scholarly journals Closed timelike curves make quantum and classical computing equivalent

2008 ◽  
Vol 465 (2102) ◽  
pp. 631-647 ◽  
Author(s):  
Scott Aaronson ◽  
John Watrous
Keyword(s):  
Fixed Point ◽  
Quantum Information ◽  
Consistency Condition ◽  
Quantum Circuit ◽  
Polynomial Space ◽  
Closed Timelike Curves ◽  
Large Power ◽  
Causal Consistency ◽  
Classical Computing ◽  
Conventional Computer

While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to non-trivial insights into general relativity, quantum information and other areas. In this paper, we show that, if CTCs existed, quantum computers would be no more powerful than classical computers: both would have the (extremely large) power of the complexity class polynomial space ( ), consisting of all problems solvable by a conventional computer using a polynomial amount of memory. This solves an open problem proposed by one of us in 2005, and gives an essentially complete understanding of computational complexity in the presence of CTCs. Following the work of Deutsch, we treat a CTC as simply a region of spacetime where a ‘causal consistency’ condition is imposed, meaning that nature has to produce a (probabilistic or quantum) fixed point of some evolution operator. Our conclusion is then a consequence of the following theorem: given any quantum circuit (not necessarily unitary), a fixed point of the circuit can be (implicitly) computed in . This theorem might have independent applications in quantum information.

An FPGA-based quantum circuit emulation framework using heisenberg representation

2018 ◽  
Vol 16 (06) ◽  
pp. 1850052
Author(s):  
Y. H. Lee ◽  
M. Khalil-Hani ◽  
M. N. Marsono
Keyword(s):  
Large Scale ◽  
Scale Up ◽  
Quantum Circuit ◽  
Theoretical Research ◽  
Resource Requirement ◽  
Heisenberg Representation ◽  
Speed Up ◽  
Computing Platforms ◽  
Classical Computing

While physical realization of practical large-scale quantum computers is still ongoing, theoretical research of quantum computing applications is facilitated on classical computing platforms through simulation and emulation methods. Nevertheless, the exponential increase in resource requirement with the increase in the number of qubits is an inherent issue in classical modeling of quantum systems. In the effort to alleviate the critical scalability issue in existing FPGA emulation works, a novel FPGA-based quantum circuit emulation framework based on Heisenberg representation is proposed in this paper. Unlike previous works that are restricted to the emulations of quantum circuits of small qubit sizes, the proposed FPGA emulation framework can scale-up to 120-qubit on Altera Stratix IV FPGA for the stabilizer circuit case study while providing notable speed-up over the equivalent simulation model.

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 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 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 Unitary t-Designs from Relaxed Seeds

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 92
Author(s):  
Rawad Mezher ◽  
Joe Ghalbouni ◽  
Joseph Dgheim ◽  
Damian Markham
Keyword(s):  
Quantum Information ◽  
Unitary Group ◽  
Quantum Circuit ◽  
Do So

The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary t-design is designed to tackle this challenge in an efficient way, yet constructions to date rely on heavy constraints. In particular, they are composed of ensembles of unitaries which, for technical reasons, must contain inverses and whose entries are algebraic. In this work, we reduce the requirements for generating an ε -approximate unitary t-design. To do so, we first construct a specific n-qubit random quantum circuit composed of a sequence of randomly chosen 2-qubit gates, chosen from a set of unitaries which is approximately universal on U ( 4 ) , yet need not contain unitaries and their inverses nor are in general composed of unitaries whose entries are algebraic; dubbed r e l a x e d seed. We then show that this relaxed seed, when used as a basis for our construction, gives rise to an ε -approximate unitary t-design efficiently, where the depth of our random circuit scales as p o l y ( n , t , l o g ( 1 / ε ) ) , thereby overcoming the two requirements which limited previous constructions. We suspect the result found here is not optimal and can be improved; particularly because the number of gates in the relaxed seeds introduced here grows with n and t. We conjecture that constant sized seeds such as those which are usually present in the literature are sufficient.

