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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as $\sqrt{T/N}$. When only K$\ll$T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $\sqrt{K/N}$. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2025

Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Furthermore, our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Coarse-Graining Conformational Dynamics with Multidimensional Generalized Langevin Equation: How, When, and Why

A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained (CG) conformational dynamics. Constrained by the fluctuation–dissipation theorem, the approach can build CG models in dynamical consistency (DC) with all-atom molecular dynamics. Here, we also propose practical criteria for AIGLE to enforce long-term DC. Case studies of a toy polymer, with 20 CG sites, and the alanine dipeptide, with two dihedral angles, elucidate why one should adopt AIGLE or its Markovian limit for modeling CG conformational dynamics in practice.

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

Nondegenerate Noise-Resilient Superconducting Qubit

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation 𝐸 𝐽⁢1 ⁢cos 𝜑 and 𝐸 𝐽⁢2 ⁢cos 2⁢𝜑. By constructing a circuit such that 𝐸 𝐽⁢2 is negative and |𝐸 𝐽⁢1 | ≪ |𝐸 𝐽⁢2 |, we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.

quantum error correction↗
DOE OSTI2021

Measurement-induced purification in large- N hybrid Brownian circuits

Competition between unitary dynamics that scrambles quantum information nonlocally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. Here we study this phenomenon in an analytically tractable all-to-all Brownian hybrid circuit model composed of qubits. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or totally destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables which are distinguished by the averaging procedure, and for concreteness we focus on a particular purity quantity for which the averaging is particularly simple. We represent the purity as a path integral coupling four replicas with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in 0 + 1 dimensions. In addition to studying the purity of the entire system, we study subsystem purities and relate these results to manifestations of quantum error correction in the model. Here, we also comment on the experimental feasibility for simulating this averaged purity, and corroborate our results with exact diagonalization for modest system sizes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Simulation of double buffer layer on CIGS solar cell with SCAPS software

In a CIGS thin film solar cell, the buffer layer is interposed between the absorber layer and the window layer, which plays an important role in interface electricity. CdS is often used as a buffer layer in CIGS cells. Beside the toxicity of Cd, the main drawback of CdS is its relatively narrow band gap (2.4 eV), which can lead to the current loss due to parasitic absorption. In order to reduce the use of CdS, we try other buffer layers instead of CdS and optimize buffer layer structure. Numerical simulation has been used to explore the effect of different buffer layer materials (CdS and ZnSe) on the performance of CuInGaSe{sub 2} solar cells with SCAPS-1D software. The main photovoltaic parameters of the analog device: open circuit voltage, short circuit current density, fill factor and conversion efficiency (η) were compared and analyzed. The results show that different buffer materials and thickness have great influence on the performance of the cell. In this simulation, CdS buffer layer was replaced by ZnSe material, which has a wider band gap. However, the efficiency of this kind of cell is lower than that of CIGS device with CdS buffer layer because of the bad energy band alignment. In order to improve the short-wave absorption and the efficiency of CIGS cell, we simulated a novel CdS/ZnSe double buffer layer structure. The efficiency of the optimized cell with double buffer layer increases from 18.47% (conventional cell with the same CdS buffer layer thickness) to 19.01%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗
DOE OSTI2023

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Coherent Detection of High-Rate Optical PPM Signals

