IA Scholar Query: Multistart Methods for Quantum Approximate optimization.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgTue, 13 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440An extensive numerical benchmark study of deterministic vs. stochastic derivative-free global optimization algorithms
https://scholar.archive.org/work/kfwihe6vbrb35knfi4jatbai2y
Research in derivative-free global optimization is under active development, and many solution techniques are available today. Therefore, the experimental comparison of previous and emerging algorithms must be kept up to date. This paper considers the solution to the bound-constrained, possibly black-box global optimization problem. It compares 64 derivative-free deterministic algorithms against classic and state-of-the-art stochastic solvers. Among deterministic ones, a particular emphasis is on DIRECT-type, where, in recent years, significant progress has been made. A set of 800 test problems generated by the well-known GKLS generator and 397 traditional test problems from DIRECTGOLib v1.2 collection are utilized in a computational study. More than 239400 solver runs were carried out, requiring more than 531 days of single CPU time to complete them. It has been found that deterministic algorithms perform excellently on GKLS-type and low-dimensional problems, while stochastic algorithms have shown to be more efficient in higher dimensions.Linas Stripinis, Remigijus Paulavičiuswork_kfwihe6vbrb35knfi4jatbai2yTue, 13 Sep 2022 00:00:00 GMTSurvey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches
https://scholar.archive.org/work/5tbj5457gnfddca7ei7i6ix6ry
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications. To accomplish these objectives, we present a multi-part survey. In part one, we focused on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. We emphasize the important characteristics of each method, and we discuss promising directions for future research. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.Ilias S. Kotsireas, Panos M. Pardalos, Alexander Semenov, William T. Trevena, Michael N. Vrahatiswork_5tbj5457gnfddca7ei7i6ix6ryWed, 17 Aug 2022 00:00:00 GMTLEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach
https://scholar.archive.org/work/wfzzkpnyezhfhcwpnhchktulve
While showing great promise, circuit synthesis techniques that combine numerical optimization with search over circuit structures face scalability challenges due to a large number of parameters, exponential search spaces, and complex objective functions. The LEAP algorithm improves scaling across these dimensions using iterative circuit synthesis, incremental re-optimization, dimensionality reduction, and improved numerical optimization. LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit. By narrowing the search space, LEAP improves scalability from four to six qubit circuits. LEAP was evaluated with known quantum circuits such as QFT and physical simulation circuits like the VQE, TFIM, and QITE. LEAP can compile four qubit unitaries up to 59 × faster than QSearch and five and six qubit unitaries with up to 1.2 × fewer CNOTs compared to the QFAST package. LEAP can reduce the CNOT count by up to 36 ×, or 7 × on average, compared to the CQC Tket compiler. Despite its heuristics, LEAP has generated optimal circuits for many test cases with a priori known solutions. The techniques introduced by LEAP are applicable to other numerical-optimization-based synthesis approaches.Ethan Smith, Marc G. Davis, Jeffrey M. Larson, Ed Younis, Lindsay Bassman, Wim Lavrijsen, Costin Iancuwork_wfzzkpnyezhfhcwpnhchktulveTue, 09 Aug 2022 00:00:00 GMTAccelerating Noisy VQE Optimization with Gaussian Processes
https://scholar.archive.org/work/yb7f6cl3lvgd3esy2l4mvrzj5e
Hybrid variational quantum algorithms, which combine a classical optimizer with evaluations on a quantum chip, are the most promising candidates to show quantum advantage on current noisy, intermediate-scale quantum (NISQ) devices. The classical optimizer is required to perform well in the presence of noise in the objective function evaluations, or else it becomes the weakest link in the algorithm. We introduce the use of Gaussian Processes (GP) as surrogate models to reduce the impact of noise and to provide high quality seeds to escape local minima, whether real or noise-induced. We build this as a framework on top of local optimizations, for which we choose Implicit Filtering (ImFil) in this study. ImFil is a state-of-the-art, gradient-free method, which in comparative studies has been shown to outperform on noisy VQE problems. The result is a new method: "GP+ImFil". We show that when noise is present, the GP+ImFil approach finds results closer to the true global minimum in fewer evaluations than standalone ImFil, and that it works particularly well for larger dimensional problems. Using GP to seed local searches in a multi-modal landscape shows mixed results: although it is capable of improving on ImFil standalone, it does not do so consistently and would only be preferred over other, more exhaustive, multistart methods if resources are constrained.Juliane Mueller, Wim Lavrijsen, Costin Iancu, Wibe de Jongwork_yb7f6cl3lvgd3esy2l4mvrzj5eWed, 03 Aug 2022 00:00:00 GMTCopositive programming for mixed-binary quadratic optimization via Ising solvers
