scholarly journals Incoherent quantum algorithm dynamics of an open system with near-term devices

2020 ◽  
Vol 19 (9) ◽  
Author(s):  
Mahmoud Mahdian ◽  
H. Davoodi Yeganeh
Keyword(s):  
Open System ◽  
Quantum Algorithm ◽  
Near Term

scholarly journals Qulacs: a fast and versatile quantum circuit simulator for research purpose

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 559
Author(s):  
Yasunari Suzuki ◽  
Yoshiaki Kawase ◽  
Yuya Masumura ◽  
Yuria Hiraga ◽  
Masahiro Nakadai ◽  
...  
Keyword(s):  
Fault Tolerant ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Research Purpose ◽  
Numerical Techniques ◽  
Circuit Simulator ◽  
Speed Up ◽  
Near Term

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.

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

Quantum ◽  
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.

scholarly journals Quantum advantage with shallow circuits

Science ◽  
2018 ◽  
Vol 362 (6412) ◽  
pp. 308-311 ◽  
Author(s):  
Sergey Bravyi ◽  
David Gosset ◽  
Robert König
Keyword(s):  
Quadratic Forms ◽  
Nearest Neighbor ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Nonlocality ◽  
Binary Quadratic Forms ◽  
Time Period ◽  
Speed Up ◽  
Active Debate ◽  
Near Term

Quantum effects can enhance information-processing capabilities and speed up the solution of certain computational problems. Whether a quantum advantage can be rigorously proven in some setting or demonstrated experimentally using near-term devices is the subject of active debate. We show that parallel quantum algorithms running in a constant time period are strictly more powerful than their classical counterparts; they are provably better at solving certain linear algebra problems associated with binary quadratic forms. Our work gives an unconditional proof of a computational quantum advantage and simultaneously pinpoints its origin: It is a consequence of quantum nonlocality. The proposed quantum algorithm is a suitable candidate for near-future experimental realizations, as it requires only constant-depth quantum circuits with nearest-neighbor gates on a two-dimensional grid of qubits (quantum bits).

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

Entropy ◽  
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.

scholarly journals Near-term quantum algorithms for linear systems of equations with regression loss functions

2021 ◽  
Vol 23 (11) ◽  
pp. 113021
Author(s):  
Hsin-Yuan Huang ◽  
Kishor Bharti ◽  
Patrick Rebentrost
Keyword(s):  
Linear Systems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Systems Of Equations ◽  
Quantum Devices ◽  
Near Term ◽  
Variational Algorithms ◽  
Core Idea ◽  
Classical Combination ◽  
Linear Systems Of Equations

Abstract Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2300 × 2300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

scholarly journals Quantum walk-based portfolio optimisation

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 513
Author(s):  
N. Slate ◽  
E. Matwiejew ◽  
S. Marsh ◽  
J. B. Wang
Keyword(s):  
Potential Application ◽  
Quantum Algorithm ◽  
Quantum Walk ◽  
Quantum Computers ◽  
Portfolio Optimisation ◽  
High Quality ◽  
Intermediate Scale ◽  
Portfolio Rebalancing ◽  
Optimisation Algorithm ◽  
Near Term

This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale quantum computers. Recent work by Hodson et al. (2019) explored potential application of hybrid quantum-classical algorithms to the problem of financial portfolio rebalancing. In particular, they deal with the portfolio optimisation problem using the Quantum Approximate Optimisation Algorithm and the Quantum Alternating Operator Ansatz. In this paper, we demonstrate substantially better performance using a newly developed Quantum Walk Optimisation Algorithm in finding high-quality solutions to the portfolio optimisation problem.

scholarly journals Quantum annealing initialization of the quantum approximate optimization algorithm

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 491
Author(s):  
Stefan H. Sack ◽  
Maksym Serbyn
Keyword(s):  
Optimization Algorithm ◽  
Quantum Algorithm ◽  
External Parameter ◽  
Quantum Annealing ◽  
Time Step ◽  
Quantum Devices ◽  
Approximate Optimization ◽  
Optimal Value ◽  
Random Initialization ◽  
Near Term

The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.

scholarly journals Extending C++ for Heterogeneous Quantum-Classical Computing

2021 ◽  
Vol 2 (2) ◽  
pp. 1-36
Author(s):  
Alexander Mccaskey ◽  
Thien Nguyen ◽  
Anthony Santana ◽  
Daniel Claudino ◽  
Tyler Kharazi ◽  
...  
Keyword(s):  
Forward Error Correction ◽  
Quantum Algorithm ◽  
System Level ◽  
Circuit Optimization ◽  
Language Extension ◽  
Quantum Programming ◽  
Near Term ◽  
Classical Computing ◽  
High Level ◽  
Forward Error

We present qcor—a language extension to C++ and compiler implementation that enables heterogeneous quantum-classical programming, compilation, and execution in a single-source context. Our work provides a first-of-its-kind C++ compiler enabling high-level quantum kernel (function) expression in a quantum-language agnostic manner, as well as a hardware-agnostic, retargetable compiler workflow targeting a number of physical and virtual quantum computing backends. qcor leverages novel Clang plugin interfaces and builds upon the XACC system-level quantum programming framework to provide a state-of-the-art integration mechanism for quantum-classical compilation that leverages the best from the community at-large. qcor translates quantum kernels ultimately to the XACC intermediate representation, and provides user-extensible hooks for quantum compilation routines like circuit optimization, analysis, and placement. This work details the overall architecture and compiler workflow for qcor, and provides a number of illuminating programming examples demonstrating its utility for near-term variational tasks, quantum algorithm expression, and feed-forward error correction schemes.

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