SEARCH · Engineering Papers

Results for “Quantum approximate optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Diabatic quantum annealing for the frustrated ring model

Abstract Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N " M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N$\gg$M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Toward computing bounds for Ramsey numbers using quantum annealing

Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems, such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum annealing as a tool for use in exploring combinatorial mathematics research problems. We consider the monochromatic triangle problem and the Ramsey number problem, both examples of graph coloring. Conversion to quadratic unconstrained binary optimization (QUBO) form is required to run on quantum hardware. While the monochromatic triangle problem is quadratic by nature, the Ramsey number problem requires the use of order reduction methods for a quadratic formulation. The goal is to provide a method for producing special colorings of graphs which if successful would provide lower bounds for certain Ramsey numbers. We discuss implementations, limitations, and results when running on the D-Wave Advantage quantum annealer.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Online Convex Optimization of Programmable Quantum Computers to Simulate Time-Varying Quantum Channels

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2018

QAOA Tutorial Outline

In this tutorial we discuss the quantum alternating operator ansatz (QAOA), which is a variational algorithm that can be used for approximate optimization of combinatorial problems with soft and hard constraints.We go through the design of the quantum circuit and its actual implementation in real hardware, discussing compilation issues such as gate synthesis and scheduling of all the required gates and qubit-swapping overhead.

Venturelli, Davide↗

DOE OSTI2022

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Exploring Quantum State Preparation Using Tensor Networks and Sparse Wavefunction Simulations

The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.

quantum computing↗

DOE OSTI2025

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗

DOE OSTI2021

QUBO formulations for training machine learning models

Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an ever-increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers can approximately solve NP-hard problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore’s law era. In order to solve problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Quantum-Accelerated Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; One for producing an approximately optimal Steiner Tree, and one for producing an exact Minimum Directed Spanning tree. These use O(n1/4) rounds of communication and O(n9/4) messages, leading to a quantum speedup in round and message complexity compared to any known algorithms in the classical CONGEST-CLIQUE model (vs O(n1/3) and O(n7/3)). At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Further, these problems can not be sped up in the CONGEST (non-clique) setting, and we characterize the constants involved.

Phillip Kerger↗

DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Tough Errors Are no Match (TEAM): Optimizing the Quantum Compiler for Noise Resilience

This report summarizes research performed under the Tough Errors Are no Match (TEAM) project. The primary focus of TEAM has been to research and develop a compilation toolbox leveraging techniques from quantum characterization and control, probabilistic programming, and approximate computing. Our goal was to develop robust protocols that can be integrated into quantum compilers to optimize and enhance the robustness of noisy computation. Here, we provide a summary of TEAM work focused on characterization and control of quantum systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Flux-pumped impedance-engineered broadband Josephson parametric amplifier

Broadband quantum-limited amplifiers play a critical role in the single-shot readout of superconducting qubits, but a popular implementation, the traveling wave parametric amplifier, involves a complex design and fabrication process. Here, we present a simple design for a Josephson parametric amplifier, using a lumped element resonator comprising a superconducting quantum interference device whose useful bandwidth is enhanced with an on-chip impedance-matching circuit. Additionally, we demonstrate a flux-coupling geometry that maximizes the coupling to the Josepson loop and minimizes spurious excitation of the amplifier resonant circuit. The amplifier, which operates in a flux-pumped mode, is demonstrated with a power gain of more than 20dB over a bandwidth of about 300MHz, where approximate noise measurements indicate quantum-limited pehrformance. A procedure is given for optimizing the bandwidth for this kind of amplifier, using a linearized circuit simulation while minimizing non-linearities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST- CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses O ̃(n1/4) rounds of communication and O ̃(n9/4) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗

DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST- CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses O ̃(n 1/4 ) rounds of communication and O ̃(n 9/4 ) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