https://scholar.archive.org/work/uy5x3i4g2jcx3cb2dwx5y353h4
Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization problems has spurred an increased interest in exploring methods to integrate Ising problems as part of their solution process, with existing approaches ranging from direct transcription to hybrid quantum-classical approaches rooted in existing optimization algorithms. Due to the heuristic and black-box nature of the underlying Ising solvers, many such approaches have limited optimality guarantees. While some hybrid algorithms may converge to global optima, their underlying classical algorithms typically rely on exhaustive search, making it unclear if such algorithmic scaffolds are primed to take advantage of speed-ups that the Ising solver may offer. In this paper, we propose a framework for solving mixed-binary quadratic programs (MBQP) to global optimality using black-box and heuristic Ising solvers. We show the exactness of a convex copositive reformulation of MBQPs, which we propose to solve via a hybrid quantum-classical cutting-plane algorithm. The classical portion of this hybrid framework is guaranteed to be polynomial time, suggesting that when applied to NP-hard problems, the complexity of the solution is shifted onto the subroutine handled by the Ising solver.Robin Brown, David E. Bernal Neira, Davide Venturelli, Marco Pavonework_uy5x3i4g2jcx3cb2dwx5y353h4Wed, 27 Jul 2022 00:00:00 GMTCoincidence ion pair production (cipp) spectroscopy of diiodine
https://scholar.archive.org/work/ut6ust5n4jhd5bklzerjmkzzse
Coincidence ion pair production (I+ + I-) (cipp) spectra of I2 were recorded in a double imaging coincidence experiment in the one-photon excitation region of 71 600-74 000 cm-1. The I+ + I- coincidence signal shows vibrational band head structure corresponding to iodine molecule Rydberg states crossing over to ion-pair (I+I-) potential curves above the dissociation limit. The band origin (ν0), vibrational wavenumber (ωe) and anharmonicity constants (ωexe) were determined for the identified Rydberg states. The analysis revealed a number of previously unidentified states and a reassignment of others following a discrepancy in previous assignments. Since the ion pair production threshold is well established, the electric field-dependent spectral intensities were used to derive the cutoff energy in the transitions to the rotational levels of the 7pσ(1/2) (v' = 3) state.Kristján Matthíasson, Ágúst Kvaran, Gustavo A Garcia, Peter Weidner, Bálint Sztáraywork_ut6ust5n4jhd5bklzerjmkzzseWed, 13 Jul 2022 00:00:00 GMTSyndrome decoding by quantum approximate optimization
https://scholar.archive.org/work/ssoainwp2ncclietvcbqtmfbte
The syndrome decoding problem is known to be NP-hard. We use the quantum approximate optimization algorithm (QAOA) to solve the syndrome decoding problem with elegantly-designed generator- and check-based cost Hamiltonians for classical and quantum codes. Simulations of the level-4 check-based QAOA decoding of the [7,4,3] Hamming code, as well as the level-4 generator-based QAOA decoding of the [[5,1,3]] quantum code, demonstrate decoding performances that match the maximum likelihood decoding. In addition, we show that a combinatorial optimization problem with additional redundant clauses may be more suitable for QAOA, while the number of qubits remains the same. Furthermore, we show that the QAOA decoding of a quantum code is inherently degenerate. That is, degenerate errors of comparable weight will be returned by QAOA with comparable probability. This is supported by simulations of the generator-based QAOA decoding of the [[9,1,3]] Shor code.Ching-Yi Lai, Kao-Yueh Kuo, Bo-Jyun Liaowork_ssoainwp2ncclietvcbqtmfbteWed, 13 Jul 2022 00:00:00 GMTThe Quantum Approximate Optimization Algorithm performance with low entanglement and high circuit depth
https://scholar.archive.org/work/iy5jw7dcfvc7znzqlsrqyasrzm
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot simulate them classically for intermediate sizes. Since entanglement lies at the core of quantum computing power, we investigate its role in these heuristic methods for solving optimization problems. In particular, we use matrix product states to simulate the quantum approximate optimization algorithm with reduced bond dimensions D, a parameter bounding the system entanglement. Moreover, we restrict the simulation further by deterministically sampling solutions. We conclude that entanglement plays a minor role in the MaxCut and Exact Cover 3 problems studied here since the simulated algorithm analysis, with up to 60 qubits and p=100 algorithm layers, shows that it provides solutions for bond dimension D ≈ 10 and depth p ≈ 30. Additionally, we study the classical optimization loop in the approximated algorithm simulation with 12 qubits and depth up to p=4 and show that the approximated optimal parameters with low entanglement approach the exact ones.Rishi Sreedhar, Pontus Vikstål, Marika Svensson, Andreas Ask, Göran Johansson, Laura García-Álvarezwork_iy5jw7dcfvc7znzqlsrqyasrzmThu, 07 Jul 2022 00:00:00 GMTNon-Convex Optimization by Hamiltonian Alternation
