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Tough Errors Are no Match (TEAM): Optimizing the Quantum Compiler for Noise Resilience

This report summarizes research performed under the Tough Errors Are no Match (TEAM) project. The primary focus of TEAM has been to research and develop a compilation toolbox leveraging techniques from quantum characterization and control, probabilistic programming, and approximate computing. Our goal was to develop robust protocols that can be integrated into quantum compilers to optimize and enhance the robustness of noisy computation. Here, we provide a summary of TEAM work focused on characterization and control of quantum systems.

97 MATHEMATICS AND COMPUTING↗

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗

Quantum 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 directed minimum spanning tree, each of which uses O ̃(n1/4) rounds of communication and O ̃(n9/4) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗

Quantum 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 directed minimum spanning tree, each of which uses O ̃(n 1/4 ) rounds of communication and O ̃(n 9/4 ) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related classical algorithms, revealing that advances are needed to render both practical.

quantum computing↗

Quantum optimization algorithms: Energetic implications

Since the dawn of quantum computing (QC), theoretical developments like Shor's algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the technical challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using parameterized quantum circuits in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. Here in this article, we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like quantum natural gradient descent, simultaneous perturbation stochastic approximations or circuit learning methods, are at least 2x to 4x more energy efficient than their classical counterparts; why feedback-based quantum optimization is energy-inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of ≥2 0 x. Finally, we use the NchooseK high-level programming model to run optimization problems on both gate-based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate-based counterparts.

97 MATHEMATICS AND COMPUTING↗

The Quantum Alternating Operator Ansatz for Satisfiability Problems

Here, we comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

97 MATHEMATICS AND COMPUTING↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

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↗

Optimization of two dimensional gratings for very long wavelength quantum well infrared photodetectors

We have performed a detailed study of two-dimensional grating coupling for quantum well infrared photodetectors in the very long wavelength spectral region lambda is approximately 16 - 17 microns. Using calculations based on the modal expansion method we quantitatively explain the double peaked responsivity spectrum. By optimizing the grating parameters we achieve a normal incidence responsivity and detectivity which are three times larger than the 45 deg angle of incidence geometry.

Sarusi, G.↗

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↗

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↗

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]↗

Collective neutrino oscillations in three flavors on qubit and qutrit processors

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions, which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and Advanced Quantum Testbed device at the Lawrence Berkeley National Laboratory for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. Finally, while hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphysical qubit space, unlike the qubit setup.

Neutrino oscillations↗

Quantum State Engineering Via Coherent-State Superpositions

The quantum interference between the two parts of the optical Schrodinger-cat state makes possible to construct a wide class of quantum states via discrete superpositions of coherent states. Even a small number of coherent states can approximate the given quantum states at a high accuracy when the distance between the coherent states is optimized, e. g. nearly perfect Fock state can be constructed by discrete superpositions of n + 1 coherent states lying in the vicinity of the vacuum state.

Janszky, Jozsef↗

Exciton Transfer Between Extended Electronic States in Conjugated Inter-Polyelectrolyte Complexes

Artificial light harvesting, a process that involves converting sunlight into chemical potential energy, is considered to be a promising part of the overall solution to address urgent global energy challenges. Conjugated polyelectrolyte complexes (CPECs) are particularly attractive for this purpose due to their extended electronic states, tunable assembly thermodynamics, and sensitivity to their local environment. Importantly, ionically assembled complexes of conjugated polyelectrolytes can act as efficient donor-acceptor pairs for electronic energy transfer (EET). However, to be of use in material applications, we must understand how modifying the chemical structure of the CPE backbone alters the EET rate beyond spectral overlap considerations. In this report we investigate the dependence of the EET efficiency and rate on the electronic structure and excitonic wave function of the CPE backbone. To do so, we synthesized a series of alternating copolymers where the electronic states are systematically altered by introducing comonomers with electron withdrawing and electron-rich character while keeping the linear ionic charge density nearly fixed. We find evidence that the excitonic coupling may be significantly affected by the exciton delocalization radius, in accordance with analytical models based on the line-dipole approximation and quantum chemistry calculations. Our results imply that care should be taken when selecting CPE components for optimal CPEC EET. These results have implications for using CPECs as key components in water-based light-harvesting materials, either as standalone assemblies or as adsorbates on nanoparticles and thin films.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Noise-aware circuit compilations for a continuously parameterized two-qubit gateset

State-of-the-art noisy-intermediate-scale quantum processors are currently implemented across a variety of hardware platforms, each with their own distinct gatesets. As such, circuit compilation should not only be aware of but also deeply connect to the native gateset and noise properties of each. Trapped-ion processors are one such platform that provides a gateset that can be continuously parameterized across both one- and two-qubit gates. Here we use the Quantum Scientific Computing Open User Testbed to study noise-aware compilations focused on continuously parameterized two-qubit 𝑍⁢𝑍 gates (based on the Mølmer-Sørensen interaction) using $\scriptsize{SUPERSTAQ}$, a quantum software platform for hardware-aware circuit compiler optimizations. We discuss the realization of 𝑍⁢𝑍 gates with arbitrary angle on the all-to-all connected trapped-ion system. Then we discuss a variety of different compiler optimizations that innately target these 𝑍⁢𝑍 gates and their noise properties. These optimizations include moving from a restricted maximally entangling gateset to a continuously parameterized one, swap mirroring to further reduce the total entangling angle of the operations, focusing the heaviest 𝑍⁢𝑍 angle participation on the best-performing gate pairs, and circuit approximation to remove the least impactful 𝑍⁢𝑍 gates. We demonstrate these compilation approaches on the hardware with randomized quantum volume circuits, observing the potential to realize a larger quantum volume as a result of these optimizations. Using differing yet complementary analysis techniques, we observe the distinct improvements in system performance provided by these noise-aware compilations and study the role of stochastic and coherent error channels for each compilation choice.

Noise↗

Surrogate Optimization for Quantum Circuits

Variational quantum Eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has yet to be realized with few claims of quantum advantage and high resource estimates mainly due to the need for optimization in the presence of noise. Finding algorithms and methods to improve the convergence is essential to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal we look to use modern approaches recently developed in circuit simulations and stochastic classical optimization that can be combined in a surrogate optimization approach to classical circuits. Using an approximate state vector simulator, we efficiently calculate an approximate Hessian, fed as an input for a detailed quantum circuit simulator. We demonstrate the capabilities of such an approach with and without sampling noise. We also show that this method outperforms Powell in the presence of quantum circuit shot noise by a factor of 2-4

quantum computing↗

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