Exploiting Dynamic Quantum Circuits in a Quantum Algorithm with Superconducting Qubits

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks.

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An efficient quantum algorithm for the time evolution of parameterized circuits

Quantum ◽

10.22331/q-2021-07-28-512 ◽

2021 ◽

Vol 5 ◽

pp. 512

Author(s):

Stefano Barison ◽

Filippo Vicentini ◽

Giuseppe Carleo

Keyword(s):

Variational Principle ◽

Time Evolution ◽

Quantum Dynamics ◽

Quantum Algorithm ◽

Quantum Systems ◽

Small Time ◽

Quantum Circuits ◽

Time Step ◽

Optimal Linear ◽

Global Nature

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

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Analyzing Heuristic-based Randomized Search Strategies for the Quantum Circuit Compilation Problem

Fundamenta Informaticae ◽

10.3233/fi-2020-1942 ◽

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.

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Quantum-based algorithm and circuit design for bounded Knapsack optimization problem

Quantum Information and Computation ◽

10.26421/qic20.9-10-4 ◽

2020 ◽

Vol 20 (9&10) ◽

pp. 766-786

Author(s):

Wenjun Hou ◽

Marek Perkowski

Keyword(s):

Circuit Design ◽

Knapsack Problem ◽

Decision Problem ◽

Optimization Problem ◽

Quantum Algorithm ◽

Quantum Circuits ◽

Local Quantum ◽

Speed Up ◽

Grover Search ◽

Quantum Simulator

The Knapsack Problem is a prominent problem that is used in resource allocation and cryptography. This paper presents an oracle and a circuit design that verifies solutions to the decision problem form of the Bounded Knapsack Problem. This oracle can be used by Grover Search to solve the optimization problem form of the Bounded Knapsack Problem. This algorithm leverages the quadratic speed-up offered by Grover Search to achieve a quantum algorithm for the Knapsack Problem that shows improvement with regard to classical algorithms. The quantum circuits were designed using the Microsoft Q# Programming Language and verified on its local quantum simulator. The paper also provides analyses of the complexity and gate cost of the proposed oracle. The work in this paper is the first such proposed method for the Knapsack Optimization Problem.

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Automated Quantum Hardware Selection for Quantum Workflows

Electronics ◽

10.3390/electronics10080984 ◽

2021 ◽

Vol 10 (8) ◽

pp. 984

Author(s):

Benjamin Weder ◽

Johanna Barzen ◽

Frank Leymann ◽

Marie Salm

Keyword(s):

Quantum Computer ◽

Quantum Algorithm ◽

Software Tool ◽

Quantum Circuit ◽

Quantum Circuits ◽

Quantum Computers ◽

Workflow Model ◽

Selection For ◽

Selection Of

The execution of a quantum algorithm typically requires various classical pre- and post-processing tasks. Hence, workflows are a promising means to orchestrate these tasks, benefiting from their reliability, robustness, and features, such as transactional processing. However, the implementations of the tasks may be very heterogeneous and they depend on the quantum hardware used to execute the quantum circuits of the algorithm. Additionally, today’s quantum computers are still restricted, which limits the size of the quantum circuits that can be executed. As the circuit size often depends on the input data of the algorithm, the selection of quantum hardware to execute a quantum circuit must be done at workflow runtime. However, modeling all possible alternative tasks would clutter the workflow model and require its adaptation whenever a new quantum computer or software tool is released. To overcome this problem, we introduce an approach to automatically select suitable quantum hardware for the execution of quantum circuits in workflows. Furthermore, it enables the dynamic adaptation of the workflows, depending on the selection at runtime based on reusable workflow fragments. We validate our approach with a prototypical implementation and a case study demonstrating the hardware selection for Simon’s algorithm.

