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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Sampling frequency thresholds for the quantum advantage of the quantum approximate optimization algorithm

We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers Gurobi and MQLib to solve the MaxCut problem on 3-regular graphs. We identify the minimum noiseless sampling frequency and depth p required for a quantum device to outperform classical algorithms. There is potential for quantum advantage on hundreds of qubits and moderate depth with a sampling frequency of 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizes N, a quantum device must support depth p > 11. Additionally, multi-shot QAOA is not efficient on large graphs, indicating that QAOA p ≤ 11 does not scale with N. These results limit achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on verification of an analog quantum simulation, in which the verifier need only run an O ( λ 2 ) -time classical computation, and the prover need only prepare O ( 1 ) samples of a history state and perform O ( λ 2 ) single-qubit measurements, for a security parameter λ . We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations. Published by the American Physical Society 2025

Liu, Zhenning (ORCID:000000020794419X)↗
DOE OSTI2025

Accuracy Guarantees and Quantum Advantage in Analog Open Quantum Simulation with and without Noise

Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analog quantum simulation of geometrically local open quantum systems and provide evidence that this problem both is hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly mixing local observables in geometrically local Lindbladians can be obtained to a precision of ϵ in time that is poly ( ϵ − 1 ) and uniform in system size. Furthermore, we establish that the quantum simulator would provide a superpolynomial advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian’s decay rate (when simulating fixed points), over any classical algorithm for these problems, assuming BQP ≠ BPP . We then consider the presence of noise in the quantum simulator in the form of additional geometrically local Lindbladian terms. We show that the simulation tasks considered in this paper are stable to errors; i.e., they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that, assuming BQP ≠ BPP , there are stable geometrically local Lindbladian simulation problems such that, as the noise rate on the simulator is reduced, classical algorithms must take time superpolynomially longer in the inverse noise rate to attain the same precision as the analog quantum simulator. Published by the American Physical Society 2025

Kashyap, Vikram (ORCID:0000000208195207)↗
NASA NTRS2020

A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealing

A class of quantum-classical hybrid machine-learning algorithms can be obtained by integrating classical deep generative models with quantum probability distributions as 'priors' over their latent variables. We introduce a hybrid implementation of variational autoencoders (QVAE) and also present a technique to hybridize flow-based invertible generative models. We demonstrate the use of D-Wave quantum annealers as physical simulators of quantum Boltzmann machines (QBM) to perform quantum-assisted training of QVAE. Latent-space QBM develop slowly mixing modes, opening a path to obtain quantum advantage in generative modeling with available quantum devices.

Vinci, Walter↗
DOE OSTI2024

Unconventional Quantum Advantages for Computation (U-QuAC)

While quantum computing offers the promise of exponential advantages, limited quantum speedups are known, especially for practical applications. To open new avenues for quantum advantages, we propose Unconventional Quantum Advantages for Computation (U-QuACs), with respect to unconventional resources such as space (number of bits or quantum bits of memory required to solve a problem), accuracy of solution, communication, or energy consumption. We focus on space-efficient quantum algorithms, where we seek to design algorithms that solve a problem using much less space than the total size of the input. A natural setting in which space is critical is the streaming model of computation, where the input data arrives sequentially in pieces that must each be processed individually. Streaming is motivated by a variety of problems including analysis of internet traffic or social networks. We design the first exponential quantum space advantage for a natural streaming problem, which also constitutes the first quantum advantage for approximating a discrete optimization problem, albeit with respect to space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Information-Theoretic Bounds on Quantum Advantage in Machine Learning

We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data; the classical or quantum data are then used to predict the outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving an accurate prediction on all inputs, we prove that the exponential quantum advantage is possible. For example, to predict the expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2 Ω(n) copies of ρ, but we present a quantum ML model using only O(n) copies. Our results clarify where the quantum advantage is possible and highlight the potential for classical ML models to address challenging quantum problems in physics and chemistry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum advantage for noisy channel discrimination

