scholarly journals Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Geng-Li Zhang ◽  
Di Liu ◽  
Man-Hong Yung
Keyword(s):  
Large Scale ◽  
Quantum Circuit ◽  
Higher Order ◽  
Quantum Circuits ◽  
Exceptional Point ◽  
Large Scale Systems ◽  
Zeno Effect ◽  
Programming Framework ◽  
Circuit Structure ◽  
Quantum Programming

AbstractExceptional points (EPs), the degeneracy points of non-Hermitian systems, have recently attracted great attention because of their potential of enhancing the sensitivity of quantum sensors. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although EPs have been widely explored, the range of EPs studied is largely limited by the underlying systems, for instance, higher-order EPs are hard to achieve. Here we propose an extendable method to simulate non-Hermitian systems and study EPs with quantum circuits. The system is inherently parity-time (PT) broken due to the non-symmetric controlling effects of the circuit. Inspired by the quantum Zeno effect, the circuit structure guarantees the success rate of the post-selection. A sample circuit is implemented in a quantum programming framework, and the phase transition at EP is demonstrated. Considering the scalable and flexible nature of quantum circuits, our model is capable of simulating large-scale systems with higher-order EPs.

scholarly journals OpenQL: A Portable Quantum Programming Framework for Quantum Accelerators

2022 ◽  
Vol 18 (1) ◽  
pp. 1-24
Author(s):  
N. Khammassi ◽  
I. Ashraf ◽  
J. V. Someren ◽  
R. Nane ◽  
A. M. Krol ◽  
...  
Keyword(s):  
Programming Language ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Operations ◽  
Programming Framework ◽  
Quantum Processor ◽  
Control Electronics ◽  
Quantum Programming ◽  
High Level ◽  
Programming Interface

With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving, and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language and making them executable on a quantum processor while abstracting away hardware details is a challenging task. First, a quantum programming language should provide an intuitive programming interface to describe those algorithms. Then a compiler has to transform the program into a quantum circuit, optimize it, and map it to the target quantum processor respecting the hardware constraints such as the supported quantum operations, the qubit connectivity, and the control electronics limitations. In this article, we propose a quantum programming framework named OpenQL, which includes a high-level quantum programming language and its associated quantum compiler. We present the programming interface of OpenQL, we describe the different layers of the compiler and how we can provide portability over different qubit technologies. Our experiments show that OpenQL allows the execution of the same high-level algorithm on two different qubit technologies, namely superconducting qubits and Si-Spin qubits. Besides the executable code, OpenQL also produces an intermediate quantum assembly code, which is technology independent and can be simulated using the QX simulator.

Energy Cost of Quantum Circuit Optimisation: Predicting That Optimising Shor’s Algorithm Circuit Uses 1 GWh

2022 ◽  
Vol 3 (1) ◽  
pp. 1-14
Author(s):  
Alexandru Paler ◽  
Robert Basmadjian
Keyword(s):  
Programming Languages ◽  
Energy Cost ◽  
Large Scale ◽  
State Of The Art ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Bucket Brigade ◽  
Depth Study ◽  
Cost Metrics ◽  
Optimisation Methods

Quantum circuits are difficult to simulate, and their automated optimisation is complex as well. Significant optimisations have been achieved manually (pen and paper) and not by software. This is the first in-depth study on the cost of compiling and optimising large-scale quantum circuits with state-of-the-art quantum software. We propose a hierarchy of cost metrics covering the quantum software stack and use energy as the long-term cost of operating hardware. We are going to quantify optimisation costs by estimating the energy consumed by a CPU doing the quantum circuit optimisation. We use QUANTIFY, a tool based on Google Cirq, to optimise bucket brigade QRAM and multiplication circuits having between 32 and 8,192 qubits. Although our classical optimisation methods have polynomial complexity, we observe that their energy cost grows extremely fast with the number of qubits. We profile the methods and software and provide evidence that there are high constant costs associated to the operations performed during optimisation. The costs are the result of dynamically typed programming languages and the generic data structures used in the background. We conclude that state-of-the-art quantum software frameworks have to massively improve their scalability to be practical for large circuits.

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.

A method for synthesis and optimization for linear nearest neighbor quantum circuits by parallel processing

2018 ◽  
Vol 18 (13&14) ◽  
pp. 1095-1114
Author(s):  
Zongyuan Zhang ◽  
Zhijin Guan ◽  
Hong Zhang ◽  
Haiying Ma ◽  
Weiping Ding
Keyword(s):  
Parallel Processing ◽  
Large Scale ◽  
Nearest Neighbor ◽  
Matrix Multiplication ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Cost ◽  
The Matrix ◽  
Speed Up ◽  
Serial Algorithm

In order to realize the linear nearest neighbor{(LNN)} of the quantum circuits and reduce the quantum cost of linear reversible quantum circuits, a method for synthesizing and optimizing linear reversible quantum circuits based on matrix multiplication of the structure of the quantum circuit is proposed. This method shows the matrix representation of linear quantum circuits by multiplying matrices of different parts of the whole circuit. The LNN realization by adding the SWAP gates is proposed and the equivalence of two ways of adding the SWAP gates is proved. The elimination rules of the SWAP gates between two overlapped adjacent quantum gates in different cases are proposed, which reduce the quantum cost of quantum circuits after realizing the LNN architecture. We propose an algorithm based on parallel processing in order to effectively reduce the time consumption for large-scale quantum circuits. Experiments show that the quantum cost can be improved by 34.31\% on average and the speed-up ratio of the GPU-based algorithm can reach 4 times compared with the CPU-based algorithm. The average time optimization ratio of the benchmark large-scale circuits in RevLib processed by the parallel algorithm is {95.57\%} comparing with the serial algorithm.

scholarly journals Cost function dependent barren plateaus in shallow parametrized quantum circuits

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. Cerezo ◽  
Akira Sone ◽  
Tyler Volkoff ◽  
Lukasz Cincio ◽  
Patrick J. Coles
Keyword(s):  
Cost Function ◽  
Large Scale ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Heuristic Methods ◽  
Practical Applications ◽  
Local Observables ◽  
Large Scale Simulations

AbstractVariational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is $${\mathcal{O}}(\mathrm{log}\,n)$$ O ( log n ) . Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

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