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 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 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.

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.

Computational model underlying the one-way quantum computer

2002 ◽  
Vol 2 (6) ◽  
pp. 443-486
Author(s):  
R. Raussendorf ◽  
H. Briegel
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Computational Model ◽  
Quantum Logic ◽  
Quantum Information Processing ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Single Step ◽  
Clifford Group ◽  
The One

In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. {\bf{86}}, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantum information processing that are possible with the one-way quantum computer can be understood properly in network model terms. We show that the logical depth is, for certain algorithms, lower than has so far been known for networks. For example, every quantum circuit in the Clifford group can be performed on the one-way quantum computer in a single step.

scholarly journals Comparing the randomized benchmarking figure with the average infidelity of a quantum gate-set

2019 ◽  
Vol 17 (04) ◽  
pp. 1950031
Author(s):  
Jiaan Qi ◽  
Hui Khoon Ng
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
The Other ◽  
Quantum Gate ◽  
High Fidelity ◽  
Number Formula

Randomized benchmarking (RB) is a popular procedure used to gauge the performance of a set of gates useful for quantum information processing (QIP). Recently, Proctor et al. [Phys. Rev. Lett. 119 (2017) 130502] demonstrated a practically relevant example where the RB measurements give a number [Formula: see text], very different from the actual average gate-set infidelity [Formula: see text], despite past theoretical assurances that the two should be equal. Here, we derive formulas for [Formula: see text], and for [Formula: see text] from the RB protocol, in a manner permitting easy comparison of the two. We show in general that, indeed, [Formula: see text], i.e. RB does not measure average infidelity, and, in fact, neither one bounds the other. We give several examples, all plausible in real experiments, to illustrate the differences in [Formula: see text] and [Formula: see text]. Many recent papers on experimental implementations of QIP have claimed the ability to perform high-fidelity gates because they demonstrated small [Formula: see text] values using RB. Our analysis shows that such a statement from RB alone has to be interpreted with caution.

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.

Quantum Wavelet Packet Transforms

2021 ◽  
pp. 221-245
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
High Efficiency ◽  
Quantum Information Processing ◽  
Wavelet Packet ◽  
Quantum Circuits ◽  
Multi Level ◽  
2D And 3D ◽  
First Time ◽  
Perfect Shuffle

Quantum wavelet packet transform (QWPT) may play an important role in quantum information processing. In this chapter, the authors design quantum circuits of a generalized tensor product (GTP) and a perfect shuffle permutation (PSP). Next, they propose multi-level and multi-dimensional (1D, 2D and 3D) QWPTs, including Haar QWPT (HQWPT), D4 QWPT (DQWPT) based on the periodization extension and their inverse transforms for the first time, and prove the correctness based on the GTP and PSP. Furthermore, they analyze the quantum costs and the time complexities of the proposed QWPTs and obtain precise results. The time complexities of HQWPTs is at most six basic operations on 2n elements, which illustrates high efficiency of the proposed QWPTs.

scholarly journals Householder methods for quantum circuit design

2016 ◽  
Vol 94 (2) ◽  
pp. 150-157 ◽  
Author(s):  
Jesús Urías ◽  
Diego A. Quiñones
Keyword(s):  
Tensor Product ◽  
Circuit Design ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Single Type ◽  
Unitary Operation ◽  
Gray Codes ◽  
Combined Procedure ◽  
Unitary Transformations ◽  
Assembly Procedure

Algorithms to resolve multiple-qubit unitary transformations into a sequence of simple operations on one-qubit subsystems are central to the methods of quantum-circuit simulators. We adapt Householder’s theorem to the tensor-product character of multi-qubit state vectors and translate it to a combinatorial procedure to assemble cascades of quantum gates that recreate any unitary operation U acting on n-qubit systems. U may be recreated by any cascade from a set of combinatorial options that, in number, are not lesser than super-factorial of 2n, [Formula: see text]. Cascades are assembled with one-qubit controlled-gates of a single type. We complement the assembly procedure with a new algorithm to generate Gray codes that reduce the combinatorial options to cascades with the least number of CNOT gates. The combined procedure —factorization, gate assembling, and Gray ordering — is illustrated on an array of three qubits.

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