scholarly journals VQE method: a short survey and recent developments

2022 ◽  
Vol 6 (1) ◽  
Author(s):  
Dmitry A. Fedorov ◽  
Bo Peng ◽  
Niranjan Govind ◽  
Yuri Alexeev
Keyword(s):  
Small Molecules ◽  
Optimization Problem ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Phase Estimation ◽  
Two Factors ◽  
Recent Developments ◽  
Near Future ◽  
Classical Optimization

AbstractThe variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

scholarly journals Nonlinear Quantum Optimization Algorithms via Efficient Ising Model Encodings

2021 ◽  
Author(s):  
Taylor Patti ◽  
Jean Kossaifi ◽  
Anima Anandkumar ◽  
Susanne Yelin
Keyword(s):  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Activation Functions ◽  
Tensor Networks ◽  
Polynomial Reduction ◽  
Classical Simulation ◽  
Nonlinear Quantum ◽  
High Connectivity ◽  
Quantum Optimization ◽  
Classical Optimization

Abstract Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges to quantum advantage with two new variational quantum algorithms, which utilize multi-basis graph encodings and nonlinear activation functions to outperform existing methods with remarkably shallow quantum circuits. Both algorithms provide a polynomial reduction in measurement complexity and either a factor of two speedup a factor of two reduction in quantum resources. Typically, the classical simulation of such algorithms with many qubits is impossible due to the exponential scaling of traditional quantum formalism and the limitations of tensor networks. Nonetheless, the shallow circuits and moderate entanglement of our algorithms, combined with efficient tensor method-based simulation, enable us to successfully optimize the MaxCut of high-connectivity global graphs with up to 512 nodes (qubits) on a single GPU.

scholarly journals Applying Quantum Optimization Algorithms for Linear Programming

2017 ◽  
Author(s):  
Mert Side ◽  
Volkan Erol
Keyword(s):  
Resource Allocation ◽  
Linear Programming ◽  
Production Scheduling ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Quantum Optimization ◽  
Special Case

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

scholarly journals Iterative qubit-excitation based variational quantum eigensolver

2021 ◽  
Author(s):  
Yordan Yordanov ◽  
Vasileios Armaos ◽  
Crispin Barnes ◽  
David Arvidsson-Shukur
Keyword(s):  
Numerical Simulations ◽  
Small Molecules ◽  
Time Complexity ◽  
Molecular Simulations ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Successful Implementation ◽  
Intermediate Scale ◽  
Promising Application ◽  
Physical Features

Abstract Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansatze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansatze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansatze with ``qubit-excitation evolutions', which, contrary to fermionic excitation evolutions, obey ``qubit commutation relations'. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansatze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the iterative qubit excitation based VQE (IQEB-VQE) algorithm. The IQEB-VQE performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of single and double qubit excitation operators. By performing numerical simulations for small molecules, we benchmark the IQEB-VQE, and compare it against other competitive VQE algorithms. In terms of circuit efficiency and time complexity, we find that the IQEB-VQE systematically outperforms the previously most circuit-efficient, practically scalable VQE algorithms.

scholarly journals Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 553
Author(s):  
Xiao Xiao ◽  
J. K. Freericks ◽  
A. F. Kemper
Keyword(s):  
Phase Diagrams ◽  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Entanglement Entropy ◽  
Quantum Phase ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Model ◽  
Quantum Properties ◽  
Topological Quantum

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

scholarly journals Fisher Information in Noisy Intermediate-Scale Quantum Applications

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 539
Author(s):  
Johannes Jakob Meyer
Keyword(s):  
Fisher Information ◽  
Quantum Algorithms ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Intermediate Scale ◽  
Quantum Sensing ◽  
Near Term

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

scholarly journals Applying Quantum Optimization Algorithms for Linear Programming

2017 ◽  
Author(s):  
Mert Side ◽  
Volkan Erol
Keyword(s):  
Resource Allocation ◽  
Linear Programming ◽  
Production Scheduling ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Quantum Optimization ◽  
Special Case

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

scholarly journals Qubit-excitation-based adaptive variational quantum eigensolver

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Yordan S. Yordanov ◽  
V. Armaos ◽  
Crispin H. W. Barnes ◽  
David R. M. Arvidsson-Shukur
Keyword(s):  
Numerical Simulations ◽  
Small Molecules ◽  
Molecular Simulations ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Successful Implementation ◽  
Intermediate Scale ◽  
Commutation Relations ◽  
Promising Application ◽  
Physical Features

AbstractMolecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansätze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansätze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansätze with "qubit-excitation evolutions”, which, contrary to fermionic excitation evolutions, obey "qubit commutation relations”. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansätze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the qubit-excitation-based adaptive (QEB-ADAPT)-VQE protocol. The QEB-ADAPT-VQE is a modification of the ADAPT-VQE that performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of qubit excitation operators. By performing classical numerical simulations for small molecules, we benchmark the QEB-ADAPT-VQE, and compare it against the original fermionic-ADAPT-VQE and the qubit-ADAPT-VQE. In terms of circuit efficiency and convergence speed, we demonstrate that the QEB-ADAPT-VQE outperforms the qubit-ADAPT-VQE, which to our knowledge was the previous most circuit-efficient scalable VQE protocol for molecular simulations.

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 Computing in the NISQ era and beyond

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 79 ◽  
Author(s):  
John Preskill
Keyword(s):  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Quantum Computers ◽  
Many Body ◽  
Significant Step ◽  
Near Future

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.

scholarly journals Qibo: a framework for quantum simulation with hardware acceleration

2021 ◽  
Author(s):  
Stavros Efthymiou ◽  
Sergi Ramos-Calderer ◽  
Carlos Bravo-Prieto ◽  
Adriian Perez-Salinas ◽  
Diego García-Martín ◽  
...  
Keyword(s):  
Open Source Software ◽  
Quantum Algorithms ◽  
Hardware Acceleration ◽  
Quantum Simulation ◽  
Quantum Circuits ◽  
Simulation Framework ◽  
Fast Evaluation ◽  
Simulation Performance ◽  
Recent Developments ◽  
User Friendly

Abstract We present Qibo, a new open-source software for fast evaluation of quantum circuits and adiabatic evolution which takes full advantage of hardware accelerators. The growing interest in quantum computing and the recent developments of quantum hardware devices motivates the development of new advanced computational tools focused on performance and usage simplicity. In this work we introduce a new quantum simulation framework that enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem and quantum algorithms at hand. This software is designed from scratch with simulation performance, code simplicity and user friendly interface as target goals. It takes advantage of hardware acceleration such as multi-threading CPU, single GPU and multi-GPU devices.

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