scholarly journals A co-design framework of neural networks and quantum circuits towards quantum advantage

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Weiwen Jiang ◽  
Jinjun Xiong ◽  
Yiyu Shi
Keyword(s):  
Neural Network ◽  
Cost Reduction ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Design Framework ◽  
Unitary Matrices ◽  
Classical Computing ◽  
Classical Computer ◽  
The Cost

AbstractDespite the pursuit of quantum advantages in various applications, the power of quantum computers in executing neural network has mostly remained unknown, primarily due to a missing tool that effectively designs a neural network suitable for quantum circuit. Here, we present a neural network and quantum circuit co-design framework, namely QuantumFlow, to address the issue. In QuantumFlow, we represent data as unitary matrices to exploit quantum power by encoding n = 2k inputs into k qubits and representing data as random variables to seamlessly connect layers without measurement. Coupled with a novel algorithm, the cost complexity of the unitary matrices-based neural computation can be reduced from O(n) in classical computing to O(polylog(n)) in quantum computing. Results show that on MNIST dataset, QuantumFlow can achieve an accuracy of 94.09% with a cost reduction of 10.85 × against the classical computer. All these results demonstrate the potential for QuantumFlow to achieve the quantum advantage.

scholarly journals Can Quantum Computers Learn Like Classical Computers? A Co-Design Framework of Machine Learning and Quantum Circuits

2020 ◽  
Author(s):  
Weiwen Jiang ◽  
Jinjun Xiong ◽  
Yiyu Shi
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Binary Classification ◽  
Network Models ◽  
Quantum Circuit ◽  
Quantum Computers ◽  
Design Framework ◽  
Neural Network Models ◽  
Missing Link ◽  
Batch Normalization

Abstract Despite the pursuit of quantum supremacy in various applications, the power of quantum computers in machine learning (such as neural network models) has mostly remained unknown, primarily due to a missing link that effectively designs a neural network model suitable for quantum circuit implementation. In this article, we present the first co-design framework, namelyQuantumFlow, to fixed the missing link. QuantumFlow consists of a novel quantum-friendly neural network (QF-Net) design, an automatic tool (QF-Map) to generate the quantum circuit (QF-Circ) for QF-Net, and a theoretic-based execution engine (QF-FB) to efficiently support the training of QF-Net on a classical computer. We discover that, in order to make full use of the strength of quantum representation, data in QF-Net is best modeled as random variables rather than real numbers. Moreover, instead of using the classical batch normalization (which is key to achieve high accuracy for deep neural networks), a quantum-aware batch normalization method is proposed for QF-Net. Evaluation results show that QF-Net can achieve 97.01% accuracy in distinguishing digits 3 and 6 in the widely used MNIST dataset, which is 14.55% higher than the state-of-the-art quantum-aware implementation. A case study on a binary classification application is conducted. Running on IBM Quantum processor’s“ibmq_essex” backend, a neural network designed by QuantumFlow can achieve 82% accuracy. To the best of our knowledge,QuantumFlow is the first framework that co-designs both the machine learning model and its quantum circuit.

scholarly journals FPGA Based Hardware Abstraction of Quantum Computing System

2021 ◽  
Author(s):  
Madiha Khalid ◽  
Najam ul Islam MUHAMMAD ◽  
Umar Mujahid Khokhar ◽  
Atif Jafri ◽  
Hongsik Choi
Keyword(s):  
Quantum Computing ◽  
Embedded System ◽  
Computing System ◽  
Quantum Circuit ◽  
Atomic Scale ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Chip Design ◽  
Computational Resources ◽  
The Cost

Abstract The number of transistors per unit area are increasing every year by virtue of Moore’s law. It is estimated that the current rate of evolution in the field of chip design will reduce the transistor to atomic scale by 2024. At atomic level the quantum mechanical characteristics dominate, affecting the ability of transistors to store information in the form of bits. The quantum computers have been proposed as one way to effectively deal with this predicament. The quantum computing circuits utilize the spinning characteristics of electron to store information. This paper describes a proposition of resource efficient FPGA based quantum circuit abstraction. A non-programmable embedded system capable of storing, introducing a phase shift in the qubit and its measurement is implemented. The main objective of the proposed abstraction is to provide a FPGA based platform comprising of fundamental sub blocks for designing quantum circuits. A primary quantum key distribution algorithm i.e BB84 is implemented on the proposed platform as a proof of concept. The distinguishing feature of the proposed design is the flexibility to enhance the quantum circuit emulation accuracy at the cost of computational resources. The proposed emulation exhibits two principal properties of the quantum computing i.e. parallelism and probabilistic measurement.

