scholarly journals Cross-Platform Comparison of Arbitrary Quantum Computations

2021 ◽  
Author(s):  
Ze-Pei Cian ◽  
Daiwei Zhu ◽  
Crystal Noel ◽  
Andrew Risinger ◽  
Debopriyo Biswas ◽  
...  
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Platform Comparison ◽  
Cross Platform ◽  
Difficult Challenge ◽  
Classical Computer ◽  
Arbitrary Quantum

Abstract As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

scholarly journals Modular quantum computing and quantum-like devices

2021 ◽  
pp. 2150020
Author(s):  
R. Vilela Mendes
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Quantum Algorithms ◽  
The Other ◽  
Classical Systems ◽  
Evolution Parameter ◽  
Space Coordinate ◽  
The One ◽  
Classical Computer

The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and on the other hand, that such modules may be constructed out of classical systems obeying quantum-like equations where a space coordinate is the evolution parameter (thus playing the role of time in the quantum algorithms).

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 Quantum Computing Concepts with Deutsch Jozsa Algorithm

2019 ◽  
Vol 3 (1) ◽  
Author(s):  
Poornima Aradyamath ◽  
Naghabhushana N M ◽  
Rohitha Ujjinimatad
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Computation ◽  
Mathematical Description ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Basic Concepts ◽  
Classical Computer

In this paper, we briefly review the basic concepts of quantum computation,  entanglement,  quantum cryptography and quantum fourier  transform.   Quantum algorithms like Deutsch Jozsa, Shor’s   factorization and Grover’s data search are developed using fourier  transform  and quantum computation concepts to build quantum computers.  Researchers are finding a way to build quantum computer that works more efficiently than classical computer.  Among the  standard well known  algorithms  in the field of quantum computation  and communication we  describe  mathematically Deutsch Jozsa algorithm  in detail for  2  and 3 qubits.  Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.

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.

scholarly journals Quantum Factoring Algorithm: Resource Estimation and Survey of Experiments

2020 ◽  
pp. 39-55
Author(s):  
Noboru Kunihiro
Keyword(s):  
Large Scale ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Small Scale ◽  
Quantum Computers ◽  
Resource Estimation ◽  
Shor's Algorithm ◽  
Order Of An Element ◽  
Factoring Algorithm

Abstract It is known that Shor’s algorithm can break many cryptosystems such as RSA encryption, provided that large-scale quantum computers are realized. Thus far, several experiments for the factorization of the small composites such as 15 and 21 have been conducted using small-scale quantum computers. In this study, we investigate the details of quantum circuits used in several factoring experiments. We then indicate that some of the circuits have been constructed under the condition that the order of an element modulo a target composite is known in advance. Because the order must be unknown in the experiments, they are inappropriate for designing the quantum circuit of Shor’s factoring algorithm. We also indicate that the circuits used in the other experiments are constructed by relying considerably on the target composite number to be factorized.

scholarly journals Expressibility of the alternating layered ansatz for quantum computation

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 434
Author(s):  
Kouhei Nakaji ◽  
Naoki Yamamoto
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Critical Issue ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Intermediate Scale ◽  
State Generation ◽  
Proper Definition ◽  
Definition Of ◽  
Designing Method

The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.

scholarly journals Optimal two-qubit circuits for universal fault-tolerant quantum computation

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Andrew N. Glaudell ◽  
Neil J. Ross ◽  
Jacob M. Taylor
Keyword(s):  
Lower Bound ◽  
Normal Form ◽  
Quantum Computation ◽  
Normal Forms ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Worst Case ◽  
Synthesis Algorithm ◽  
Phase Gate ◽  
Controlled Phase Gate

AbstractWe study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.

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 Density Guarantee on Finding Multiple Subgraphs and Subtensors

2021 ◽  
Vol 15 (5) ◽  
pp. 1-32
Author(s):  
Quang-huy Duong ◽  
Heri Ramampiaro ◽  
Kjetil Nørvåg ◽  
Thu-lan Dam
Keyword(s):  
Lower Bound ◽  
State Of The Art ◽  
The State ◽  
The Other ◽  
Exact Methods ◽  
Practical Solution ◽  
Novel Approach ◽  
Wide Range ◽  
Real World Datasets ◽  
Tensor Data

Dense subregion (subgraph & subtensor) detection is a well-studied area, with a wide range of applications, and numerous efficient approaches and algorithms have been proposed. Approximation approaches are commonly used for detecting dense subregions due to the complexity of the exact methods. Existing algorithms are generally efficient for dense subtensor and subgraph detection, and can perform well in many applications. However, most of the existing works utilize the state-or-the-art greedy 2-approximation algorithm to capably provide solutions with a loose theoretical density guarantee. The main drawback of most of these algorithms is that they can estimate only one subtensor, or subgraph, at a time, with a low guarantee on its density. While some methods can, on the other hand, estimate multiple subtensors, they can give a guarantee on the density with respect to the input tensor for the first estimated subsensor only. We address these drawbacks by providing both theoretical and practical solution for estimating multiple dense subtensors in tensor data and giving a higher lower bound of the density. In particular, we guarantee and prove a higher bound of the lower-bound density of the estimated subgraph and subtensors. We also propose a novel approach to show that there are multiple dense subtensors with a guarantee on its density that is greater than the lower bound used in the state-of-the-art algorithms. We evaluate our approach with extensive experiments on several real-world datasets, which demonstrates its efficiency and feasibility.

scholarly journals Tripartite entropic uncertainty relation under phase decoherence

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. A. Abdelghany ◽  
A.-B. A. Mohamed ◽  
M. Tammam ◽  
Watson Kuo ◽  
H. Eleuch
Keyword(s):  
Lower Bound ◽  
Uncertainty Relation ◽  
Nearest Neighbors ◽  
The Other ◽  
Uncertainty In Measurement ◽  
Entropic Uncertainty Relation ◽  
Specific Choice ◽  
Phase Decoherence ◽  
Time Invariant ◽  
Incompatible Observables

AbstractWe formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.

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