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DOE OSTI2023

Short-Depth QAOA circuits and Quantum Annealing on Higher-Order Ising Models (Rev.2)

The Quantum Alternating Operator Ansatz (QAOA) and Quantum Annealing (QA) are quantum algorithms that are both based on the adiabatic theorem and both have the goal of sampling the optimal solution(s) of combinatorial optimization problems. Quantum annealing has been physically instantiated on D-Wave devices using superconducting flux qubits, and QAOA can be programmed on digital gate-model quantum computers such as the programmable superconducting transmon qubits devices of the IBMQ series, for instance ibm washington. QAOA and QA address the same types of problems, but it is unclear how they will scale to large problem sizes and to larger and higher-fidelity quantum computers. In this article, we present a direct comparison between QAOA, one and two rounds, run on all 127 qubits of ibm washington and QA run on D-Wave Advantage system4.1 and Advantage system6.1. The problems which allow for this comparison are random Ising model problems whose connectivity matches the heavy hexagonal lattice topology of ibm washington and the Pegasus graph connectivity of the two D-Wave devices. We create two classes of problem instances for this comparison: one with higher order terms (ZZZ variable interactions), linear terms, and quadratic terms, and a separate problem type with only linear and quadratic terms. Our QAOA circuits are novel and extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of ibm washington’s heavy hexagonal lattice and can be applied to future heavy-hex chips. We also test the effectiveness of the error suppression technique digital dynamical decoupling on the QAOA circuits. The QAOA circuits compiled to ibm washington are composed of several thousand circuit instructions, approximately 3, 000 depending on the details of the circuit, making these some the largest quantum circuits ever executed on a digital quantum processor. QAOA and QA are compared against the classical heuristic algorithm of simulated annealing and all problem instances are exactly solved using CPLEX in order to evaluate which samplers, if any, correctly found the ground state solution(s) of the problem instances. We find that (i) QA outperforms QAOA on all problem instances, (ii) QAOA samples the problems better than random sampling, and (iii) QAOA angle computation exhibits clear parameter concentration across the ensemble of Ising models.

127 Qubits↗

DOE OSTI2023

Leakage Reduces Device Coherence Demands for Pulse-Level Molecular Simulations

Quantum simulation on noisy intermediate-scale quantum devices is severely limited by short qubit coherence times. A variational pulse-shaping algorithm known as ctrl-VQE was recently proposed to address this issue by eliminating the need for parameterized quantum circuits, which lead to long state preparation times. Here, in this study, we find the fastest possible pulses that prepare target molecular wave functions for a given device Hamiltonian describing coupled transmon qubits using simulations. We find that the resulting time-optimal pulses develop a bang-bang form consistent with Pontryagin’s maximum principle. We further investigate how the minimal state preparation time is impacted by the number of energy levels active in the transmon simulations. We find that leakage outside the computational subspace (something that is usually considered problematic) speeds up the state preparation, further reducing device coherence-time demands. Our analysis reveals that this speedup is due to both an enlarged solution space of target wave functions and the appearance of additional channels connecting initial and target states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

State Dependent Optimization with Quantum Circuit Cutting

Quantum circuits can be reduced through optimization to better fit the constraints of quantum hardware. One such method, initial-state dependent optimization (ISDO), reduces gate count by leveraging knowledge of the input quantum states. Surprisingly, we found that ISDO is broadly applicable to the downstream circuits produced by circuit cutting. Circuit cutting also requires measuring upstream qubits and has some flexibility of selection observables to do reconstruction. Therefore, we propose a state-dependent optimization (SDO) framework that incorporates ISDO, our newly proposed measure-state dependent optimization (MSDO), and a biased observable selection strategy. Building on the strengths of the SDO framework and recognizing the scalability challenges of circuit cutting, we propose nonseparate circuit cutting-a more flexible approach that enables optimizing gates without fully separating them. We validate our methods on noisy simulations of QAOA, QFT, and BV circuits. Results show that our approach consistently mitigates noise and improves overall circuit performance, demonstrating its promise for enhancing quantum algorithm execution on near-term hardware.