Many quantum mechanical experiments can be viewed as multiround interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum “coherent” access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single-qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between the performance of fully coherent and fully incoherent protocols as a function of noise strength. Moreover, the size of the region of coherent quantum advantage shrinks inverse polynomially in the number of channel uses, and in an intermediate regime an improved strategy is a hybrid of fully coherent and fully incoherent subroutines. The fully coherent protocol is based on quantum signal processing, suggesting a generalizable algorithmic framework for the study of quantum advantage in the presence of realistic noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Comparison of quantum advantage experiments using random circuit sampling

Random circuit sampling, the task of sampling bit strings from a random unitary operator, has been implemented to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it was claimed that classical computers using tensor network simulation could catch on to current noisy quantum processors for random circuit sampling. While the linear cross-entropy benchmark fidelity was used to certify all these claims, it may not capture statistical properties of outputs in detail. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [F. Pan, K. Chen, and P. Zhang, Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [G. Kalachev, P. Panteleev, P. Zhou, and M.-H. Yung, arXiv:2112.15083] with the bit strings from the Sycamore quantum processor. It is shown that all of Kalachev et al.'s samples passed the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuchongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically closer to the Sycamore samples than Pan et al.'s while the three datasets have similar values for the linear cross-entropy fidelity. In conclusion, our finding implies that further study is needed to certify or beat the claims of quantum advantage using random circuit sampling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Classically verifiable quantum advantage from a computational Bell test

Existing experimental demonstrations of quantum computational advantage have had the limitation that verifying the correctness of the quantum device requires exponentially costly classical computations. Here we propose and analyse an interactive protocol for demonstrating quantum computational advantage, which is efficiently classically verifiable. Our protocol relies on a class of cryptographic tools called trapdoor claw-free functions. Although this type of function has been applied to quantum advantage protocols before, our protocol employs a surprising connection to Bell’s inequality to avoid the need for a demanding cryptographic property called the adaptive hardcore bit, while maintaining essentially no increase in the quantum circuit complexity and no extra assumptions. Leveraging the relaxed cryptographic requirements of the protocol, we present two trapdoor claw-free function constructions, based on Rabin’s function and the Diffie–Hellman problem, which have not been used in this context before. We also present two independent innovations that improve the efficiency of our implementation and can be applied to other quantum cryptographic protocols. First, we give a scheme to discard so-called garbage bits, removing the need for reversibility in the quantum circuits. Second, we show a natural way of performing postselection that reduces the fidelity needed to demonstrate quantum advantage. Combining these results, we describe a blueprint for implementing our protocol on Rydberg atom-based quantum devices, using hardware-native operations that have already been demonstrated experimentally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum advantage in learning from experiments

Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today’s quantum processors.

Science & Technology - Other Topics↗
DOE OSTI2025

Quantum Advantage in Trading: A Game-Theoretic Approach

Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.

Khan, Faisal Shah [Taqtics LLC, USA, Rethinc. Labs↗
DOE OSTI2025

Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems

Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.

Miao, Qiang [Duke Quantum Center, Duke University,↗
DOE OSTI2022

Quantum advantage for differential equation analysis

Quantum algorithms for differential equation solving, data processing, and machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in useful problem instances. The essential obstacle for quantum differential equation solving is that outputting useful information may require difficult postprocessing, and the essential obstacle for quantum data processing and machine learning is that inputting the data is a difficult task just by itself. In this study, we demonstrate that, when combined, these difficulties solve one another. We show how the output of quantum differential equation solving can serve as the input for quantum data processing and machine learning, allowing dynamical analysis in terms of principal components, power spectra, and wavelet decompositions. To illustrate this, we consider continuous-time Markov processes on epidemiological and social networks. These quantum algorithms provide an exponential advantage over existing classical Monte Carlo methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Potential quantum advantage for simulation of fluid dynamics

Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

42 ENGINEERING↗