Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

AbstractQuantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

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Solving Combinatorial Optimization Problems on Quantum Computers

Cybernetics and Computer Technologies ◽

10.34229/2707-451x.20.2.1 ◽

2020 ◽

pp. 5-13

Author(s):

Vyacheslav Korolyov ◽

Oleksandr Khodzinskyi

Keyword(s):

Combinatorial Optimization ◽

Optimization Problems ◽

Quantum Computer ◽

Independent Set ◽

Cloud Services ◽

Quantum Computers ◽

Maximal Independent Set ◽

Maximum Independent Set ◽

Combinatorial Optimization Problems ◽

D Wave

Introduction. Quantum computers provide several times faster solutions to several NP-hard combinatorial optimization problems in comparison with computing clusters. The trend of doubling the number of qubits of quantum computers every year suggests the existence of an analog of Moore's law for quantum computers, which means that soon they will also be able to get a significant acceleration of solving many applied large-scale problems. The purpose of the article is to review methods for creating algorithms of quantum computer mathematics for combinatorial optimization problems and to analyze the influence of the qubit-to-qubit coupling and connections strength on the performance of quantum data processing. Results. The article offers approaches to the classification of algorithms for solving these problems from the perspective of quantum computer mathematics. It is shown that the number and strength of connections between qubits affect the dimensionality of problems solved by algorithms of quantum computer mathematics. It is proposed to consider two approaches to calculating combinatorial optimization problems on quantum computers: universal, using quantum gates, and specialized, based on a parameterization of physical processes. Examples of constructing a half-adder for two qubits of an IBM quantum processor and an example of solving the problem of finding the maximum independent set for the IBM and D-wave quantum computers are given. Conclusions. Today, quantum computers are available online through cloud services for research and commercial use. At present, quantum processors do not have enough qubits to replace semiconductor computers in universal computing. The search for a solution to a combinatorial optimization problem is performed by achieving the minimum energy of the system of coupled qubits, on which the task is mapped, and the data are the initial conditions. Approaches to solving combinatorial optimization problems on quantum computers are considered and the results of solving the problem of finding the maximum independent set on the IBM and D-wave quantum computers are given. Keywords: quantum computer, quantum computer mathematics, qubit, maximal independent set for a graph.

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Improving Variational Quantum Optimization using CVaR

Quantum ◽

10.22331/q-2020-04-20-256 ◽

2020 ◽

Vol 4 ◽

pp. 256 ◽

Cited By ~ 3

Author(s):

Panagiotis Kl. Barkoutsos ◽

Giacomo Nannicini ◽

Anton Robert ◽

Ivano Tavernelli ◽

Stefan Woerner

Keyword(s):

Combinatorial Optimization ◽

Value At Risk ◽

Optimization Problems ◽

Conditional Value At Risk ◽

Quantum Computers ◽

Sample Mean ◽

Combinatorial Optimization Problems ◽

Classical Simulation ◽

Variational Algorithms ◽

Quantum Optimization

Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the expectation of the problem Hamiltonian for a parameterized trial quantum state. The expectation is estimated as the sample mean of a set of measurement outcomes, while the parameters of the trial state are optimized classically. This procedure is fully justified for quantum mechanical observables such as molecular energies. In the case of classical optimization problems, which yield diagonal Hamiltonians, we argue that aggregating the samples in a different way than the expected value is more natural. In this paper we propose the Conditional Value-at-Risk as an aggregation function. We empirically show -- using classical simulation as well as quantum hardware -- that this leads to faster convergence to better solutions for all combinatorial optimization problems tested in our study. We also provide analytical results to explain the observed difference in performance between different variational algorithms.

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Filtering variational quantum algorithms for combinatorial optimization

Quantum Science and Technology ◽

10.1088/2058-9565/ac3e54 ◽

2021 ◽

Author(s):

David Amaro ◽

Carlo Modica ◽

Matthias Rosenkranz ◽

Mattia Fiorentini ◽

Marcello Benedetti ◽

...

Keyword(s):

Combinatorial Optimization ◽

Optimization Algorithm ◽

Quantum Computer ◽

Quantum Algorithms ◽

Optimal Solution ◽

Quantum Computers ◽

Trapped Ion ◽

Quantum Processor ◽

Computational Advantage ◽

Better Than

Abstract Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the Filtering Variational Quantum Eigensolver (F-VQE) which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the Quantum Approximate Optimization Algorithm (QAOA). We also demonstrate the experimental feasibility of our algorithms on a Honeywell trapped-ion quantum processor.

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