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Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

Quantum ◽

10.22331/q-2020-10-11-341 ◽

2020 ◽

Vol 4 ◽

pp. 341

Author(s):

Xiu-Zhe Luo ◽

Jin-Guo Liu ◽

Pan Zhang ◽

Lei Wang

Keyword(s):

Automatic Differentiation ◽

State Of The Art ◽

Algorithm Design ◽

Quantum Algorithm ◽

Quantum Circuits ◽

Gpu Acceleration ◽

Intermediate Representation ◽

Reversible Computing ◽

Open Source Framework ◽

Near Term

We introduce Yao, an extensible, efficient open-source framework for quantum algorithm design. Yao features generic and differentiable programming of quantum circuits. It achieves state-of-the-art performance in simulating small to intermediate-sized quantum circuits that are relevant to near-term applications. We introduce the design principles and critical techniques behind Yao. These include the quantum block intermediate representation of quantum circuits, a builtin automatic differentiation engine optimized for reversible computing, and batched quantum registers with GPU acceleration. The extensibility and efficiency of Yao help boost innovation in quantum algorithm design.

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Efficient quantum circuits for approximating the Jones polynomial

Quantum Information and Computation ◽

10.26421/qic8.5-8 ◽

2008 ◽

Vol 8 (5) ◽

pp. 489-500

Author(s):

Y. Nakajima ◽

Y. Kawano ◽

H. Sekigawa

Keyword(s):

Field Theory ◽

Jones Polynomial ◽

Quantum Algorithm ◽

Large Degree ◽

Quantum Circuits ◽

Quantum Field ◽

Degree Polynomial ◽

Root Of Unity ◽

Knot Invariant ◽

The Difference

Freedman, Kitaev, and Wang proved the equivalence between quantum field theory and quantum computation, and consequently showed that the problem of approximating the Jones polynomial (a knot invariant) at the fifth root of unity is BQP-complete. Recently, Aharonov, Jones, and Landau proposed a concrete quantum algorithm, called the AJL algorithm, that approximates the Jones polynomial at the $k$th root of unity in polynomial time. In this paper, we propose a new method for implementing the AJL algorithm, which improves the performance from $O(mn\log^2k)$ to $O(mn)$. Here, $n$ is the number of strands, $m$ is the number of the crossings in a braid. Since, in the AJL algorithm, $m$ and $k$ are assumed to be given as polynomials in $n$, the difference in the performance between the original implementation and our design is significant if $k$ is a large-degree polynomial.

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Characterization of a fabrication process for the integration of superconducting qubits and rapid-single-flux-quantum circuits

Superconductor Science and Technology ◽

10.1088/0953-2048/19/8/030 ◽

2006 ◽

Vol 19 (8) ◽

pp. 860-864 ◽

Cited By ~ 19

Author(s):

Maria Gabriella Castellano ◽

Leif Grönberg ◽

Pasquale Carelli ◽

Fabio Chiarello ◽

Carlo Cosmelli ◽

...

Keyword(s):

Fabrication Process ◽

Superconducting Qubits ◽

Quantum Circuits ◽

Flux Quantum ◽

Rapid Single Flux Quantum

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F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits

Entropy ◽

10.3390/e23101281 ◽

2021 ◽

Vol 23 (10) ◽

pp. 1281

Author(s):

Chiara Leadbeater ◽

Louis Sharrock ◽

Brian Coyle ◽

Marcello Benedetti

Keyword(s):

Fault Tolerant ◽

Quantum Algorithm ◽

Quantum Circuit ◽

Quantum Circuits ◽

Quantum Devices ◽

Leibler Divergence ◽

Variation Distance ◽

Near Term ◽

Generative Modelling

Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit born machine. In particular, we consider training a quantum circuit born machine using f-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any f-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the born machine. The first is based on f-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing f-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback–Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another f-divergence, namely, the Pearson divergence.

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Quantum circuit optimization using quantum Karnaugh map

Scientific Reports ◽

10.1038/s41598-020-72469-7 ◽

2020 ◽

Vol 10 (1) ◽

Cited By ~ 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.

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