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

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

Quantum ◽

10.22331/q-2021-10-06-559 ◽

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.

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Clifford recompilation for faster classical simulation of quantum circuits

Quantum ◽

10.22331/q-2019-08-05-170 ◽

2019 ◽

Vol 3 ◽

pp. 170

Author(s):

Hammam Qassim ◽

Joel J. Wallman ◽

Joseph Emerson

Keyword(s):

Fault Tolerant ◽

State Of The Art ◽

Quantum Circuit ◽

Quantum Circuits ◽

Monte Carlo Algorithm ◽

Quantum Devices ◽

Output State ◽

Classical Simulation ◽

Main Technique ◽

Near Term

Simulating quantum circuits classically is an important area of research in quantum information, with applications in computational complexity and validation of quantum devices. One of the state-of-the-art simulators, that of Bravyi et al, utilizes a randomized sparsification technique to approximate the output state of a quantum circuit by a stabilizer sum with a reduced number of terms. In this paper, we describe an improved Monte Carlo algorithm for performing randomized sparsification. This algorithm reduces the runtime of computing the approximate state by the factorℓ/m, whereℓandmare respectively the total and non-Clifford gate counts. The main technique is a circuit recompilation routine based on manipulating exponentiated Pauli operators. The recompilation routine also facilitates numerical search for Clifford decompositions of products of non-Clifford gates, which can further reduce the runtime in certain cases by reducing the 1-norm of the vector of expansion,‖a‖1. It may additionally lead to a framework for optimizing circuit implementations over a gate-set, reducing the overhead for state-injection in fault-tolerant implementations. We provide a concise exposition of randomized sparsification, and describe how to use it to estimate circuit amplitudes in a way which can be generalized to a broader class of gates and states. This latter method can be used to obtain additive error estimates of circuit probabilities with a faster runtime than the full techniques of Bravyi et al. Such estimates are useful for validating near-term quantum devices provided that the target probability is not exponentially small.

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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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A quantum convolutional neural network on NISQ devices

AAPPS Bulletin ◽

10.1007/s43673-021-00030-3 ◽

2022 ◽

Vol 32 (1) ◽

Author(s):

ShiJie Wei ◽

YanHu Chen ◽

ZengRong Zhou ◽

GuiLu Long

Keyword(s):

Neural Network ◽

Machine Learning ◽

Convolutional Neural Network ◽

Quantum Circuits ◽

Image Smoothing ◽

Quantum Devices ◽

Computing Complexity ◽

Machine Learning Model ◽

Mask Size ◽

Near Term

AbstractQuantum machine learning is one of the most promising applications of quantum computing in the noisy intermediate-scale quantum (NISQ) era. We propose a quantum convolutional neural network(QCNN) inspired by convolutional neural networks (CNN), which greatly reduces the computing complexity compared with its classical counterparts, with O((log2M)6) basic gates and O(m2+e) variational parameters, where M is the input data size, m is the filter mask size, and e is the number of parameters in a Hamiltonian. Our model is robust to certain noise for image recognition tasks and the parameters are independent on the input sizes, making it friendly to near-term quantum devices. We demonstrate QCNN with two explicit examples. First, QCNN is applied to image processing, and numerical simulation of three types of spatial filtering, image smoothing, sharpening, and edge detection is performed. Secondly, we demonstrate QCNN in recognizing image, namely, the recognition of handwritten numbers. Compared with previous work, this machine learning model can provide implementable quantum circuits that accurately corresponds to a specific classical convolutional kernel. It provides an efficient avenue to transform CNN to QCNN directly and opens up the prospect of exploiting quantum power to process information in the era of big data.

