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.

Embedded Nanowire Network Growth and Node Device Fabrication for GaAs-Based High-Density Hexagonal Binary Decision Diagram Quantum Circuits

2006 ◽  
Vol 45 (4B) ◽  
pp. 3614-3620 ◽  
Author(s):  
Takahiro Tamura ◽  
Isao Tamai ◽  
Seiya Kasai ◽  
Taketomo Sato ◽  
Hideki Hasegawa ◽  
...  
Keyword(s):  
Binary Decision Diagram ◽  
Device Fabrication ◽  
High Density ◽  
Quantum Circuits ◽  
Network Growth ◽  
Binary Decision ◽  
Nanowire Network

scholarly journals Quantum Implementation of Powell’s Conjugate Direction Method

2019 ◽  
Vol 23 (4) ◽  
pp. 726-734
Author(s):  
Kehan Chen ◽  
Fei Yan ◽  
Kaoru Hirota ◽  
Jianping Zhao ◽  
◽  
...  
Keyword(s):  
Search Algorithm ◽  
Quantum Circuit ◽  
Data Fitting ◽  
Quadratic Equation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Circuit Implementation ◽  
One Dimensional ◽  
Conjugate Direction ◽  
Conjugate Direction Method

A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.

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 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 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 Exact Ising model simulation on a quantum computer

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 114 ◽  
Author(s):  
Alba Cervera-Lierta
Keyword(s):  
Ground State ◽  
Quantum Computer ◽  
Thermal Evolution ◽  
Model Simulation ◽  
Quantum Circuit ◽  
Quantum Devices ◽  
One Dimensional ◽  
Evolution Simulation ◽  
Ising Spin ◽  
Computational Basis

We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for n=4 spins, we compute the expected value of the ground state transverse magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.

scholarly journals Synthesis of quantum circuits based on incompletely specified functions and if-decision diagrams

2021 ◽  
pp. 84-97
Author(s):  
Anatoly A. Prihozhy
Keyword(s):  
Boolean Function ◽  
Quantum Circuit ◽  
Binary Decision Diagram ◽  
Quantum Circuits ◽  
Graph Representation ◽  
Decision Diagrams ◽  
Decomposition Products ◽  
Binary Decision ◽  
Binary Diagram ◽  
Functional Specification

The problem of synthesis and optimisation of logical reversible and quantum circuits from functional descriptions represented as decision diagrams is considered. It is one of the key problems being solved with the aim of creating quantum computing technology and quantum computers. A new method of stepwise transformation of the initial functional specification to a quantum circuit is proposed, which provides for the following project states: reduced ordered binary decision diagram, if-decision diagram, functional if-decision diagram, reversible circuit and quantum circuit. The novelty of the method consists in extending the Shannon and Davio expansions of a Boolean function on a single variable to the expansions of the same Boolean function on another function with obtaining decomposition products that are represented by incompletely defined Boolean functions. Uncertainty in the decomposition products gives remarkable opportunities for minimising the graph representation of the specified function. Instead of two outgoing branches of the binary diagram vertex, three outgoing branches of the if-diagram vertex are generated, which increase the level of parallelism in reversible and quantum circuits. For each transformation step, appropriate mapping rules are proposed that reduce the number of lines, gates and the depth of the reversible and quantum circuit. The comparison of new results with the results given by the known method of mapping the vertices of binary decision diagram into cascades of reversible and quantum gates shows a significant improvement in the quality of quantum circuits that are synthesised by the proposed method.

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