scholarly journals A two-qubit photonic quantum processor and its application to solving systems of linear equations

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Stefanie Barz ◽  
Ivan Kassal ◽  
Martin Ringbauer ◽  
Yannick Ole Lipp ◽  
Borivoje Dakić ◽  
...  
Keyword(s):  
Large Scale ◽  
Linear Equations ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Single Qubit ◽  
Quantum Processor ◽  
Systems Of Linear Equations ◽  
Significant Obstacle

Abstract Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations.

scholarly journals Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

2022 ◽  
Vol 3 (1) ◽  
pp. 1-37
Author(s):  
Almudena Carrera Vazquez ◽  
Ralf Hiptmair ◽  
Stefan Woerner
Keyword(s):  
Necessary Conditions ◽  
Linear Equations ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Richardson Extrapolation ◽  
Classical Simulation ◽  
Hamiltonian Simulation ◽  
Systems Of Linear Equations ◽  
Amplitude Amplification ◽  
Theoretical Results

We present a quantum algorithm to solve systems of linear equations of the form Ax = b , where A is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of O (1/√ε, poly (log κ, log N )), where N denotes the number of equations, ε is the accuracy, and κ the condition number. The repeat-until-success algorithm has to be run O (κ/(1-ε)) times to succeed, leveraging amplitude amplification, and needs to be sampled O (1/ε 2 ) times. Thus, the algorithm achieves an exponential improvement with respect to N over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation, and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/√ ε instead of 1/ε. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.

scholarly journals New Algorithms for Secure Outsourcing of Large-Scale Systems of Linear Equations

2020 ◽  
Vol 9 (5) ◽  
pp. 545-550
Keyword(s):  
Cloud Computing ◽  
Distributed Computing ◽  
Data Storage ◽  
Large Scale ◽  
Homomorphic Encryption ◽  
Linear Equations ◽  
Force Transmission ◽  
Large Scale Systems ◽  
Secure Outsourcing ◽  
Systems Of Linear Equations

Cloud computing is the on-request accessibility of computer system resources, specially data storage and computing power, without direct dynamic management by the client. In the simplest terms, cloud computing means storing and accessing data and programs over the Internet instead of your computer’s hard drive. Along the improvement of cloud computing, more and more applications are migrated into the cloud. A significant element of distributed computing is pay-more only as costs arise. Distributed computing gives strong computational capacity to the general public at diminished cost that empowers clients with least computational assets to redistribute their huge calculation outstanding burdens to the cloud, and monetarily appreciate the monstrous computational force, transmission capacity, stockpiling, and even reasonable programming that can be partaken in a compensation for each utilization way Tremendous bit of leeway is the essential objective that forestalls the wide scope of registering model for clients when their secret information are expended during the figuring procedure. Critical thinking is a system to arrive at the pragmatic objective of specific instruments that tackles the issues as well as shield from pernicious practices.. In this paper, we examine secure outsourcing for large-scale systems of linear equations, which are the most popular problems in various engineering disciplines. Linear programming is an operation research technique formulates private data by the customer for LP problem as a set of matrices and vectors, to develop a set of efficient privacypreserving problem transformation techniques, which allow customers to transform original LP problem into some arbitrary one while protecting sensitive input/output information. Identify that LP problem solving in Cloud component is efficient extra cost on cloud server. In this paper we are utilizing Homomorphic encryption system to increase the performance and time efficiency

scholarly journals Quantum gate teleportation between separated qubits in a trapped-ion processor

Science ◽  
2019 ◽  
Vol 364 (6443) ◽  
pp. 875-878 ◽  
Author(s):  
Yong Wan ◽  
Daniel Kienzler ◽  
Stephen D. Erickson ◽  
Karl H. Mayer ◽  
Ting Rei Tan ◽  
...  
Keyword(s):  
Confidence Level ◽  
Large Scale ◽  
Ion Trap ◽  
Quantum Gate ◽  
Quantum Computers ◽  
Mixed Species ◽  
Cnot Gate ◽  
Classical Communication ◽  
Trapped Ion ◽  
Single Qubit

Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval (0.845, 0.872) at the 95% confidence level. The implementation combines ion shuttling with individually addressed single-qubit rotations and detections, same- and mixed-species two-qubit gates, and real-time conditional operations, thereby demonstrating essential tools for scaling trapped-ion quantum computers combined in a single device.

LSI-BASED EFFICIENT EMULATION OVERCOMING ALGORITHMIC RESTRICTIONS INHERENT IN QUANTUM COMPUTERS

2003 ◽  
Vol 03 (04) ◽  
pp. C9-C17
Author(s):  
MINORU FUJISHIMA
Keyword(s):  
Periodic Function ◽  
Integrated Circuit ◽  
High Speed ◽  
Large Scale ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Np Problems

Quantum computers are believed to perform high-speed calculations, compared with conventional computers. However, the quantum computer solves NP (non-deterministic polynomial) problems at a high speed only when a periodic function can be used in the process of calculation. To overcome the restrictions stemming from the quantum algorithm, we are studying the emulation by a LSI (large scale integrated circuit). In this report, first, it is explained why a periodic function is required for the algorithm of a quantum computer. Then, it is shown that the LSI emulator can solve NP problems at a high speed without using a periodic function.

scholarly journals Accelerating advanced preconditioning methods on hybrid architectures

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Ernesto Dufrechou
Keyword(s):  
Linear Systems ◽  
Large Scale ◽  
Krylov Subspace ◽  
Linear Equations ◽  
Memory Systems ◽  
Sparse Linear Systems ◽  
Data Parallel ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Computational Bottleneck

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Krylov subspace methods that relies on a modern inverse-based multilevel ILU (incomplete LU) preconditioning technique.We present new data-parallel versions of the preconditioner and the most important solvers contained in the package that significantly improve its performance without affecting its accuracy. Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration. The results obtained show a sensible reduction in the runtime of the methods, as well as the possibility of addressing large-scale problems efficiently.

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