scholarly journals Electronic structure with direct diagonalization on a D-wave quantum annealer

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Alexander Teplukhin ◽  
Brian K. Kendrick ◽  
Sergei Tretiak ◽  
Pavel A. Dub
Keyword(s):  
Electronic Structure ◽  
Quantum Chemistry ◽  
Quantum Information Processing ◽  
Optimization Problems ◽  
Quantum Computers ◽  
Matrix Formulation ◽  
Molecular Systems ◽  
The Matrix ◽  
Near Term ◽  
D Wave

AbstractQuantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

scholarly journals Quantum chemistry as a benchmark for near-term quantum computers

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Alexander J. McCaskey ◽  
Zachary P. Parks ◽  
Jacek Jakowski ◽  
Shirley V. Moore ◽  
Titus D. Morris ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Mitigation Strategies ◽  
Quantum Computers ◽  
Molecular Systems ◽  
Active Space ◽  
Space Reduction ◽  
Error Mitigation ◽  
Near Term ◽  
Reduced Density ◽  
Specific Error

AbstractWe present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active-space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark using 4 of the available qubits on the 20-qubit IBM Tokyo and 16-qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH), with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings and a selected range of problems, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.

scholarly journals Solving Combinatorial Optimization Problems on Quantum Computers

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.

scholarly journals QUBO Formulations for a System of Linear Equations

2022 ◽  
Author(s):  
Kyungtaek Jun
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Quantum Algorithm ◽  
Least Square ◽  
Quantum Computers ◽  
Binary Representation ◽  
Wave System ◽  
The Matrix ◽  
Almost All ◽  
D Wave

Abstract With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all of science and engineering. Harrow-Hassidim-Lloyd algorithm, a monumental quantum algorithm for solving linear systems on the gate model quantum computers, was invented and several advanced variations have been developed. For a given square matrix A∈R(n×n) and a vector b∈R(n), we will find unconstrained binary optimization (QUBO) models for a vector x∈R(n) that satisfies Ax=b. To formulate QUBO models for a linear system solving problem, we make use of a linear least-square problem with binary representation of the solution. We validate those QUBO models on the D-Wave system and discuss the results. For a simple system, We provide a python code to calculate the matrix characterizing the relationship between the variables and to print the test code that can be used directly in D-Wave system.

Structural/Property Relationships for Optical Materials

1993 ◽  
Vol 329 ◽  
Author(s):  
Vivien D.
Keyword(s):  
Crystal Structure ◽  
Optical Properties ◽  
Electronic Structure ◽  
Chemical Composition ◽  
Field Strength ◽  
Optical Materials ◽  
Site Occupancy ◽  
Laser Materials ◽  
Crystal Field Strength ◽  
The Matrix

AbstractIn this paper the relationships between the crystal structure, chemical composition and electronic structure of laser materials, and their optical properties are discussed. A brief description is given of the different laser activators and of the influence of the matrix on laser characteristics in terms of crystal field strength, symmetry, covalency and phonon frequencies. The last part of the paper lays emphasis on the means to optimize the matrix-activator properties such as control of the oxidation state and site occupancy of the activator and influence of its concentration.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

scholarly journals Quantum HF/DFT-embedding algorithms for electronic structure calculations: Scaling up to complex molecular systems

2021 ◽  
Vol 154 (11) ◽  
pp. 114105
Author(s):  
Max Rossmannek ◽  
Panagiotis Kl. Barkoutsos ◽  
Pauline J. Ollitrault ◽  
Ivano Tavernelli
Keyword(s):  
Electronic Structure ◽  
Electronic Structure Calculations ◽  
Scaling Up ◽  
Molecular Systems ◽  
Structure Calculations

scholarly journals Scaling up electronic structure calculations on quantum computers: The frozen natural orbital based method of increments

