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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2022

Neural network accelerator for quantum control

Efficient quantum control is necessary for practical quantum computing implementations with current technologies. Conventional algorithms for determining optimal control parameters are computationally expensive, largely excluding them from use outside of the simulation. Existing hardware solutions structured as lookup tables are imprecise and costly. By designing a machine learning model to approximate the results of traditional tools, a more efficient method can be produced. Such a model can then be synthesized into a hardware accelerator for use in quantum systems. In this study, we demonstrate a machine learning algorithm for predicting optimal pulse parameters. This algorithm is lightweight enough to fit on a low-resource FPGA and perform inference with a latency of 175 ns and pipeline interval of 5 ns with > 0.99 gate fidelity. In the long term, such an accelerator could be used near quantum computing hardware where traditional computers cannot operate, enabling quantum control at a reasonable cost at low latencies without incurring large data bandwidths outside of the cryogenic environment.

43 PARTICLE ACCELERATORS↗
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 OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗
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 spanning arborescence of minimum weight, the analog of a Minimum Spanning Tree in a directed graph, each of which uses O~(n^(1/4)) rounds of communication and O~(n^(9/4)) messages, achieving a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. The CONGEST distributed computational model allows limited-sized messages to be transmitted within a network described by a communication graph of size n in a series of rounds to address a computational problem. The size limitation for such messages isO(log(n)) bits at each edge of the communication graph per round. The communication graph in the CONGEST-CLIQUE model is fully connected. In the Quantum CONGEST-CLIQUE model, at most O(log(n)) classical and quantum bits (qubits) can be communicated across each edge of the communication graph per round. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. These speedups further contribute to understanding what problems can be solved more efficiently when we allow quantum communication in this CONGEST-CLIQUE model of distributed computation.

quantum distributed algorithms↗
DOE OSTI2024

Performance Analysis of an Optimization Algorithm for Metamaterial Design on the Integrated High-Performance Computing and Quantum Systems

Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still faces difficulties in optimizing complex structures that have potentially high performance. In this work, we comprehensively analyze the performance of an optimization algorithm for metamaterial design on the integrated HPC and quantum systems. We demonstrate significant time advantages through message-passing interface (MPI) parallelization on the high-performance computing (HPC) system showing approximately 54% faster ML tasks and 67 times faster optical simulation against serial workloads. Furthermore, we analyze the performance of a quantum algorithm designed for optimization, which runs with various quantum simulators on a local computer or HPC-quantum system. Results showcase ~24 times speedup when executing the optimization algorithm on the HPC-quantum hybrid system. This study paves a way to optimize complex metamaterials using the integrated HPC-quantum system.

Kim, Seongmin↗
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 OSTI2023

Collective neutrino oscillations on a quantum computer with hybrid quantum-classical algorithm

We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps are further optimized using the Cartan decomposition of two-qubit unitary gates U ϵ SU(4) in the minimum number of controlled-NOT (CNOT) gates making the algorithm more resilient to the hardware noise. As a result, a more efficient hybrid quantum-classical algorithm is also explored to solve the problem on noisy intermediate-scale quantum devices.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Faster Tensor Network Decoding for Topological Quantum Codes

We present a fast and Bayes-optimal-approximating tensor network decoder for planar quantum LDPC codes based on the tensor renormalization group algorithm, originally proposed by Levin, and Nave. By precomputing the renormalization group flow for the null syndrome, we need only recompute tensor contractions in the causal cone of the measured syndrome at the time of decoding. This allows us to achieve an overall runtime complexity of ($pnχ^6$) where p is the depolarizing noise rate, and χ is the cutoff value used to control singular value decomposition approximations used in the algorithm. We apply our decoder to the surface code in the code capacity noise model and compare its performance to the original matrix product state (MPS) tensor network decoder introduced by Bravyi, Suchara, and Vargo. The MPS decoder has a p-independent runtime complexity of $\mathcal{O}(nχ^3)$ resulting in significantly slower decoding times compared to our algorithm in the low-p regime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation

We present a classically tractable model that leads to optimized low-depth quantum circuits leveraging separable-pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the long term, provide significantly improved initial states for quantum algorithms. The associated wave functions can be represented with linear memory requirement, which allows classical optimization of the circuits and naturally defines a minimum benchmark for quantum algorithms. In this work we employ directly determined pair-natural orbitals within a basis-set-free approach. This leads to accurate representation of the one- and many-body parts for weakly correlated systems and we explicitly illustrate how the model can be integrated into other quantum algorithms for stronger correlated systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
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 OSTI2024

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2023

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over Trotterized adiabatic quantum computation and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critical Hamming radius, or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. This work proposes IST-SAT a new quantum algorithm, which improves upon solutions obtained from initial classical or quantum optimization algorithms. The steering mechanism we introduce through IST-SAT presents a new path toward achieving quantum advantage in optimization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp ( t H ) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. Here, we provide optimized decompositions up to order t 6 . The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n = 2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