scholarly journals Quantum circuit cutting with maximum-likelihood tomography

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Michael A. Perlin ◽  
Zain H. Saleem ◽  
Martin Suchara ◽  
James C. Osborn
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Numerical Experiments ◽  
Measurement Data ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Devices ◽  
Standard Tool ◽  
Classical Computing

AbstractWe introduce maximum-likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution for the output of a quantum circuit, given the measurement data obtained from the circuit’s fragments. We demonstrate the benefits of MLFT for accurately estimating the output of a fragmented quantum circuit with numerical experiments on random unitary circuits. Finally, we show that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.

scholarly journals QUANTUM COMPUTING

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Titu-Marius I. Băjenescu ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Computer Science ◽  
Quantum Computer ◽  
Quantum Bits ◽  
Data Object ◽  
Quantum Phenomena ◽  
Classical Computing ◽  
Scientific Fields ◽  
Conventional Computer

The quantum computer, is a "supercomputer" that relies on the phenomena of quantum mechanics to perform operations on data. Object of suppositions, sometimes farfetched, quantum mechanics gave birth to the quantum computer, a machine capable of processing data tens of millions of times faster than a conventional computer. A quantum computer doesn't use the same memory as a conventional computer. Rather than a sequence of 0 and 1, it works with qubits or quantum bits. The quantum computer is a combination of two major scientific fields: quantum mechanics and computer science. Quantum mechanics, on which this computer is based, governs the movement of bodies in the atomic, molecular and corpuscular domains, is a theory whose logic is totally contrary to intuition and it is essential to use mathematics to fully grasp it. Quantum computing is the sub-domain of computer science that deals with quantum computers using quantum mechanical phenomena, as opposed to those of electricity exclusively, for so-called "classical" computing. The quantum phenomena used are quantum entanglement and superposition. The article examines some aspects related to the development, operation, advantages and difficulties, applications and future of the quantum computer.

scholarly journals Quantum K-Means Clustering Method For Detecting Heart Disease Using Quantum Circuit Approach

2021 ◽  
Author(s):  
Kavitha S S ◽  
Narasimha Kaulgud
Keyword(s):  
Heart Disease ◽  
Clustering Algorithm ◽  
Performance Metrics ◽  
Quantum Circuit ◽  
Machine Learning Algorithms ◽  
Quantum Computers ◽  
Clustering Method ◽  
Main Approach ◽  
Speed Up ◽  
Classical Computing

Abstract The development of Noisy Intermediate Scale Quantum computers is expected to signify potential advantages of quantum computing over classical computing. This paper focuses on quantum paradigm usage to speed up unsupervised machine learning algorithms particularly the K-means clustering method. The main approach is to build a quantum circuit that performs the distance calculation required for the clustering process. This proposed technique is a collaboration of data mining techniques with quantum computation. Initially extracted heart disease dataset is preprocessed and classical K-means performance is evaluated. Later, the quantum concept is applied to the classical approach of the clustering algorithm. The comparative analysis is performed between quantum and classical processing to check performance metrics.

scholarly journals Introduction to Quantum Gates : Implementation of Single and Multiple Qubit Gates

2021 ◽  
pp. 385-392
Author(s):  
Ropa Roy ◽  
Asoke Nath
Keyword(s):  
Quantum Logic ◽  
Digital Circuits ◽  
Logic Gate ◽  
Logic Gates ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Quantum Logic Gate ◽  
Quantum Logic Gates ◽  
Classical Computing ◽  
Superposition States

A quantum gate or quantum logic gate is an elementary quantum circuit working on a small number of qubits. It means that quantum gates can grasp two primary feature of quantum mechanics that are entirely out of reach for classical gates : superposition and entanglement. In simpler words quantum gates are reversible. In classical computing sets of logic gates are connected to construct digital circuits. Similarly, quantum logic gates operates on input states that are generally in superposition states to compute the output. In this paper the authors will discuss in detail what is single and multiple qubit gates and scope and challenges in quantum gates.

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