https://scholar.archive.org/work/aftdwxacovh6dhpjm4otyhvudm
A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only within a chosen energy range. We find that repeatedly minimizing each Hamiltonian in sequence allows an algorithm to escape local minima. This technique is particularly straightforward when the ground state energy is known, and one obtains an improvement even without this knowledge. We demonstrate this technique by using it to find the ground state for instances of a Sherrington-Kirkpatrick spin glass.Anuj Apte, Kunal Marwaha, Arvind Muruganwork_aftdwxacovh6dhpjm4otyhvudmTue, 28 Jun 2022 00:00:00 GMTQuantum Circuit Optimization and Transpilation via Parameterized Circuit Instantiation
https://scholar.archive.org/work/4y3tfzqluraxplvn3b23y6cafa
Parameterized circuit instantiation is a common technique encountered in the generation of circuits for a large class of hybrid quantum-classical algorithms. Despite being supported by popular quantum compilation infrastructures such as IBM Qiskit and Google Cirq, instantiation has not been extensively considered in the context of circuit compilation and optimization pipelines. In this work, we describe algorithms to apply instantiation during two common compilation steps: circuit optimization and gate-set transpilation. When placed in a compilation workflow, our circuit optimization algorithm produces circuits with an average of 13% fewer gates than other optimizing compilers. Our gate-set transpilation algorithm can target any gate-set, even sets with multiple two-qubit gates, and produces circuits with an average of 12% fewer two-qubit gates than other compilers. Overall, we show how instantiation can be incorporated into a compiler workflow to improve circuit quality and enhance portability, all while maintaining a reasonably low compile time overhead.Ed Younis, Costin Iancuwork_4y3tfzqluraxplvn3b23y6cafaThu, 16 Jun 2022 00:00:00 GMTSimulating strongly interacting Hubbard chains with the variational Hamiltonian ansatz on a quantum computer
https://scholar.archive.org/work/aaqlu4rrvfgqtj3gahctqdoz74
Hybrid quantum-classical algorithms have been proposed to circumvent noise limitations in quantum computers. Such algorithms delegate only a calculation of the expectation value to the quantum computer. Among them, the variational quantum eigensolver has been implemented to study molecules and condensed matter systems on small size quantum computers. Condensed matter systems described by the Hubbard model exhibit a rich phase diagram alongside exotic states of matter. In this paper we try to answer the question: How much of the underlying physics of a 1D Hubbard chain is described by a problem-inspired variational Hamiltonian ansatz in a broad range of parameter values? We start by probing how much the solution increases fidelity with increasing ansatz complexity. Our findings suggest that even low fidelity solutions capture energy and number of doubly occupied sites well, while spin-spin correlations are not well captured even when the solution is of high fidelity. Our powerful simulation platform allows us to incorporate a realistic noise model and shows a successful implementation of noise-mitigation strategies-postselection and the Richardson extrapolation. Finally, we compare our results with an experimental realization of the algorithm on IBM Quantum's ibmq_quito device.Baptiste Anselme Martin, Pascal Simon, Marko J. Rančićwork_aaqlu4rrvfgqtj3gahctqdoz74Mon, 06 Jun 2022 00:00:00 GMTNoisy Bayesian optimization for variational quantum eigensolvers
https://scholar.archive.org/work/pvrz7m5bcrdgjm2v7ygbglzkly
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to find the ground state of a Hamiltonian using variational methods. In the context of this Lattice symposium, the procedure can be used to study lattice gauge theories (LGTs) in the Hamiltonian formulation. Bayesian optimization (BO) based on Gaussian process regression (GPR) is a powerful algorithm for finding the global minimum of a cost function, e.g. the energy, with a very low number of iterations using data affected by statistical noise. This work proposes an implementation of GPR and BO specifically tailored to perform VQE on quantum computers already available today.Giovanni Iannelli, Karl Jansenwork_pvrz7m5bcrdgjm2v7ygbglzklyMon, 16 May 2022 00:00:00 GMTHigh Power Irradiance Dependence of Charge Species Dynamics in Hybrid Perovskites and Kinetic Evidence for Transient Vibrational Stark Effect in Formamidinium
https://scholar.archive.org/work/kompjflsfrbpda4xe4qdscquxa
