scholarly journals Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

2022 ◽  
Vol 12 (2) ◽  
pp. 759
Author(s):  
Anna M. Krol ◽  
Aritra Sarkar ◽  
Imran Ashraf ◽  
Zaid Al-Ars ◽  
Koen Bertels
Keyword(s):  
Quantum Algorithms ◽  
Optimization Method ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Underlying Structure ◽  
Quantum Computers ◽  
Unitary Matrices ◽  
Quantum Operations ◽  
Test Part ◽  
Input Gate

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

scholarly journals Deep neural networks for quantum circuit mapping

2021 ◽  
Author(s):  
Giovanni Acampora ◽  
Roberto Schiattarella
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Machine Learning Techniques ◽  
Quantum Computers ◽  
Physical Constraints ◽  
Proper Mapping ◽  
Correct Execution

AbstractQuantum computers have become reality thanks to the effort of some majors in developing innovative technologies that enable the usage of quantum effects in computation, so as to pave the way towards the design of efficient quantum algorithms to use in different applications domains, from finance and chemistry to artificial and computational intelligence. However, there are still some technological limitations that do not allow a correct design of quantum algorithms, compromising the achievement of the so-called quantum advantage. Specifically, a major limitation in the design of a quantum algorithm is related to its proper mapping to a specific quantum processor so that the underlying physical constraints are satisfied. This hard problem, known as circuit mapping, is a critical task to face in quantum world, and it needs to be efficiently addressed to allow quantum computers to work correctly and productively. In order to bridge above gap, this paper introduces a very first circuit mapping approach based on deep neural networks, which opens a completely new scenario in which the correct execution of quantum algorithms is supported by classical machine learning techniques. As shown in experimental section, the proposed approach speeds up current state-of-the-art mapping algorithms when used on 5-qubits IBM Q processors, maintaining suitable mapping accuracy.

scholarly journals OpenQL: A Portable Quantum Programming Framework for Quantum Accelerators

2022 ◽  
Vol 18 (1) ◽  
pp. 1-24
Author(s):  
N. Khammassi ◽  
I. Ashraf ◽  
J. V. Someren ◽  
R. Nane ◽  
A. M. Krol ◽  
...  
Keyword(s):  
Programming Language ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Operations ◽  
Programming Framework ◽  
Quantum Processor ◽  
Control Electronics ◽  
Quantum Programming ◽  
High Level ◽  
Programming Interface

With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving, and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language and making them executable on a quantum processor while abstracting away hardware details is a challenging task. First, a quantum programming language should provide an intuitive programming interface to describe those algorithms. Then a compiler has to transform the program into a quantum circuit, optimize it, and map it to the target quantum processor respecting the hardware constraints such as the supported quantum operations, the qubit connectivity, and the control electronics limitations. In this article, we propose a quantum programming framework named OpenQL, which includes a high-level quantum programming language and its associated quantum compiler. We present the programming interface of OpenQL, we describe the different layers of the compiler and how we can provide portability over different qubit technologies. Our experiments show that OpenQL allows the execution of the same high-level algorithm on two different qubit technologies, namely superconducting qubits and Si-Spin qubits. Besides the executable code, OpenQL also produces an intermediate quantum assembly code, which is technology independent and can be simulated using the QX simulator.

scholarly journals A co-design framework of neural networks and quantum circuits towards quantum advantage

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Weiwen Jiang ◽  
Jinjun Xiong ◽  
Yiyu Shi
Keyword(s):  
Neural Network ◽  
Cost Reduction ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Design Framework ◽  
Unitary Matrices ◽  
Classical Computing ◽  
Classical Computer ◽  
The Cost

AbstractDespite the pursuit of quantum advantages in various applications, the power of quantum computers in executing neural network has mostly remained unknown, primarily due to a missing tool that effectively designs a neural network suitable for quantum circuit. Here, we present a neural network and quantum circuit co-design framework, namely QuantumFlow, to address the issue. In QuantumFlow, we represent data as unitary matrices to exploit quantum power by encoding n = 2k inputs into k qubits and representing data as random variables to seamlessly connect layers without measurement. Coupled with a novel algorithm, the cost complexity of the unitary matrices-based neural computation can be reduced from O(n) in classical computing to O(polylog(n)) in quantum computing. Results show that on MNIST dataset, QuantumFlow can achieve an accuracy of 94.09% with a cost reduction of 10.85 × against the classical computer. All these results demonstrate the potential for QuantumFlow to achieve the quantum advantage.

Can Quantum Computers Solve Linear Algebra Problems to Advance Engineering Applications?

