scholarly journals On the Expressibility and Overfitting of Quantum Circuit Learning

2021 ◽  
Vol 2 (2) ◽  
pp. 1-24
Author(s):  
Chih-Chieh Chen ◽  
Masaya Watabe ◽  
Kodai Shiba ◽  
Masaru Sogabe ◽  
Katsuyoshi Sakamoto ◽  
...  
Keyword(s):  
Performance Improvement ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
High Dimensional ◽  
Supporting Evidence ◽  
Generalization Error ◽  
Vc Dimension ◽  
Learning Problem ◽  
Quantum Devices ◽  
Function Approximator

Applying quantum processors to model a high-dimensional function approximator is a typical method in quantum machine learning with potential advantage. It is conjectured that the unitarity of quantum circuits provides possible regularization to avoid overfitting. However, it is not clear how the regularization interplays with the expressibility under the limitation of current Noisy-Intermediate Scale Quantum devices. In this article, we perform simulations and theoretical analysis of the quantum circuit learning problem with hardware-efficient ansatz. Thorough numerical simulations show that the expressibility and generalization error scaling of the ansatz saturate when the circuit depth increases, implying the automatic regularization to avoid the overfitting issue in the quantum circuit learning scenario. This observation is supported by the theory on PAC learnability, which proves that VC dimension is upper bounded due to the locality and unitarity of the hardware-efficient ansatz. Our study provides supporting evidence for automatic regularization by unitarity to suppress overfitting and guidelines for possible performance improvement under hardware constraints.

scholarly journals WPG-Controlled Quantum BDD Circuits with BDD Architecture on GaAs-Based Hexagonal Nanowire Network Structure

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Hong-Quan ZHao ◽  
Seiya Kasai
Keyword(s):  
Quantum Logic ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Combinational Circuit ◽  
Quantum Devices ◽  
Binary Decision ◽  
One Dimensional ◽  
Nanowire Network ◽  
Dimensional Electron Gas ◽  
Very High

One-dimensional nanowire quantum devices and basic quantum logic AND and OR unit on hexagonal nanowire units controlled by wrap gate (WPG) were designed and fabricated on GaAs-based one-dimensional electron gas (1-DEG) regular nanowire network with hexagonal topology. These basic quantum logic units worked correctly at 35 K, and clear quantum conductance was achieved on the node device, logic AND circuit unit, and logic OR circuit unit. Binary-decision-diagram- (BDD-) based arithmetic logic unit (ALU) is realized on GaAs-based regular nanowire network with hexagonal topology by the same fabrication method as that of the quantum devices and basic circuits. This BDD-based ALU circuit worked correctly at room temperature. Since these quantum devices and circuits are basic units of the BDD ALU combinational circuit, the possibility of integrating these quantum devices and basic quantum circuits into the BDD-based quantum circuit with more complicated structures was discussed. We are prospecting the realization of quantum BDD combinational circuitries with very small of energy consumption and very high density of integration.

scholarly journals Clifford recompilation for faster classical simulation of quantum circuits

Quantum ◽  
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.

scholarly journals Layerwise learning for quantum neural networks

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Andrea Skolik ◽  
Jarrod R. McClean ◽  
Masoud Mohseni ◽  
Patrick van der Smagt ◽  
Martin Leib
Keyword(s):  
Learning Strategy ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Devices ◽  
Error Surface ◽  
Effective Training ◽  
One Step ◽  
Near Term ◽  
Lower Test ◽  
Learning Schemes

AbstractWith the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.

scholarly journals Quantum circuit cutting with maximum-likelihood tomography

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Michael A. Perlin ◽  
Zain H. Saleem ◽  
Martin Suchara ◽  
James C. Osborn
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Numerical Experiments ◽  
Measurement Data ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Devices ◽  
Standard Tool ◽  
Classical Computing

AbstractWe introduce maximum-likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution for the output of a quantum circuit, given the measurement data obtained from the circuit’s fragments. We demonstrate the benefits of MLFT for accurately estimating the output of a fragmented quantum circuit with numerical experiments on random unitary circuits. Finally, we show that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.

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 Estimating Gibbs partition function with quantum Clifford sampling

2022 ◽  
Author(s):  
Yusen Wu ◽  
Jingbo B Wang
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Sampling Technique ◽  
Quantum Circuit ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Partition Functions ◽  
Stochastic Matrices ◽  
Many Body ◽  
Quantum Devices

Abstract The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantumclassical algorithm to estimate the partition function, utilising a novel Clifford sampling technique. Note that previous works on quantum estimation of partition functions require O(1/ε√∆)-depth quantum circuits [17, 23], where ∆ is the minimum spectral gap of stochastic matrices and ε is the multiplicative error. Our algorithm requires only a shallow O(1)-depth quantum circuit, repeated O(n/ε2) times, to provide a comparable ε approximation. Shallow-depth quantum circuits are considered vitally important for currently available NISQ (Noisy Intermediate-Scale Quantum) devices.

scholarly journals A divide-and-conquer algorithm for quantum state preparation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Israel F. Araujo ◽  
Daniel K. Park ◽  
Francesco Petruccione ◽  
Adenilton J. da Silva
Keyword(s):  
Computational Cost ◽  
Quantum Circuit ◽  
Divide And Conquer ◽  
Computational Time ◽  
Quantum Computers ◽  
Dimensional Vector ◽  
Quantum Devices ◽  
Divide And Conquer Algorithm ◽  
Quantum State Preparation ◽  
Quantum Device

AbstractAdvantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with exponential time advantage using a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

scholarly journals Spacetime as a quantum circuit

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. Ramesh Chandra ◽  
Jan de Boer ◽  
Mario Flory ◽  
Michal P. Heller ◽  
Sergio Hörtner ◽  
...  
Keyword(s):  
Path Integral ◽  
Constant Scalar Curvature ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Special Role ◽  
Gravitational Action ◽  
Volume Conjecture ◽  
Interesting Connection ◽  
Kinematic Space ◽  
Boundary States

Abstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $$ T\overline{T} $$ T T ¯ , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

Quantum generative adversarial networks for learning and loading quantum image in noisy environment

2021 ◽  
pp. 2150360
Author(s):  
Wanghao Ren ◽  
Zhiming Li ◽  
Yiming Huang ◽  
Runqiu Guo ◽  
Lansheng Feng ◽  
...  
Keyword(s):  
Image Processing ◽  
Quantum Circuit ◽  
Quantum Image Processing ◽  
Quantum Circuits ◽  
Generative Adversarial Networks ◽  
Channel Noise ◽  
Quantum Image ◽  
Adversarial Networks ◽  
Potential Applications ◽  
Classical Image

Quantum machine learning is expected to be one of the potential applications that can be realized in the near future. Finding potential applications for it has become one of the hot topics in the quantum computing community. With the increase of digital image processing, researchers try to use quantum image processing instead of classical image processing to improve the ability of image processing. Inspired by previous studies on the adversarial quantum circuit learning, we introduce a quantum generative adversarial framework for loading and learning a quantum image. In this paper, we extend quantum generative adversarial networks to the quantum image processing field and show how to learning and loading an classical image using quantum circuits. By reducing quantum gates without gradient changes, we reduced the number of basic quantum building block from 15 to 13. Our framework effectively generates pure state subject to bit flip, bit phase flip, phase flip, and depolarizing channel noise. We numerically simulate the loading and learning of classical images on the MINST database and CIFAR-10 database. In the quantum image processing field, our framework can be used to learn a quantum image as a subroutine of other quantum circuits. Through numerical simulation, our method can still quickly converge under the influence of a variety of noises.

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