Hybrid halide perovskites materials have the potential for both photovoltaic and light-emitting devices. Relatively little has been reported on the kinetics of charge relaxation upon intense excitation. In order to evaluate the illumination power density dependence on the charge recombination mechanism, we have applied a femtosecond transient mid-IR absorption spectroscopy with strong excitation to directly measure the charge kinetics via electron absorption. The irradiance-dependent relaxation processes of the excited, photo-generated charge pairs were quantified in polycrystalline MAPbI3, MAPbBr3, and (FAPbI3)0.97(MAPbBr3)0.03 thin films that contain either methylamonium (MA) or formamidinium (FA). This report identifies the laser-generated charge species and provides the kinetics of Auger, bimolecular and excitonic decay components. The inter-band electron-hole (bimolecular) recombination was found to dominate over Auger recombination at very high pump irradiances, up to the damage threshold. The kinetic analysis further provides direct evidence for the carrier field origin of the vibrational Stark effect in a formamidinium containing perovskite material. The results suggest that radiative excitonic and bimolecular recombination in MAPbI3 at high excitation densities could support light-emitting applications.Rafal Rakowski, William Fisher, Joaquín Calbo, Muhamad Z. Mokhtar, Xinxing Liang, Dong Ding, Jarvist M. Frost, Saif A. Haque, Aron Walsh, Piers R. F. Barnes, Jenny Nelson, Jasper J. Van Thorwork_kompjflsfrbpda4xe4qdscquxaTue, 10 May 2022 00:00:00 GMTQuantum Annealing for Jet Clustering with Thrust
https://scholar.archive.org/work/lt6xmvxg45dybag3dwg7fgj2ua
Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called "thrust" in electron-positron collision events. We find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, but only after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.Andrea Delgado, Jesse Thalerwork_lt6xmvxg45dybag3dwg7fgj2uaThu, 05 May 2022 00:00:00 GMTParameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo
https://scholar.archive.org/work/aokigfhnp5az7fub7a4p6wazym
Bayesian-inference-based approaches, in particular the random-walk Markov Chain Monte Carlo (MCMC) method, have received much attention recently for X-ray scattering analysis. Hamiltonian MCMC, a state-of-the-art development in the field of MCMC, has become popular in recent years. It utilizes Hamiltonian dynamics for indirect but much more efficient drawings of the model parameters. We described the principle of the Hamiltonian MCMC for inversion problems in X-ray scattering analysis by estimating high-dimensional models for several motivating scenarios in small-angle X-ray scattering, reflectivity, and X-ray fluorescence holography. Hamiltonian MCMC with appropriate preconditioning can deliver superior performance over the random-walk MCMC, and thus can be used as an efficient tool for the statistical analysis of the parameter distributions, as well as model predictions and confidence analysis.Zhang Jiang, Jin Wang, Matthew V. Tirrell, Juan J. de Pablo, Wei Chenwork_aokigfhnp5az7fub7a4p6wazymFri, 22 Apr 2022 00:00:00 GMTPerformance Evaluation and Acceleration of the QTensor Quantum Circuit Simulator on GPUs
https://scholar.archive.org/work/kogi74334zbwjloz6gbrivhehi
This work studies the porting and optimization of the tensor network simulator QTensor on GPUs, with the ultimate goal of simulating quantum circuits efficiently at scale on large GPU supercomputers. We implement NumPy, PyTorch, and CuPy backends and benchmark the codes to find the optimal allocation of tensor simulations to either a CPU or a GPU. We also present a dynamic mixed backend to achieve optimal performance. To demonstrate the performance, we simulate QAOA circuits for computing the MaxCut energy expectation. Our method achieves 176× speedup on a GPU over the NumPy baseline on a CPU for the benchmarked QAOA circuits to solve MaxCut problem on a 3-regular graph of size 30 with depth p=4.Danylo Lykov, Angela Chen, Huaxuan Chen, Kristopher Keipert, Zheng Zhang, Tom Gibbs, Yuri Alexeevwork_kogi74334zbwjloz6gbrivhehiTue, 12 Apr 2022 00:00:00 GMTA Heuristically Generated Metric Approach to the Solution of Chase Problem
https://scholar.archive.org/work/lhyzt5hvfjgltdokg3x24uz2lq
In this work, heuristic, hyper-heuristic, and metaheuristic approaches are reviewed. Distance metrics are also examined to solve the "puzzle problems by searching" in AI. A viewpoint is brought by introducing the so-called Heuristically Generated Angular Metric Approach (HAMA) through the explanation of the metrics world. Distance metrics are applied to "cat and mouse" problem where cat and mouse makes smart moves relative to each other and therefore makes more appropriate decisions. The design is built around Fuzzy logic control to determine route finding between the pursuer and prey. As the puzzle size increases, the effect of HAMA can be distinguished more clearly in terms of computation time towards a solution. Hence, mouse will gain more time in perceiving the incoming danger, thus increasing the percentage of evading the danger. 'Caught and escape percentages vs. number of cats' for three distance metrics have been created and the results evaluated comparatively. Given three termination criteria, it is never inconsistent to define two different objective functions: either the cat travels the distance to catch the mouse, or the mouse increases the percentage of escape from the cat.İhsan Ömür Bucakwork_lhyzt5hvfjgltdokg3x24uz2lqWed, 16 Feb 2022 00:00:00 GMTStochastic Processes Under Linear Differential Constraints : Application to Gaussian Process Regression for the 3 Dimensional Free Space Wave Equation