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Error mitigation with Clifford quantum-circuit data

Quantum ◽

10.22331/q-2021-11-26-592 ◽

2021 ◽

Vol 5 ◽

pp. 592

Author(s):

Piotr Czarnik ◽

Andrew Arrasmith ◽

Patrick J. Coles ◽

Lukasz Cincio

Keyword(s):

State Energy ◽

Quantum Computer ◽

Quantum Circuit ◽

Training Data ◽

Quantum Circuits ◽

Accurate Estimation ◽

Error Mitigation ◽

Order Of Magnitude ◽

Quantum Observables ◽

Near Term

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

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Exploiting Dynamic Quantum Circuits in a Quantum Algorithm with Superconducting Qubits

Physical Review Letters ◽

10.1103/physrevlett.127.100501 ◽

2021 ◽

Vol 127 (10) ◽

Cited By ~ 1

Author(s):

A. D. Córcoles ◽

Maika Takita ◽

Ken Inoue ◽

Scott Lekuch ◽

Zlatko K. Minev ◽

...

Keyword(s):

Quantum Algorithm ◽

Superconducting Qubits ◽

Quantum Circuits

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

Quantum Information Processing ◽

10.1007/s11128-020-02800-8 ◽

2020 ◽

Vol 19 (9) ◽

Author(s):

Mahmoud Mahdian ◽

H. Davoodi Yeganeh

Keyword(s):

Open System ◽

Quantum Algorithm ◽

Near Term

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A Simple and Efficient Tensor Calculus

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i04.5881 ◽

2020 ◽

Vol 34 (04) ◽

pp. 4527-4534

Author(s):

Sören Laue ◽

Matthias Mitterreiter ◽

Joachim Giesen

Keyword(s):

Machine Learning ◽

Efficient Method ◽

Automatic Differentiation ◽

State Of The Art ◽

Higher Order ◽

Tensor Representation ◽

Tensor Calculus ◽

Correct Algorithm ◽

Previous State ◽

Derivatives Of

Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of these expressions. Recently, an algorithm for computing higher order derivatives of tensor expressions like Jacobians or Hessians has been introduced that is a few orders of magnitude faster than previous state-of-the-art approaches. Unfortunately, the approach is based on Ricci notation and hence cannot be incorporated into automatic differentiation frameworks like TensorFlow, PyTorch, autograd, or JAX that use the simpler Einstein notation. This leaves two options, to either change the underlying tensor representation in these frameworks or to develop a new, provably correct algorithm based on Einstein notation. Obviously, the first option is impractical. Hence, we pursue the second option. Here, we show that using Ricci notation is not necessary for an efficient tensor calculus and develop an equally efficient method for the simpler Einstein notation. It turns out that turning to Einstein notation enables further improvements that lead to even better efficiency.

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Amplitude estimation without phase estimation

Quantum Information Processing ◽

10.1007/s11128-019-2565-2 ◽

2020 ◽

Vol 19 (2) ◽

Cited By ~ 10

Author(s):

Yohichi Suzuki ◽

Shumpei Uno ◽

Rudy Raymond ◽

Tomoki Tanaka ◽

Tamiya Onodera ◽

...

Keyword(s):

Measurement Data ◽

Likelihood Estimation ◽

Estimation Algorithm ◽

Quantum Circuits ◽

Phase Estimation ◽

Amplitude Estimation ◽

Quantum Amplitude ◽

Phase Estimation Algorithm ◽

Near Term ◽

Quantum Speedup

AbstractThis paper focuses on the quantum amplitude estimation algorithm, which is a core subroutine in quantum computation for various applications. The conventional approach for amplitude estimation is to use the phase estimation algorithm, which consists of many controlled amplification operations followed by a quantum Fourier transform. However, the whole procedure is hard to implement with current and near-term quantum computers. In this paper, we propose a quantum amplitude estimation algorithm without the use of expensive controlled operations; the key idea is to utilize the maximum likelihood estimation based on the combined measurement data produced from quantum circuits with different numbers of amplitude amplification operations. Numerical simulations we conducted demonstrate that our algorithm asymptotically achieves nearly the optimal quantum speedup with a reasonable circuit length.

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