Li, Xinpeng↗

DOE OSTI2026

Realization of fermionic Laughlin state on a quantum processor

Strongly correlated topological phases of matter are central to modern condensed matter physics and quantum information technology but often challenging to probe and control in material systems. The experimental difficulty of accessing these phases has motivated the use of engineered quantum platforms for simulation and manipulation of exotic topological states. Among these, the Laughlin state stands as a cornerstone for topological matter, embodying fractionalization, anyonic excitations, and incompressibility. Although its bosonic analogs have been realized on programmable quantum simulators, a genuine fermionic Laughlin state has yet to be demonstrated on a quantum processor. Here, we realize the ν = 1/3 fermionic Laughlin state on IonQ’s trapped-ion quantum computer using an efficient and scalable Hamiltonian variational ansatz with 369 two-qubit gates on a 16-qubit circuit. Employing symmetry-verification error mitigation, we extract key observables that characterize the Laughlin state, including correlation hole, bulk-edge correspondence, and topological entanglement entropy, with strong agreement to exact diagonalization benchmarks. This work demonstrates an end-to-end workflow to simulate material-intrinsic topological orders and provides a starting point to explore its dynamics and excitations on digital quantum processors.

Shen, Lingnan [Univ. of Washington, Seattle, WA (U↗

DOE OSTI2019

Design of a readout circuit incorporating a 12-bit analog-to-digital converter for cooled infrared focal plane array

The infrared focal plane array (IRFPA) is gradually becoming more systematic. In order to enhance the signal processing capabilities, analog-to-digital converters (ADC) integrated into the readout integrated circuit (ROIC) is an important development trend. However, the cryogenic effects of MOSFET devices will affect the conversion accuracy of the ADC at 77 K. In this paper, the main parameters of MOSFET are extracted at 77 K in 0.18 μm CMOS process, and a cryogenic model is established. Based on this, a digital ROIC is designed, which integrates a 12-bit single-slope integral ADC in pixel unit. By applying continuous integral ramp generator and mixed-voltage comparator, a high-linearity and low-power consumption single-slope ADC is realized for the cooled readout circuit. The measured dynamic effective number of bits of the ADC at 77 K is 10.92 bits, the static no-missing code resolution reaches 11.99 bits, the maximum differential nonlinear |DNL| < 1LSB and maximum integral nonlinear |INL| < 1LSB. This paper realizes the design of a digital ROIC for IRFPA and improves the simulation accuracy at 77 K.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

VQE method: a short survey and recent developments

Abstract The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Fedorov, Dmitry A. (ORCID:0000000316598580)↗

DOE OSTI2024

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Programmable Heisenberg interactions between Floquet qubits

Abstract The trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, quantum architectures are often designed to achieve high coherence at the expense of tunability. Many current qubit designs have fixed energy levels and consequently limited types of controllable interactions. Here by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model can act as the primitive for an expressive set of quantum operations, but is also the basis for quantum simulations of spin systems. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ and SWAP gates with good estimated fidelities. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate, also with a competitive fidelity. Our protocol applies to multiple fixed-frequency high-coherence platforms, providing a collection of interactions for high-performance quantum information processing. It also establishes the potential of the Floquet framework as a tool for exploring quantum electrodynamics and optimal control.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Characterization and Optimization of Building Blocks for Specialized Computing Platforms

As noise limits the performance of quantum processors, the ability to characterize this noise and develop methods to overcome it is essential for the future of quantum computing. In this report, we develop a complete set of tools for improving quantum processor performance at the application level, including low-level physical models of quantum gates, a numerically efficient method of producing process matrices that span a wide range of model parameters, and full-channel quantum simulations. We then provide a few examples of how to use these tools to study the effects of noise on quantum circuits.