2018 ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Quantum Computing ◽  
Linear Algebra ◽  
Quantum Algorithms ◽  
Finite Difference Methods ◽  
Engineering Application ◽  
Quantum Circuit ◽  
Quantum Computers ◽  
Measurement Methodology ◽  
Classical Computing ◽  
Richard Feynman

Since its inception by Richard Feynman in 1982, quantum computing has provided an intriguing opportunity to advance computational capabilities over classical computing. Classical computers use bits to process information in terms of zeros and ones. Quantum computers use the complex world of quantum mechanics to carry out calculations using qubits (the quantum analog of a classical bit). The qubit can be in a superposition of the zero and one state simultaneously unlike a classical bit. The true power of quantum computing comes from the complexity of entanglement between many qubits. When entanglement is realized, quantum algorithms for problems such as factoring numbers and solving linear algebra problems show exponential speed-up relative to any known classical algorithm. Linear algebra problems are of particular interest in engineering application for solving problems that use finite element and finite difference methods. Here, we explore quantum linear algebra problems where we design and implement a quantum circuit that can be tested on IBM’s quantum computing hardware. A set of quantum gates are assimilated into a circuit and implemented on the IBM Q system to demonstrate its algorithm capabilities and its measurement methodology.

scholarly journals On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity

2020 ◽  
Vol 20 (9&10) ◽  
pp. 787-806 ◽  
Author(s):  
Steven Herbert
Keyword(s):  
Quantum Algorithms ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Interaction Graph ◽  
Finite Degree ◽  
Near Term

This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable general qubit interactions. This paper proves that there exist quantum circuits where a depth overhead in Omega(\log n) must necessarily be incurred when running quantum circuits with n qubits on quantum computers whose qubit interaction graph has finite degree, but that such a logarithmic depth overhead is achievable. The latter is shown by the construction of a 4-regular qubit interaction graph and associated compilation algorithm that can execute any quantum circuit with only a logarithmic depth overhead.

Universal quantum circuit for n-qubit quantum gate: a programmable quantum gate

2007 ◽  
Vol 7 (3) ◽  
pp. 228-242
Author(s):  
P.B.M. Sousa ◽  
R.V. Ramos
Keyword(s):  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Gate ◽  
Quantum Circuits ◽  
Unitary Matrices ◽  
Quantum Operations ◽  
Universal Quantum ◽  
Np Problems ◽  
Universal Quantum Circuit ◽  
Specific Quantum

Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the basic steps is to implement the quantum circuit able to realize a given unitary operation. This task has been solved using decomposition of unitary matrices in simpler ones till reach quantum circuits having only single-qubits and CNOTs gates. Usually the goal is to find the minimal quantum circuit able to solve a given problem. In this paper we go in a different direction. We propose a general quantum circuit able to implement any specific quantum circuit by just setting correctly the parameters. In other words, we propose a programmable quantum circuit. This opens the possibility to construct a real quantum computer where several different quantum operations can be realized in the same hardware. The configuration is proposed and its optical implementation is discussed.

scholarly journals Robustly decorrelating errors with mixed quantum gates

2021 ◽  
Author(s):  
Anthony Polloreno ◽  
Kevin Young
Keyword(s):  
Optimal Control ◽  
Quantum Information ◽  
Marked Reduction ◽  
Quantum Circuit ◽  
Physical Review ◽  
Quantum Gates ◽  
Superconducting Qubit ◽  
Convex Programs ◽  
Quantum Operations ◽  
Quantum Optimal Control

Abstract Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As shown by Hastings [1] and Campbell [2], by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs able to solve this problem, as well as a set of secondary objectives designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error. [1] M. B. Hastings, Quantum Information & Computation 17, 488 (2017). [2] E. Campbell, Physical Review A 95, 042306 (2017).

scholarly journals Cost function dependent barren plateaus in shallow parametrized quantum circuits

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. Cerezo ◽  
Akira Sone ◽  
Tyler Volkoff ◽  
Lukasz Cincio ◽  
Patrick J. Coles
Keyword(s):  
Cost Function ◽  
Large Scale ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Heuristic Methods ◽  
Practical Applications ◽  
Local Observables ◽  
Large Scale Simulations

AbstractVariational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is $${\mathcal{O}}(\mathrm{log}\,n)$$ O ( log n ) . Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Classical Physics ◽  
Core Set ◽  
The World ◽  
Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

scholarly journals DECOMPOSITION OF UNITARY MATRICES AND QUANTUM GATES

2013 ◽  
Vol 11 (01) ◽  
pp. 1350015 ◽  
Author(s):  
CHI-KWONG LI ◽  
REBECCA ROBERTS ◽  
XIAOYAN YIN
Keyword(s):  
General Scheme ◽  
Quantum Gate ◽  
Quantum Gates ◽  
Unitary Matrix ◽  
Additional Structure ◽  
Unitary Matrices ◽  
Decomposition Scheme ◽  
Single Qubit ◽  
Matlab Program

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2n-1(2n-1) fully controlled single-qubit gates chosen from 2n-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.

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