Quantum circuits for calculating the squared sum of the inner product of quantum states and its application

2019 ◽  
Vol 17 (05) ◽  
pp. 1950043
Author(s):  
Panchi Li ◽  
Jiahui Guo ◽  
Bing Wang ◽  
Mengqi Hao
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Experimental Results ◽  
Quantum Circuits ◽  
Inner Product ◽  
Superposition State ◽  
Initial State ◽  
Control Rules ◽  
Control Qubit ◽  
Classical Computer

In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.

Optimal LSBs-based quantum watermarking with lower distortion

2018 ◽  
Vol 16 (07) ◽  
pp. 1850058 ◽  
Author(s):  
Ri-Gui Zhou ◽  
Wen Wen Hu ◽  
Gao Feng Luo ◽  
Ping Fan ◽  
Hou Ian
Keyword(s):  
Complexity Analysis ◽  
Computer Software ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Cover Image ◽  
Absolute Value ◽  
Binary Images ◽  
Quantum Watermarking ◽  
Classical Computer ◽  
Watermarking Scheme

Based on the NEQR representation of quantum grayscale images and binary images, the optimal LSBs-based quantum watermarking scheme is investigated in this paper, which embeds several binary images (watermark images) into a grayscale image (cover image). The size of the cover image and secret image are both assumed to be [Formula: see text]. Compared to quantum simple LSBs substitution method generating one stego-pixel, our presented quantum optimal LSBs-based method can generate three stego-pixel simultaneously first. Then one of them with lowest visual distortion is chosen as the final stego-pixel. To this end, first of all, the quantum circuits for a few basic quantum modules (i.e. Quantum Comparator, Parallel CNOT, Parallel Swap, ADDER MOD, Subtracter (SUB.ER) MOD and Absolute Value) are predefined. Following that, based on these simple modules, two composite quantum modules (i.e. the ADDER and SUB.ER MOD [Formula: see text] module and Choose final stego-pixel module) are further constructed. With the help of the basic and composite quantum modules, the integrated quantum circuit implementation of the optimal LSBs-based quantum watermark images embedding/extracting procedures are illustrated. Then, the experiment result are simulated under the classical computer software MATLAB 2014(b), which illustrates our presented optimal LSBs-based quantum watermarking methods are superior to the simple LSBs scheme in terms of PSNR and histogram graphs on the basis of visual effect, and the circuit’s complexity analysis also demonstrates our investigated scheme with a very low computational complexity. Finally, we analyze the security of quantum cryptography system, which verifies the quantum watermarking data can be securely transmitted to other legal normal users.

scholarly journals Automated Quantum Hardware Selection for Quantum Workflows

Electronics ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 984
Author(s):  
Benjamin Weder ◽  
Johanna Barzen ◽  
Frank Leymann ◽  
Marie Salm
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithm ◽  
Software Tool ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Workflow Model ◽  
Selection For ◽  
Selection Of

The execution of a quantum algorithm typically requires various classical pre- and post-processing tasks. Hence, workflows are a promising means to orchestrate these tasks, benefiting from their reliability, robustness, and features, such as transactional processing. However, the implementations of the tasks may be very heterogeneous and they depend on the quantum hardware used to execute the quantum circuits of the algorithm. Additionally, today’s quantum computers are still restricted, which limits the size of the quantum circuits that can be executed. As the circuit size often depends on the input data of the algorithm, the selection of quantum hardware to execute a quantum circuit must be done at workflow runtime. However, modeling all possible alternative tasks would clutter the workflow model and require its adaptation whenever a new quantum computer or software tool is released. To overcome this problem, we introduce an approach to automatically select suitable quantum hardware for the execution of quantum circuits in workflows. Furthermore, it enables the dynamic adaptation of the workflows, depending on the selection at runtime based on reusable workflow fragments. We validate our approach with a prototypical implementation and a case study demonstrating the hardware selection for Simon’s algorithm.

