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DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Gu, Shouzhen [Yale U.]↗

DOE OSTI2026

Quantum Computing in Next-Generation Transportation Optimization

We explore how quantum computing (QC) can advance transportation optimization, with a focus on two high-impact areas: traffic signal control and vehicle electrification with grid integration. As transportation systems grow in complexity, classical optimization methods increasingly struggle to deliver scalable and efficient solutions, particularly for real-time, data-rich environments. This work identifies key challenges within these two domains where QC may offer advantages, particularly in handling combinatorial decision spaces and dynamic constraints. We begin by outlining the limitations of classical approaches for traffic signal control optimization and electric vehicle charging coordination, highlighting where computational limitations arise. Previous quantum formulations are presented and new formulations are proposed to demonstrate how emerging quantum algorithms, including quantum annealing and the Quantum Approximation Optimization Algorithm, could be leveraged to reformulate and address these problems. We also evaluate the suitability of current quantum hardware and discuss recent trends that indicate when QC may become a viable tool for transportation applications. While acknowledging the present limitations of QC technologies, this poster emphasizes the importance of preparing quantum-compatible models today. By reviewing and establishing formulations that align with the strengths of quantum algorithms, researchers and practitioners can better position themselves to take advantage of QC advancements as they occur. This work aims to provide a practical, forward-looking perspective on the near-term potential of quantum computing in transportation optimization.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Numerical gate synthesis for quantum heuristics on bosonic quantum processors

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity ( > 0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Multireference Embedding and Fragmentation Methods for Classical and Quantum Computers: From Model Systems to Realistic Applications

One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this Review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. Here, by extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

Algorithms↗

DOE OSTI2021

Weak Simulation v.0.1

The SPARSIFY algorithm implemented by the code allows for classical simulation of universal quantum computer sample outcomes. The code sparsifies the stabilizer decomposition of a qubit t-tensored T gate magic state to some additive error. This is accomplished by either independent L1 sampling or with correlated L1 sampling to supplement an independent subset, which offers a more efficient decomposition: for a given t, a sparser decomposition is sufficient with correlated L1 sampling to satisfy a given additive error. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-8296 O

SciDAC↗

DOE OSTI2022

Cross-platform comparison of arbitrary quantum states

As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information of executing specific tasks for a single QC. On the other hand, a comparison between different QCs preparing nominally the same arbitrary circuit provides an insight for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform state fidelities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Noise resilience of variational quantum compiling

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry

State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space–unitary coupled cluster (LAS–UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. Here, in this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We test the two state preparation methods on three systems, ranging from a model system, a set of interacting hydrogen molecules, to more realistic chemical problems, like the C–C double bond breaking in transbutadiene and the spin ladder in a bimetallic system. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits that can be used for realistic chemical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Efficiently embedding QUBO problems on adiabatic quantum computers

Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. Yet, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. Here, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Large-scale simulations of Floquet physics on near-term quantum computers

Abstract Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ω but also a linear advantage in simulation time t compared to Trotterization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Spatiotemporal multiplexing based on hexagonal multicore optical fibres

Based on a genetic algorithm, we have solved in this paper the problem of finding the parameters of optical Gaussian pulses which make their efficient nonlinear combining possible in one of the peripheral cores of a 7-core hexagonal fibre. Two approaches based on individual selection of peak powers and field phases of the pulses launched into the fibre are considered. Finally, the found regimes of Gaussian pulse combining open up new possibilities for the development of devices for controlling optical radiation.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A semi-agnostic ansatz with variable structure for variational quantum algorithms

Quantum machine learning—and specifically Variational Quantum Algorithms (VQAs)—offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for VQAs. Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

A High-Efficiency Delayed Update Algorithm for Evaluating Slater Determinants in Quantum Monte Carlo

