scholarly journals Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 279 ◽  
Author(s):  
Ross Duncan ◽  
Aleks Kissinger ◽  
Simon Perdrix ◽  
John van de Wetering
Keyword(s):  
Extraction Procedure ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Nearest Neighbour ◽  
Theoretic Property ◽  
New Approach ◽  
Graph Theoretic ◽  
Underlying Graph ◽  
Circuit Extraction ◽  
General Circuits

We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using the rules of the ZX-calculus, we give a simplification strategy for ZX-diagrams based on the two graph transformations of local complementation and pivoting and show that the resulting reduced diagram can be transformed back into a quantum circuit. While little is known about extracting circuits from arbitrary ZX-diagrams, we show that the underlying graph of our simplified ZX-diagram always has a graph-theoretic property called generalised flow, which in turn yields a deterministic circuit extraction procedure. For Clifford circuits, this extraction procedure yields a new normal form that is both asymptotically optimal in size and gives a new, smaller upper bound on gate depth for nearest-neighbour architectures. For Clifford+T and more general circuits, our technique enables us to to `see around' gates that obstruct the Clifford structure and produce smaller circuits than naïve `cut-and-resynthesise' methods.

scholarly journals A New Approach for Optimization of Distributed Quantum Circuits

2021 ◽  
Author(s):  
Davood Dadkhah ◽  
Mariam Zomorodi ◽  
Seyed Ebrahim Hosseini
Keyword(s):  
Genetic Algorithm ◽  
Quantum System ◽  
Quantum Circuit ◽  
Heuristic Approach ◽  
Quantum Circuits ◽  
Equivalent Circuits ◽  
New Approach ◽  
Novel Approach ◽  
Quantum Protocol

AbstractIn the present work, a novel approach was proposed to optimize the teleportation cost in Distributed Quantum Circuits (DQCs) by applying a new approach. To overcome the difficulty with keeping a large number of qubits next to each other, DQCs, as a well-known solution, have always been employed. In a distributed quantum system, qubits are transferred from a subsystem to another subsystem by a quantum protocol such as teleportation. First, we proposed a heuristic approach through which we could replace the equivalent circuits in the initial quantum circuit. Then, we used a genetic algorithm to partition the placement of qubits so that the number of teleportations could be optimized for the communications of a DQC. Finally, results showed that the proposed approach could impressively work.

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 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.

Implementation of Shor's algorithm on a linear nearest neighbour qubit array

2004 ◽  
Vol 4 (4) ◽  
pp. 237-251
Author(s):  
A.G. Fowler ◽  
S.J. Devitt ◽  
L.C.L. Hollenberg
Keyword(s):  
Quantum Computer ◽  
Computer Architectures ◽  
Quantum Circuits ◽  
Single Line ◽  
Nearest Neighbour ◽  
Leading Order ◽  
Shor's Algorithm

Shor's algorithm, which given appropriate hardware can factorise an integer N in a time polynomial in its binary length L, has arguably spurred the race to build a practical quantum computer. Several different quantum circuits implementing Shor's algorithm have been designed, but each tacitly assumes that arbitrary pairs of qubits within the computer can be interacted. While some quantum computer architectures possess this property, many promising proposals are best suited to realising a single line of qubits with nearest neighbour interactions only. In light of this, we present a circuit implementing Shor's factorisation algorithm designed for such a linear nearest neighbour architecture. Despite the interaction restrictions, the circuit requires just 2L+4 qubits and to leading order requires 8L^4 2-qubit gates arranged in a circuit of depth 32L^3 --- identical to leading order to that possible using an architecture that can interact arbitrary pairs of qubits.

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