42 ENGINEERING↗

DOE OSTI2025

Quantum Software Engineering (Dagstuhl Seminar 24512)

The Dagstuhl Seminar 24512 on "Quantum Software Engineering" was held from December 15 to 20, 2024. It brought together 26 participants from industry and academia from 13 different countries, including senior and junior researchers as well as practitioners in the field of Quantum Software Engineering. The aim of the seminar was to advance software engineering methods and tools for the engineering of hybrid quantum systems by promoting personal interaction and open discussion among researchers who are already working in this emerging area of knowledge. The first day of the seminar was devoted to the topic "When software engineering meets quantum mechanics", while the second day focused on "Quantum software engineering and its challenges." During both days, 16 invited presentations were given. The rest of the seminar was organized into three working groups to address the topics "Quantum Software Design, Modelling and Architecturing", "Adaptive Hybrid Quantum Systems", and "Quantum Software Quality Assurance". The seminar was a very fruitful experience for all participants both in terms of scientific outcomes and in terms of the personal relationships that were generated to jointly address future experiences.

97 MATHEMATICS AND 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↗

DOE OSTI2024

Quantum Davidson algorithm for excited states

Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Adaptive Variational Quantum Computing Approaches for Green’s Functions and Nonlinear Susceptibilities

Here, we present and benchmark quantum computing approaches for calculating real-time single-particle Green’s functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation. Using automatically generated compact circuits, the dynamical evolution is performed over sufficiently long times to achieve adequate frequency resolution of the response functions. We showcase accurate Green’s function calculations using a statevector simulator on classical hardware for Fermi-Hubbard chains of 4 and 6 sites, with maximal ansatz circuit depths of 65 and 424 layers, respectively, and for the molecule LiH with a maximal ansatz circuit depth of 81 layers. Additionally, we consider an antiferromagnetic quantum spin-1 model that incorporates the Dzyaloshinskii-Moriya interaction to illustrate calculations of the third-order nonlinear susceptibilities, which can be measured in two-dimensional coherent spectroscopy experiments. These results demonstrate that real-time approaches using adaptive parametrized circuits to evaluate linear and nonlinear response functions can be feasible with near-term quantum processors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗

DOE OSTI2022

Noise-Resilient Quantum Machine Learning for Stability Assessment of Power Systems

Transient stability assessment (TSA) is a cornerstone for resilient operations of todays interconnected power grids. This paper is a confluence of quantum computing, data science and machine learning to potentially address the power system TSA issue. Here, we devise a quantum TSA (QTSA) method to enable scalable and efficient data-driven transient stability prediction for bulk power systems, which is the first attempt to tackle the TSA issue with quantum computing. Our contributions are three-fold: 1) A high expressibility, low-depth (HELD) quantum circuit is designed for accurate and noise-resilient TSA; 2) A quantum natural gradient descent algorithm is developed for efficient HELD circuit training; 3) A systematical analysis on QTSAs performance under various quantum factors is per-formed. QTSA underpins a foundation of quantum-enabled and data-driven power grid stability analytics. It renders the intractable TSA straightforward and effortless in the Hilbert space, and therefore provides stability information for power system operations. Extensive experiments on quantum simulators and real quantum computers verify the accuracy, noise-resilience, scalability and universality of QTSA.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Simulation of Linear Non-Hermitian Boundary-Value Problems with Quantum Singular-Value Transformation

Herein we propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the propagation of electromagnetic waves in a one-dimensional system with outgoing boundary conditions. The corresponding measurement procedure is also discussed. Limitations of the QSVT algorithm are identified in connection with the large condition numbers that the dispersion matrices exhibit at weak dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Digital quantum simulation of Floquet symmetry-protected topological phases

Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions, solid-state spin systems, ultracold atoms and superconducting qubits. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Photon-Number-Dependent Hamiltonian Engineering for Cavities

Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quantum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number-dependent Hamiltonian for the cavities while minimizing the operation errors. Here, the engineered Hamiltonian admits various applications including canceling unwanted cavity self-Kerr interactions, creating higher-order nonlinearities for quantum simulations, and designing quantum gates resilient to noise. Our scheme can be implemented with coupled microwave cavities and transmon qubits in superconducting circuit systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