2021 ◽  
Vol 155 (3) ◽  
pp. 034110
Author(s):  
Prakash Verma ◽  
Lee Huntington ◽  
Marc P. Coons ◽  
Yukio Kawashima ◽  
Takeshi Yamazaki ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Electronic Structure Calculations ◽  
Scaling Up ◽  
Quantum Computers ◽  
Natural Orbital ◽  
Structure Calculations

scholarly journals Optical spin-state polarization in a binuclear europium complex towards molecule-based coherent light-spin interfaces

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kuppusamy Senthil Kumar ◽  
Diana Serrano ◽  
Aline M. Nonat ◽  
Benoît Heinrich ◽  
Lydia Karmazin ◽  
...  
Keyword(s):  
Ground State ◽  
Quantum Information Processing ◽  
Optical Transition ◽  
Molecular Engineering ◽  
Coherent Light ◽  
Nuclear Spins ◽  
Rare Earth Ion ◽  
Molecular Systems ◽  
Homogeneous Linewidth ◽  
State Spin

AbstractThe success of the emerging field of solid-state optical quantum information processing (QIP) critically depends on the access to resonant optical materials. Rare-earth ion (REI)-based molecular systems, whose quantum properties could be tuned taking advantage of molecular engineering strategies, are one of the systems actively pursued for the implementation of QIP schemes. Herein, we demonstrate the efficient polarization of ground-state nuclear spins—a fundamental requirement for all-optical spin initialization and addressing—in a binuclear Eu(III) complex, featuring inhomogeneously broadened 5D0 → 7F0 optical transition. At 1.4 K, long-lived spectral holes have been burnt in the transition: homogeneous linewidth (Γh) = 22 ± 1 MHz, which translates as optical coherence lifetime (T2opt) = 14.5 ± 0.7 ns, and ground-state spin population lifetime (T1spin) = 1.6 ± 0.4 s have been obtained. The results presented in this study could be a progressive step towards the realization of molecule-based coherent light-spin QIP interfaces.

scholarly journals Benchmarking Quantum Annealing Against “Hard” Instances of the Bipartite Matching Problem

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Daniel Vert ◽  
Renaud Sirdey ◽  
Stéphane Louise
Keyword(s):  
Simulated Annealing ◽  
Polynomial Time ◽  
Optimal Solution ◽  
Quantum Computers ◽  
Quantum Annealing ◽  
Maximum Cardinality ◽  
Matching Problem ◽  
Bipartite Matching ◽  
Wave Device ◽  
D Wave

AbstractThis paper experimentally investigates the behavior of analog quantum computers as commercialized by D-Wave when confronted to instances of the maximum cardinality matching problem which is specifically designed to be hard to solve by means of simulated annealing. We benchmark a D-Wave “Washington” (2X) with 1098 operational qubits on various sizes of such instances and observe that for all but the most trivially small of these it fails to obtain an optimal solution. Thus, our results suggest that quantum annealing, at least as implemented in a D-Wave device, falls in the same pitfalls as simulated annealing and hence provides additional evidences suggesting that there exist polynomial-time problems that such a machine cannot solve efficiently to optimality. Additionally, we investigate the extent to which the qubits interconnection topologies explains these latter experimental results. In particular, we provide evidences that the sparsity of these topologies which, as such, lead to QUBO problems of artificially inflated sizes can partly explain the aforementioned disappointing observations. Therefore, this paper hints that denser interconnection topologies are necessary to unleash the potential of the quantum annealing approach.

scholarly journals Coreset Clustering on Small Quantum Computers

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1690
Author(s):  
Teague Tomesh ◽  
Pranav Gokhale ◽  
Eric R. Anschuetz ◽  
Frederic T. Chong
Keyword(s):  
Quantum Algorithms ◽  
Quantum Computers ◽  
Data Sets ◽  
New Paradigm ◽  
Data Set ◽  
Small Quantum ◽  
Natural Data ◽  
Near Term ◽  
Classical Computing ◽  
Quantum Speedup

Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.

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