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 QUANTUM AUCTIONS USING ADIABATIC EVOLUTION: THE CORRUPT AUCTIONEER AND CIRCUIT IMPLEMENTATIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 815-839 ◽  
Author(s):  
SAIKAT GUHA ◽  
TAD HOGG ◽  
DAVID FATTAL ◽  
TIMOTHY SPILLER ◽  
RAYMOND G. BEAUSOLEIL
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Quantum Circuits ◽  
Adiabatic Evolution ◽  
Auction Algorithm ◽  
Final Measurement

We examine a proposed auction algorithm using quantum states to represent bids and distributed adiabatic search to find the winner.1 When the auctioneer follows the protocol, the final measurement giving the outcome of the auction also destroys the bid states, thereby preserving the privacy of losing bidders. We describe how a dishonest auctioneer could alter the protocol to violate this privacy guarantee, and present methods by which bidders can counter such attacks. We also suggest possible quantum circuit implementations of the auction protocol, and quantum circuits to perpetrate and to counter attacks by a dishonest auctioneer.

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 Consequences of preserving reversibility in quantum superchannels

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 441
Author(s):  
Wataru Yokojima ◽  
Marco Túlio Quintino ◽  
Akihito Soeda ◽  
Mio Murao
Keyword(s):  
Quantum Mechanics ◽  
Physical Interpretation ◽  
Quantum Circuit ◽  
Quantum States ◽  
Quantum Circuits ◽  
Causal Order ◽  
Quantum Operations ◽  
Coherent Superposition ◽  
Physical Implementation ◽  
Quantum Objects

Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations which take independent quantum operations as inputs. While they are enforced to respect the laws of quantum mechanics, the use of input operations may lack a definite causal order, and characterizations of general superchannels in terms of quantum objects with a physical implementation have been missing. In this paper, we provide a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superchannels preserving the reversibility of quantum operations. We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a quantum circuit only consisting of unitary operations or a coherent superposition of two unitary quantum circuits where the two input operations are differently ordered. The latter may be seen as a generalization of the quantum switch, allowing a physical interpretation for pure two-slot superchannels. An immediate corollary is that purifiable bipartite processes cannot violate device-independent causal inequalities.

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.

QUANTUM-STATISTICAL SIMULATIONS FOR QUANTUM CIRCUITS

2002 ◽  
Vol 13 (07) ◽  
pp. 931-945 ◽  
Author(s):  
KURT FISCHER ◽  
HANS-GEORG MATUTTIS ◽  
NOBUYASU ITO ◽  
MASAMICHI ISHIKAWA
Keyword(s):  
Prime Numbers ◽  
Quantum Circuits ◽  
Decomposition Technique ◽  
Shor's Algorithm ◽  
Quantum Statistical ◽  
Classical Computer

Using a Hubbard–Stratonovich like decomposition technique, we implemented simulations for the quantum circuits of Simon's algorithm for the detection of the periodicity of a function and Shor's algorithm for the factoring of prime numbers on a classical computer. Our approach has the advantage that the dimension of the problem does not grow exponentially with the number of qubits.

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.

scholarly journals Error mitigation with Clifford quantum-circuit data

Quantum ◽  
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.

scholarly journals A Boosting Framework of Factorization Machine

2021 ◽  
pp. 2159036
Author(s):  
Jun Zhou ◽  
Longfei Li ◽  
Ziqi Liu ◽  
Chaochao Chen
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Experimental Results ◽  
Low Rank ◽  
Inner Product ◽  
Adaptive Boosting ◽  
Rank Matrix ◽  
Factorization Machine ◽  
Fixed Rank ◽  
Low Rank Matrix

Recently, Factorization Machine (FM) has become more and more popular for recommendation systems due to its effectiveness in finding informative interactions between features. Usually, the weights for the interactions are learned as a low rank weight matrix, which is formulated as an inner product of two low rank matrices. This low rank matrix can help improve the generalization ability of Factorization Machine. However, to choose the rank properly, it usually needs to run the algorithm for many times using different ranks, which clearly is inefficient for some large-scale datasets. To alleviate this issue, we propose an Adaptive Boosting framework of Factorization Machine (AdaFM), which can adaptively search for proper ranks for different datasets without re-training. Instead of using a fixed rank for FM, the proposed algorithm will gradually increase its rank according to its performance until the performance does not grow. Extensive experiments are conducted to validate the proposed method on multiple large-scale datasets. The experimental results demonstrate that the proposed method can be more effective than the state-of-the-art Factorization Machines.

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