A method of coherent detection of high-rate pulse-position modulation (PPM) on a received laser beam has been conceived as a means of reducing the deleterious effects of noise and atmospheric turbulence in free-space optical communication using focal-plane detector array technologies. In comparison with a receiver based on direct detection of the intensity modulation of a PPM signal, a receiver based on the present method of coherent detection performs well at much higher background levels. In principle, the coherent-detection receiver can exhibit quantum-limited performance despite atmospheric turbulence. The key components of such a receiver include standard receiver optics, a laser that serves as a local oscillator, a focal-plane array of photodetectors, and a signal-processing and data-acquisition assembly needed to sample the focal-plane fields and reconstruct the pulsed signal prior to detection. The received PPM-modulated laser beam and the local-oscillator beam are focused onto the photodetector array, where they are mixed in the detection process. The two lasers are of the same or nearly the same frequency. If the two lasers are of different frequencies, then the coherent detection process is characterized as heterodyne and, using traditional heterodyne-detection terminology, the difference between the two laser frequencies is denoted the intermediate frequency (IF). If the two laser beams are of the same frequency and remain aligned in phase, then the coherent detection process is characterized as homodyne (essentially, heterodyne detection at zero IF). As a result of the inherent squaring operation of each photodetector, the output current includes an IF component that contains the signal modulation. The amplitude of the IF component is proportional to the product of the local-oscillator signal amplitude and the PPM signal amplitude. Hence, by using a sufficiently strong local-oscillator signal, one can make the PPM-modulated IF signal strong enough to overcome thermal noise in the receiver circuits: this is what makes it possible to achieve near-quantum-limited detection in the presence of strong background. Following quantum-limited coherent detection, the outputs of the individual photodetectors are automatically aligned in phase by use of one or more adaptive array compensation algorithms [e.g., the least-mean-square (LMS) algorithm]. Then the outputs are combined and the resulting signal is processed to extract the high-rate information, as though the PPM signal were received by a single photodetector. In a continuing series of experiments to test this method (see Fig. 1), the local oscillator has a wavelength of 1,064 nm, and another laser is used as a signal transmitter at a slightly different wavelength to establish an IF of about 6 MHz. There are 16 photodetectors in a 4 4 focal-plane array; the detector outputs are digitized at a sampling rate of 25 MHz, and the signals in digital form are combined by use of the LMS algorithm. Convergence of the adaptive combining algorithm in the presence of simulated atmospheric turbulence for optical PPM signals has already been demonstrated in the laboratory; the combined output is shown in Fig. 2(a), and Fig. 2(b) shows the behavior of the phase of the combining weights as a function of time (or samples). We observe that the phase of the weights has a sawtooth shape due to the continuously changing phase in the down-converted output, which is not exactly at zero frequency. Detailed performance analysis of this coherent free-space optical communication system in the presence of simulated atmospheric turbulence is currently under way.

Vilnrotter, Victor↗
DOE OSTI2024

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗
DOE OSTI2024

Primitive quantum gates for an S U ( 3 ) discrete subgroup: Σ ( 36 × 3 )

We construct the primitive gate set for the digital quantum simulation of the 108-element Σ ( 36 × 3 ) group. This is the first time a non-Abelian crystal-like subgroup of S U ( 3 ) has been constructed for quantum simulation. The gauge link registers and necessary primitives—the inversion gate, the group multiplication gate, the trace gate, and the Σ ( 36 × 3 ) Fourier transform—are presented for both an eight-qubit encoding and a heterogeneous three-qutrit plus two-qubit register. For the latter, a specialized compiler was developed for decomposing arbitrary unitaries onto this architecture. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work, we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the “clean and dirty” setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in the concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution; thus, avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Phase dynamics in an AC-driven multiterminal Josephson junction analog

In the presence of an AC drive, multiterminal Josephson junctions exhibit the inverse AC Josephson effect, where the oscillations of the superconducting phase of each junction can lock onto one another or onto the external drive. The competition between these different phase-locked states results in a complex array of quantized voltage plateaus whose stability strongly depend on the circuit parameters of the shunted junctions. This phase diagram cannot be explored with low-temperature transport experiments alone, given the breadth of the parameter space, so we present an easily tunable analog circuit whose dynamical properties emulate those of a three-terminal junction. We focus on the observation of the multiterminal inverse AC Josephson effect, and we discuss how to identify Shapiro steps associated with each of the three junctions as well as their quartet states. We only observe integer phase-locked states in strongly overdamped networks, but fractional Shapiro steps appear as well when the quality factor of the junctions increases. Finally, we discuss the role of transverse coupling in the synchronization of the junctions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

PCB-on-DBC GaN Power Module Design with High-Density Integration and Double-Sided Cooling

Lateral gallium nitride (GaN) high-electron-mobility transistors (HEMTs) present better electrical characteristics compared to silicon or silicon carbide devices such as high switching speed and low gate charge, but also present additional challenges on the module design. Here, this paper discusses a high-density GaN power module with double-sided cooling, low inductance, on-package decoupling capacitors, and integrated gate drivers. The GaN dies as well as the gate drive are sandwiched between the printed circuit board (PCB) and direct bonded copper (DBC) substrate to achieve compact loop and double-sided cooling effect. Design considerations and thermal performance are analyzed. A module assembly procedure is presented utilizing the layer-by-layer attachment process. Finally, a 2.7 cm x 1.8 cm half-bridge GaN power module is fabricated and tested, achieving a low power-loop inductance of 1.03 nH, and the overshoot voltage of the switching waveform is less than 5% under a 400-V/25-A double-pulse test. The thermal resistance is 0.32 K/W, verified by simulation and experimental results. The design and assembly process can be generalized and applied to high power applications to achieve high power density and high performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

97 MATHEMATICS AND COMPUTING↗