https://scholar.archive.org/work/52xuv3j3pne7doievuwtcsdzgy
Let P be a linear differential operator over 𝒟⊂ℝ^d and U = (U_x)_x ∈𝒟 a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition for all the trajectories of U to verify the partial differential equation (PDE) T(U) = 0. This condition is formulated in terms of the covariance kernel of U. When compared to previous similar results, the novelty lies in that the equality T(U) = 0 is understood in the sense of distributions, which is a relevant framework for PDEs. This theorem provides precious insights during the second part of this article, devoted to performing "physically informed" machine learning for the homogeneous 3 dimensional free space wave equation. We perform Gaussian process regression (GPR) on pointwise observations of a solution of this PDE. To do so, we propagate Gaussian processes (GP) priors over its initial conditions through the wave equation. We obtain explicit formulas for the covariance kernel of the propagated GP, which can then be used for GPR. We then explore the particular cases of radial symmetry and point source. For the former, we derive convolution-free GPR formulas; for the latter, we show a direct link between GPR and the classical triangulation method for point source localization used in GPS systems. Additionally, this Bayesian framework provides a new answer for the ill-posed inverse problem of reconstructing initial conditions for the wave equation with a limited number of sensors, and simultaneously enables the inference of physical parameters from these data. Finally, we illustrate this physically informed GPR on a number of practical examples.Iain Henderson, Pascal Noble, Olivier Roustantwork_52xuv3j3pne7doievuwtcsdzgyThu, 10 Feb 2022 00:00:00 GMTMultistart Algorithm for Identifying All Optima of Nonconvex Stochastic Functions
https://scholar.archive.org/work/ef6ca62qojemjfb764c3cqi7li
We propose a multistart algorithm to identify all local minima of a constrained, nonconvex stochastic optimization problem. The algorithm uniformly samples points in the domain and then starts a local stochastic optimization run from any point that is the "probabilistically best" point in its neighborhood. Under certain conditions, our algorithm is shown to asymptotically identify all local optima with high probability; this holds even though our algorithm is shown to almost surely start only finitely many local stochastic optimization runs. We demonstrate the performance of an implementation of our algorithm on nonconvex stochastic optimization problems, including identifying optimal variational parameters for the quantum approximate optimization algorithm.Prateek Jaiswal, Jeffrey Larsonwork_ef6ca62qojemjfb764c3cqi7liTue, 04 Jan 2022 00:00:00 GMTOpto-Electronics Review
https://scholar.archive.org/work/worzr2jom5ac3hzx5dkom2yw7m
External light outcoupling structures provide a cost-effective and highly efficient solution for light extraction in organic light-emitting diodes. Among them, different microtextures, mainly optimized for devices with isotopically oriented emission dipoles, have been proposed as an efficient light extraction solution. In the paper, the outcoupling for a preferential orientation of emission dipoles is studied for the case of a red bottom-emitting organic light-emitting diode. Optical simulations are used to analyse the preferential orientation of dipoles in combination with three different textures, namely hexagonal array of sine-textures, three-sided pyramids, and random pyramids. It is shown that while there are minimal differences between the optimized textures, the highest external quantum efficiency of 51% is predicted by using the three-sided pyramid texture. Further improvements, by employing highly oriented dipole sources, are examined. In this case, the results show that the top outcoupling efficiencies can be achieved with the same texture shape and size, regardless of the preferred orientation of the emission dipoles. Using an optimized three-sided pyramid in combination with ideally parallel oriented dipoles, an efficiency of 62% is achievable. A detailed analysis of the optical situation inside the glass substrate, dominating external light outcoupling, is presented. Depicted results and their analysis offer a simplified further research and development of external light extraction for organic light-emitting devices with highly oriented dipole emission sources.Milan Kovačičwork_worzr2jom5ac3hzx5dkom2yw7m