scholarly journals An Algorithm of Quantum Restricted Boltzmann Machine Network Based on Quantum Gates and Its Application

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Peilin Zhang ◽  
Sheng Li ◽  
Yu Zhou
Keyword(s):  
Quantum Computer ◽  
Quantum Circuit ◽  
Classification Performance ◽  
Generative Model ◽  
Restricted Boltzmann Machine ◽  
Quantum Gates ◽  
Boltzmann Machine ◽  
Discriminative Models

We present an algorithm of quantum restricted Boltzmann machine network based on quantum gates. The algorithm is used to initialize the procedure that adjusts the qubit and weights. After adjusting, the network forms an unsupervised generative model that gives better classification performance than other discriminative models. In addition, we show how the algorithm can be constructed with quantum circuit for quantum computer.

scholarly journals Experiment Improvement of Restricted Boltzmann Machine Methods for Image Classification

2021 ◽  
pp. 1-16
Author(s):  
Christine Dewi ◽  
Rung-Ching Chen ◽  
Hendry ◽  
Hsiu-Te Hung
Keyword(s):  
Image Classification ◽  
Learning Algorithm ◽  
Classification Performance ◽  
Generative Models ◽  
Restricted Boltzmann Machine ◽  
Model Complexity ◽  
Boltzmann Machine ◽  
Learning Techniques ◽  
Recent Developments ◽  
Hidden Layer

Restricted Boltzmann machine (RBM) plays an important role in current deep learning techniques, as most of the existing deep networks are based on or related to generative models and image classification. Many applications for RBMs have been developed for a large variety of learning problems. Recent developments have demonstrated the capacity of RBM to be powerful generative models, able to extract useful features from input data or construct deep artificial neural networks. In this work, we propose a learning algorithm to find the optimal model complexity for the RBM by improving the hidden layer (50–750 layers). Then, we compare and analyze the classification performance in depth of regular RBM use RBM () function, classification RBM use stackRBM() function, and Deep Belief Network (DBN) use DBN() function with the different hidden layer. As a result, Stacking RBM and DBN could improve our classification performance compared to regular RBM.

scholarly journals Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

2022 ◽  
Author(s):  
Fereshte Shahbeigi ◽  
Mahsa Karimi ◽  
Vahid Karimipour
Keyword(s):  
Parameter Space ◽  
Wide Class ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Natural Generalization ◽  
Quantum Gates ◽  
Density Matrices ◽  
Quantum Device ◽  
Initial States ◽  
X State

Abstract Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

scholarly journals Experimental demonstration of efficient high-dimensional quantum gates with orbital angular momentum

2021 ◽  
Author(s):  
Yunlong Wang ◽  
Shihao Ru ◽  
Feiran Wang ◽  
Pei Zhang ◽  
Fu-Li Li
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Degree Of Freedom ◽  
Quantum Gates ◽  
Polarization Degree ◽  
High Dimensional ◽  
Single Photons ◽  
Two Level Systems

Abstract Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even that high-dimensional quantum systems exhibit remarkable advantages over two-level systems for some quantum information and quantum computing tasks. Here we experimentally demonstrate the four-dimensional X gate and its unique higher orders with the average conversion efficiency 93\%. All these gates are based on orbital-angular-momentum degree of freedom of single photons. Besides, a set of controlled quantum gates is implemented by use of polarization degree of freedom. Our work is an important step towards the goal of achieving arbitrary high-dimensional quantum circuit and paves a way for the implementation of high-dimensional quantum communication and computation.

A complete restricted Boltzmann machine on an adiabatic quantum computer

2021 ◽  
pp. 2141003
Author(s):  
Lorenzo Rocutto ◽  
Enrico Prati
Keyword(s):  
Complete Graph ◽  
Quantum Computer ◽  
Restricted Boltzmann Machine ◽  
Computational Time ◽  
Quantum Computers ◽  
Boltzmann Machine ◽  
Computational Power ◽  
Trade Off ◽  
Boltzmann Machines ◽  
The Neural Network

Boltzmann Machines constitute a paramount class of neural networks for unsupervised learning and recommendation systems. Their bipartite version, called Restricted Boltzmann Machine (RBM), is the most developed because of its satisfactory trade-off between computability on classical computers and computational power. Though the diffusion of RBMs is quite limited as their training remains hard. Recently, a renewed interest has emerged as Adiabatic Quantum Computers (AQCs), which suggest a potential increase of the training speed with respect to conventional hardware. Due to the limited number of connections among the qubits forming the graph of existing hardware, associating one qubit per node of the neural network implies an incomplete graph. Thanks to embedding techniques, we developed a complete graph connecting nodes constituted by virtual qubits. The complete graph outperforms previous implementations based on incomplete graphs. Despite the fact that the learning rate per epoch is still slower with respect to a classical machine, the advantage is expected by the increase of number of nodes which impacts on the classical computational time but not on the quantum hardware based computation.

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 Practical Quantum Computing

2021 ◽  
Vol 2 (1) ◽  
pp. 1-35
Author(s):  
Adrien Suau ◽  
Gabriel Staffelbach ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Equation Solving ◽  
Small Quantum ◽  
Quantum Wave ◽  
Variational Algorithms ◽  
The One

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

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