both standard and LNN quantum cost models. It leads to entirely new CAD algorithms for circuit synthesis and substantially decreases the quantum cost for LNN quantum circuits. The drawback of synthesizing circuits in the presented LNN architecture is the addition of ancilla qubits.

Analyzing Heuristic-based Randomized Search Strategies for the Quantum Circuit Compilation Problem

2020 ◽  
Vol 174 (3-4) ◽  
pp. 259-281
Author(s):  
Angelo Oddi ◽  
Riccardo Rasconi
Keyword(s):  
Quantum Computing ◽  
Nearest Neighbor ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Ranking Functions ◽  
Solution Quality ◽  
Circuit Realization ◽  
Definition Of

In this work we investigate the performance of greedy randomised search (GRS) techniques to the problem of compiling quantum circuits to emerging quantum hardware. Quantum computing (QC) represents the next big step towards power consumption minimisation and CPU speed boost in the future of computing machines. Quantum computing uses quantum gates that manipulate multi-valued bits (qubits). A quantum circuit is composed of a number of qubits and a series of quantum gates that operate on those qubits, and whose execution realises a specific quantum algorithm. Current quantum computing technologies limit the qubit interaction distance allowing the execution of gates between adjacent qubits only. This has opened the way to the exploration of possible techniques aimed at guaranteeing nearest-neighbor (NN) compliance in any quantum circuit through the addition of a number of so-called swap gates between adjacent qubits. In addition, technological limitations (decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized. One core contribution of the paper is the definition of two lexicographic ranking functions for quantum gate selection, using two keys: one key acts as a global closure metric to minimise the solution makespan; the second one is a local metric, which favours the mutual approach of the closest qstates pairs. We present a GRS procedure that synthesises NN-compliant quantum circuits realizations, starting from a set of benchmark instances of different size belonging to the Quantum Approximate Optimization Algorithm (QAOA) class tailored for the MaxCut problem. We propose a comparison between the presented meta-heuristics and the approaches used in the recent literature against the same benchmarks, both from the CPU efficiency and from the solution quality standpoint. In particular, we compare our approach against a reference benchmark initially proposed and subsequently expanded in [1] by considering: (i) variable qubit state initialisation and (ii) crosstalk constraints that further restrict parallel gate execution.

scholarly journals Group theory for quantum gates and quantum coherence

2008 ◽  
Vol 41 (18) ◽  
pp. 182001 ◽  
Author(s):  
Michel Planat ◽  
Philippe Jorrand
Keyword(s):  
Group Theory ◽  
Quantum Coherence ◽  
Quantum Gates

scholarly journals Towards optimization of quantum circuits

Open Physics ◽  
2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Michal Sedlák ◽  
Martin Plesch
Keyword(s):  
Quantum Information ◽  
Quantum Information Processing ◽  
Quantum Circuit ◽  
Quantum Gate ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Unitary Operation ◽  
Short Sequence ◽  
Toffoli Gates ◽  
Universal Procedure

AbstractAny unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.

scholarly journals A general protocol for distributed quantum gates

2021 ◽  
Vol 20 (8) ◽  
Author(s):  
Moein Sarvaghad-Moghaddam ◽  
Mariam Zomorodi
Keyword(s):  
Quantum Computation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Toffoli Gate

AbstractIn distributed quantum computation, quantum remote-controlled gates are used frequently and applied on separate nodes or subsystems of a network. One of the universal and well-known controlled gates is the n-qubit controlled-NOT gate, especially Toffoli gate for the case of three qubits, which are frequently used to synthesize quantum circuits. In this paper, we considered a more general case, an n-qubit controlled-U gate, and present a general protocol for implementing these gates remotely with minimum required resources. Then, the proposed method is applied to implement a Toffoli gate in bipartite and tripartite systems. In this method, we considered cases in which a group of qubits belongs to one subsystem of the network. Then, we improved its consumption resources.

Research and development of a quantum computing system as an information process.

2021 ◽  
Vol 5 ◽  
Author(s):  
V.S. Potapov ◽  
◽  
S.M. Gushansky
Keyword(s):  
Information System ◽  
Quantum Computing ◽  
Quantum Information ◽  
Computing System ◽  
Software Implementation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Information Process ◽  
Component Structure ◽  
The Past

Over the past few decades, there has been a significant breakthrough in the field of quantum computing. Research is attracting growing interest, which has recently led to the development of quantum information systems prototypes and methods for their development. The paper describes the characteristics of the information system as an object of architecture and the representation of quantum gates using quantum circuits. A functional-component structure of a quantum information system has been built and a software implementation of a quantum information system has been made on its basis.

scholarly journals EXACT NON-IDENTITY CHECK IS NQP-COMPLETE

2010 ◽  
Vol 08 (05) ◽  
pp. 807-819
Author(s):  
YU TANAKA
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Decision Problem ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Unitary Operation ◽  
Classical Description ◽  
Quantum Polynomial ◽  
Equivalence Check

To understand quantum gate array complexity, we define a problem named exact non-identity check, which is a decision problem to determine whether a given classical description of a quantum circuit is strictly equivalent to the identity or not. We show that the computational complexity of this problem is non-deterministic quantum polynomial-time (NQP)-complete. As corollaries, it is derived that exact non-equivalence check of two given classical descriptions of quantum circuits is also NQP-complete and that minimizing the number of quantum gates for a given quantum circuit without changing the implemented unitary operation is NQP-hard.

scholarly journals Quantum circuits for incompletely specified two-qubit operators

2005 ◽  
Vol 5 (1) ◽  
pp. 48-56
Author(s):  
V.V. Shende ◽  
I.L. Markov
Keyword(s):  
Degrees Of Freedom ◽  
Unitary Operator ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Input State ◽  
Projective Measurement ◽  
Practical Challenge ◽  
Necessary And Sufficient ◽  
The Given

While the question ``how many CNOT gates are needed to simulate an arbitrary two-qubit operator'' has been conclusively answered -- three are necessary and sufficient -- previous work on this topic assumes that one wants to simulate a given unitary operator up to global phase. However, in many practical cases additional degrees of freedom are allowed. For example, if the computation is to be followed by a given projective measurement, many dissimilar operators achieve the same output distributions on all input states. Alternatively, if it is known that the input state is $\ket{0}$, the action of the given operator on all orthogonal states is immaterial. In such cases, we say that the unitary operator is incompletely specified; in this work, we take up the practical challenge of satisfying a given specification with the smallest possible circuit. In particular, we identify cases in which such operators can be implemented using fewer quantum gates than are required for generic completely specified operators.

scholarly journals Quantum Computing in the NISQ era and beyond

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 79 ◽  
Author(s):  
John Preskill
Keyword(s):  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Quantum Computers ◽  
Many Body ◽  
Significant Step ◽  
Near Future

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.

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