scholarly journals Quantum arithmetic and numerical analysis using Repeat-Until-Success circuits

2016 ◽  
pp. 134-178 ◽  
Author(s):  
Nathan Wiebe ◽  
Martin Roetteler
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Circuit Synthesis ◽  
Small Quantum ◽  
Approximate Synthesis ◽  
Quantum Arithmetic ◽  
And Inversion ◽  
Synthesis Approach ◽  
Computable Functions

We develop a method for approximate synthesis of single-qubit rotations of the form e−if(φ1,...,φk)X that is based on the Repeat-Until-Success (RUS) framework for quantum circuit synthesis. We demonstrate how smooth computable functions f can be synthesized from two basic primitives. This synthesis approach constitutes a manifestly quantum form of arithmetic that differs greatly from the approaches commonly used in quantum algorithms. The key advantage of our approach is that it requires far fewer qubits than existing approaches: as a case in point, we show that using as few as 3 ancilla qubits, one can obtain RUS circuits for approximate multiplication and reciprocals. We also analyze the costs of performing multiplication and inversion on a quantum computer using conventional approaches and find that they can require too many qubits to execute on a small quantum computer, unlike our approach.

scholarly journals Practical Quantum Computing

2021 ◽  
Vol 2 (1) ◽  
pp. 1-35
Author(s):  
Adrien Suau ◽  
Gabriel Staffelbach ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Equation Solving ◽  
Small Quantum ◽  
Quantum Wave ◽  
Variational Algorithms ◽  
The One

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

scholarly journals Developing A Quantum Circuit Simulator API

2015 ◽  
Vol 67 (1) ◽  
pp. 168-173
Author(s):  
Stancu Mihai Dorian ◽  
Popa Emil Marin
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Circuit Simulator ◽  
Design And Implementation ◽  
Computer Scientists

Abstract In this paper we propose the design and implementation of a quantum circuit simulator API. Currently the API allows users to implement, debug and test the following two quantum algorithms: Bernstein-Vazirani’s algorithm and Simon’s Algorithm. The goal is to create a framework that will allow quantum computer scientists to easily develop new quantum algorithms.

scholarly journals A random walk approach to quantum algorithms

2006 ◽  
Vol 364 (1849) ◽  
pp. 3407-3422 ◽  
Author(s):  
Vivien M Kendon
Keyword(s):  
Random Walk ◽  
Quantum Dynamics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Walk ◽  
Quantum Random Walk ◽  
Small Quantum ◽  
Starting Point ◽  
Quantum Version ◽  
Speed Up

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

scholarly journals Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 572
Author(s):  
Saad Yalouz ◽  
Bruno Senjean ◽  
Filippo Miatto ◽  
Vedran Dunjko
Keyword(s):  
Hubbard Model ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Experimental System ◽  
Quantum Circuit ◽  
Continuous Variable ◽  
Computer Application ◽  
Strongly Correlated ◽  
Many Body ◽  
Boson Systems

Variational quantum algorithms (VQA) are considered as some of the most promising methods to determine the properties of complex strongly correlated quantum many-body systems, especially from the perspective of devices available in the near term. In this context, the development of efficient quantum circuit ansatze to encode a many-body wavefunction is one of the keys for the success of a VQA. Great efforts have been invested to study the potential of current quantum devices to encode the eigenstates of fermionic systems, but little is known about the encoding of bosonic systems. In this work, we investigate the encoding of the ground state of the (simple but rich) attractive Bose-Hubbard model using a Continuous-Variable (CV) photonic-based quantum circuit. We introduce two different ansatz architectures and demonstrate that the proposed continuous variable quantum circuits can efficiently encode (with a fidelity higher than 99%) the strongly correlated many-boson wavefunction with just a few layers, in all many-body regimes and for different number of bosons and initial states. Beyond the study of the suitability of the ansatz to approximate the ground states of many-boson systems, we also perform initial evaluations of the use of the ansatz in a variational quantum eigensolver algorithm to find it through energy minimization. To this end we also introduce a scheme to measure the Hamiltonian energy in an experimental system, and study the effect of sampling noise.

scholarly journals Quantum Circuit Synthesis Using Projective Simulation

2021 ◽  
Vol 24 (67) ◽  
pp. 90-101
Author(s):  
Otto Menegasso Pires ◽  
Eduardo Inacio Duzzioni ◽  
Jerusa Marchi ◽  
Rafael De Santiago
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Optimization Techniques ◽  
Error Tolerance ◽  
Quantum Circuits ◽  
Quantum Decoherence ◽  
Circuit Synthesis ◽  
Circuit Optimization ◽  
Learning Technique

Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use.These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored.We studied the viability of using Projective Simulation, a reinforcement learning technique, to tackle the problem of quantum circuit synthesis. The agent had the task of creating quantum circuits up to 5 qubits. Our simulations demonstrated that the agent had a good performance but its capacity for learning new circuits decreased as the number of qubits increased.

scholarly journals Classification with Quantum Neural Networks on Near Term Processors

2020 ◽  
Author(s):  
Edward Farhi ◽  
Hartmut Neven
Keyword(s):  
Quantum State ◽  
Quantum Computer ◽  
Binary Classification ◽  
Quantum Circuit ◽  
Input State ◽  
Data Sets ◽  
Quantum Neural Network ◽  
Small Quantum ◽  
Classical Simulation ◽  
Near Term

We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts on an input quantum state. For binary classification a single Pauli operator is measured on a designated readout qubit. The measured output is the quantum neural network’s predictor of the binary label of the input state. We show through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. We then discuss presenting the data as quantum superpositions of computational basis states corresponding to different label values. Here we show through simulation that learning is possible. We consider using our QNN to learn the label of a general quantum state. By example we show that this can be done. Our work is exploratory and relies on the classical simulation of small quantum systems. The QNN proposed here was designed with near-term quantum processors in mind. Therefore it will be possible to run this QNN on a near term gate model quantum computer where its power can be explored beyond what can be explored with simulation.

scholarly journals Quantum circuit optimization using quantum Karnaugh map

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
J.-H. Bae ◽  
Paul M. Alsing ◽  
Doyeol Ahn ◽  
Warner A. Miller
Keyword(s):  
Quantum Computation ◽  
Quantum Algorithms ◽  
Optimization Technique ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Circuit Optimization ◽  
General Technique ◽  
Small Quantum

Abstract Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. Major obstacle to this goal is the large number of elemental quantum gates to build even small quantum circuits. Here, we propose and demonstrate a general technique that significantly reduces the number of elemental gates to build quantum circuits. This is impactful for the design of quantum circuits, and we show below this could reduce the number of gates by 60% and 46% for the four- and five-qubit Toffoli gates, two key quantum circuits, respectively, as compared with simplest known decomposition. Reduced circuit complexity often goes hand-in-hand with higher efficiency and bandwidth. The quantum circuit optimization technique proposed in this work would provide a significant step forward in the optimization of quantum circuits and quantum algorithms, and has the potential for wider application in quantum computation.

scholarly journals Quantum supremacy in end-to-end intelligent IT. PT. III. Quantum software engineering – quantum approximate optimization algorithm on small quantum processors

2020 ◽  
pp. 115-176
Author(s):  
Olga Ivancova ◽  
Vladimir Korenkov ◽  
Olga Tyatyushkina ◽  
Sergey Ulyanov ◽  
Toshio Fukuda
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Logic Gates ◽  
Circuit Implementation ◽  
New Approach ◽  
Quantum Logic Gates ◽  
Small Quantum ◽  
Universal Quantum ◽  
Arbitrary Quantum

Principles and methodologies of quantum algorithmic gate-based design on small quantum computer described. The possibilities of quantum algorithmic gates simulation on classical computers discussed. A new approach to a circuit implementation design of quantum algorithm gates for fast quantum massive parallel computing presented. SW & HW support sophisticated smart toolkit of supercomputing accelerator of quantum algorithm simulation on small quantum programmable computer algorithm gate (that can program in SW to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates) described

scholarly journals Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications

2021 ◽  
Vol 251 ◽  
pp. 03023
Author(s):  
Wonho Jang ◽  
Koji Terashi ◽  
Masahiko Saito ◽  
Christian W. Bauer ◽  
Benjamin Nachman ◽  
...  
Keyword(s):  
High Energy Physics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
High Energy ◽  
Circuit Optimization ◽  
Final State ◽  
State Radiation

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of quantum devices produced over a next decade. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and effcient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.

Transformation of quantum states using uniformly controlled rotations

2005 ◽  
Vol 5 (6) ◽  
pp. 467-473
Author(s):  
M. Mottonen ◽  
J. J. Vartiainen ◽  
V. Bergholm ◽  
M. M. Salomaa
Keyword(s):  
Pure State ◽  
Unitary Transformation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
The State ◽  
Quantum States ◽  
State Transformation ◽  
Quantum Register ◽  
Analytic Expression

We consider a unitary transformation which maps any given pure state of an $n$-qubit quantum register into another one. This transformation has applications in the initialization of a quantum computer, and also in some quantum algorithms. Employing uniformly controlled rotations, we present a quantum circuit of $2^{n+2}-4n-4$ CNOT gates and $2^{n+2}-5$ one-qubit elementary rotations that effects the state transformation. The complexity of the circuit is noticeably lower than the previously published results. Moreover, we present an analytic expression for the rotation angles needed for the transformation.

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