scholarly journals Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers

2022 ◽  
Vol 12 (2) ◽  
pp. 759
Author(s):  
Anna M. Krol ◽  
Aritra Sarkar ◽  
Imran Ashraf ◽  
Zaid Al-Ars ◽  
Koen Bertels
Keyword(s):  
Quantum Algorithms ◽  
Optimization Method ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Underlying Structure ◽  
Quantum Computers ◽  
Unitary Matrices ◽  
Quantum Operations ◽  
Test Part ◽  
Input Gate

Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.

Can Quantum Computers Solve Linear Algebra Problems to Advance Engineering Applications?

2018 ◽  
Author(s):  
Guanglei Xu ◽  
William S. Oates
Keyword(s):  
Quantum Computing ◽  
Linear Algebra ◽  
Quantum Algorithms ◽  
Finite Difference Methods ◽  
Engineering Application ◽  
Quantum Circuit ◽  
Quantum Computers ◽  
Measurement Methodology ◽  
Classical Computing ◽  
Richard Feynman

Since its inception by Richard Feynman in 1982, quantum computing has provided an intriguing opportunity to advance computational capabilities over classical computing. Classical computers use bits to process information in terms of zeros and ones. Quantum computers use the complex world of quantum mechanics to carry out calculations using qubits (the quantum analog of a classical bit). The qubit can be in a superposition of the zero and one state simultaneously unlike a classical bit. The true power of quantum computing comes from the complexity of entanglement between many qubits. When entanglement is realized, quantum algorithms for problems such as factoring numbers and solving linear algebra problems show exponential speed-up relative to any known classical algorithm. Linear algebra problems are of particular interest in engineering application for solving problems that use finite element and finite difference methods. Here, we explore quantum linear algebra problems where we design and implement a quantum circuit that can be tested on IBM’s quantum computing hardware. A set of quantum gates are assimilated into a circuit and implemented on the IBM Q system to demonstrate its algorithm capabilities and its measurement methodology.

scholarly journals ON THE GAP OF HAMILTONIANS FOR THE ADIABATIC SIMULATION OF QUANTUM CIRCUITS

2013 ◽  
Vol 11 (07) ◽  
pp. 1350063 ◽  
Author(s):  
ANAND GANTI ◽  
ROLANDO SOMMA
Keyword(s):  
Upper Bound ◽  
Spectral Gap ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Search Problem ◽  
Adiabatic Evolution ◽  
Unstructured Search ◽  
Time Quantum ◽  
The Cost ◽  
The Impact

The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases polynomially with the number of gates in the circuit, L. Because a larger gap implies a smaller cost, we study the limits of spectral gap amplification in this context. We show that, under some assumptions on the ground states and the cost of evolving with the Hamiltonians (which apply to the standard constructions), an upper bound on the gap of the order 1/L follows. In addition, if the Hamiltonians satisfy a frustration-free property, the upper bound is of the order 1/L2. Our proofs use recent results on adiabatic state transformations, spectral gap amplification, and the simulation of continuous-time quantum query algorithms. They also consider a reduction from the unstructured search problem, whose lower bound in the oracle cost translates into the upper bounds in the gaps. The impact of our results is that improving the gap beyond that of standard constructions (i.e. 1/L2), if possible, is challenging.

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 On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity

2020 ◽  
Vol 20 (9&10) ◽  
pp. 787-806 ◽  
Author(s):  
Steven Herbert
Keyword(s):  
Quantum Algorithms ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Interaction Graph ◽  
Finite Degree ◽  
Near Term

This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable general qubit interactions. This paper proves that there exist quantum circuits where a depth overhead in Omega(\log n) must necessarily be incurred when running quantum circuits with n qubits on quantum computers whose qubit interaction graph has finite degree, but that such a logarithmic depth overhead is achievable. The latter is shown by the construction of a 4-regular qubit interaction graph and associated compilation algorithm that can execute any quantum circuit with only a logarithmic depth overhead.

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