For quantum Monte Carlo simulations of molecular systems or supercells with thousands of electrons, matrix operations related to Slater determinants lead the computational cost. McDaniel et al. [J. Chem. Phys. 2017, 147, 174107] proposed a delayed update algorithm to increase computational efficiency by using matrix–matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman–Morrison–Woodbury formula remained a bottleneck. Here, in this work, we introduce an improved algorithm for CPUs and GPUs that (1) reduces this bottleneck by iteratively updating the intermediate matrices and (2) is efficient at any acceptance ratio, with no cost for rejected moves on CPUs and minimal cost on GPUs. We show the full scheme of integrating the delayed update algorithm into a single-electron move. The high efficiency of our algorithm is demonstrated on CPUs and GPUs for a 512 atom/6144 valence electron calculation, with 12× and 2× overall speed-up compared to traditional rank-1 update schemes in diffusion quantum Monte Carlo, respectively.

Luo, Ye [Argonne National Laboratory (ANL), Argonn↗

DOE OSTI2017

Ising Processing Units: Potential and Challenges for Discrete Optimization

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, presents new opportunities for hybrid-optimization algorithms that leverage these kinds of specialized hardware. In this work, we propose the idea of an Ising processing unit as a computational abstraction for these emerging tools. Challenges involved in using and bench- marking these devices are presented, and open-source software tools are proposed to address some of these challenges. The proposed benchmarking tools and methodology are demonstrated by conducting a baseline study of established solution methods to a D-Wave 2X adiabatic quantum computer, one example of a commercially available Ising processing unit.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Accelerating Scientific Computing in the Post-Moore’s Era

Novel uses of graphical processing units for accelerated computation revolutionized the field of high-performance scientific computing by providing specialized workflows tailored to algorithmic requirements. As the era of Moore’s law draws to a close, many new non–von Neumann processors are emerging as potential computational accelerators, including those based on the principles of neuromorphic computing, tensor algebra, and quantum information. While development of these new processors is continuing to mature, the potential impact on accelerated computing is anticipated to be profound. We discuss how different processing models can advance computing in key scientific paradigms: machine learning and constraint satisfaction. Significantly, each of these new processor types utilizes a fundamentally different model of computation, and this raises questions about how to best use such processors in the design and implementation of applications. While many processors are being developed with a specific domain target, the ubiquity of spin-glass models and neural networks provides an avenue for multi-functional applications. Furthermore, this also hints at the infrastructure needed to integrate next-generation processing units into future high-performance computing systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Quantum computing for a profusion of postman problem variants

In this paper we study the viability of solving the Chinese Postman Problem, a graph routing optimization problem, and many of its variants on a quantum annealing device. Routing problem variants considered include graph type, directionally varying weights, number of parties involved in routing, among others. We put emphasis on the explanation of how to convert such problems into quadratic unconstrained binary optimization (QUBO) problems. QUBO is one of two equivalent natural paradigms for quantum annealing devices, the other being the Ising Model. We also expand upon a previously discovered algorithm for solving the Chinese Postman Problem on a closed undirected graph to decrease the number of constraints and variables used in the problem. Optimal annealing parameter settings and constraint weight values are discussed based on results from implementation on the D-Wave 2000Q and Advantage. Results from classical, purely quantum, and hybrid algorithms are compared.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Quantum-assisted associative adversarial network: applying quantum annealing in deep learning

Abstract Generative models have the capacity to model and generate new examples from a dataset and have an increasingly diverse set of applications driven by commercial and academic interest. In this work, we present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum processor can be used to sample from the model to train the Boltzmann machine. This novel hybrid quantum-classical algorithm joins a growing family of algorithms that use a quantum processor sampling subroutine in deep learning, and provides a scalable framework to test the advantages of quantum-assisted learning. For the latent space model, fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies. Evaluated using the Fréchet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset. Classical sampling is used to demonstrate the algorithm on the LSUN bedrooms dataset, indicating scalability to larger and color datasets. Though the quantum processor used here is a quantum annealer, the algorithm is general enough such that any quantum processor, such as gate model quantum computers, may be substituted as a sampler.

Wilson, Max (ORCID:0000000207983391)↗