What to Support when You're Compressing: The State of Practice, Gaps, and Opportunities for Scientific Data Compression
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Computer science↗
Engineering topics
Alexeev, Yuri
Publications and source records attributed to Alexeev, Yuri.
How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits
In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits and proof-of-principle error-correction on a single logical qubit. Nevertheless, despite significant progress and excitement, the path toward a full-stack scalable technology is largely unknown. There are significant outstanding quantum hardware, fabrication, software architecture, and algorithmic challenges that are either unresolved or overlooked. These issues could seriously undermine the arrival of utility-scale quantum computers for the foreseeable future. Here, we provide a comprehensive review of these scaling challenges. We show how the road to scaling could be paved by adopting existing semiconductor technology to build much higher-quality qubits, employing system engineering approaches, and performing distributed quantum computation within heterogeneous high-performance computing infrastructures. These opportunities for research and development could unlock certain promising applications, in particular, efficient quantum simulation/learning of quantum data generated by natural or engineered quantum systems. To estimate the true cost of such promises, we provide a detailed resource and sensitivity analysis for classically hard quantum chemistry calculations on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. Furthermore, we argue that, to tackle industry-scale classical optimization and machine learning problems in a cost-effective manner, heterogeneous quantum-probabilistic computing with custom-designed accelerators should be considered as a complementary path toward scalability.
Mohseni, Masoud↗
Hybrid algorithm for the time-dependent Hartree–Fock method using the Yang–Baxter equation on quantum computers *
Abstract The time-dependent Hartree–Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single Slater determinants. One of the major advantages of performing time dynamics within Hartree–Fock theory is the free fermionic nature of the problem, which makes TDHF classically simulatable in polynomial time. Here, we present a hybrid TDHF implementation for quantum computers. This quantum circuit grows with time; but with our recent work on circuit compression via the Yang–Baxter equation (YBE), the resulting circuit is constant depth. This study provides a new way to simulate TDHF with the aid of a quantum device as well as provides a new direction for the application of YBE symmetry in quantum chemistry simulations.
97 MATHEMATICS AND COMPUTING↗
The Localized Active Space Method with Unitary Selective Coupled Cluster
Here, we introduce a hybrid quantum-classical algorithm, the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. Derived from the localized active space unitary coupled cluster (LAS-UCCSD) method, LAS-USCCSD first performs a classical LASSCF calculation, then selectively identifies the most important parameters (cluster amplitudes used to build the multireference UCC ansatz) for restoring interfragment interaction energy using this reduced set of parameters with the variational quantum eigensolver method. We benchmark LAS-USCCSD against LAS-UCCSD by calculating the total energies of (H 2 ) 2 , (H 2 ) 4 , and trans-butadiene, and the magnetic coupling constant for a bimetallic compound [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ . For these systems, we find that LAS-USCCSD reduces the number of required parameters and thus the circuit depth by at least 1 order of magnitude, an aspect which is important for the practical implementation of multireference hybrid quantum-classical algorithms like LAS-UCCSD on near-term quantum computers.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Distributionally Robust Variational Quantum Algorithms With Shifted Noise
Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.
97 MATHEMATICS AND COMPUTING↗
Quantum-centric supercomputing for materials science: A perspective on challenges and future directions
Computational models are an essential tool for the design, characterization, and discovery of novel materials. Computationally hard tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their resources for simulation, analysis, and data processing. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. Here in this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.
36 MATERIALS SCIENCE↗
Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.
97 MATHEMATICS AND COMPUTING↗
Qutrit circuits and algebraic relations: A pathway to efficient spin-1 Hamiltonian simulation
Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to d -dimensional quantum units or qudits has opened new avenues for improving computational efficiency. This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, which may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our paper outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing.
97 MATHEMATICS AND COMPUTING↗
Towards provably efficient quantum algorithms for large-scale machine-learning models
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $\mathcal{O}$(T 2 x polylog($n$)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.
97 MATHEMATICS AND COMPUTING↗
Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.
36 MATERIALS SCIENCE↗
Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.
Alexeev, Yuri↗
Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets
Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. Finally, the predicted values support the relaxation mechanisms reported in previous studies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Simulating lossy Gaussian boson sampling with matrix-product operators
Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. Here, to understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the N out ∝ √N scaling of the number of surviving photons N out in the number of input photons N. We numerically verify this result using a tensor network algorithm with U(1) symmetry, and we overcome previous challenges due to the large local Hilbert-space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
Quantum computing for finance
Quantum computers are expected to surpass the computational capabilities of classical computers and have a transformative impact on numerous industry sectors. Here, we present a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modelling, optimization and machine learning. This Review is aimed at physicists, so it outlines the classical techniques used by the financial industry and discusses the potential advantages and limitations of quantum techniques. Finally, we look at the challenges that physicists could help tackle. Quantum computers are expected to surpass classical computers and transform industries. This Review focuses on quantum computing for financial applications and provides a summary for physicists on potential advantages and limitations of quantum techniques, as well as challenges that physicists could help tackle.
97 MATHEMATICS AND COMPUTING↗
Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansätze for Hybrid Variational Quantum Computing
One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. Further, we also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Introduction to the Special Issue on Software Tools for Quantum Computing: Part 2
Quantum computing is emerging as a remarkable technology that offers the possibility of achieving major scientific breakthroughs in many areas. By leveraging the unique features of quantum mechanics, quantum computers may be instrumental in advancing many areas, including science, energy, defense, medicine, and finance. This includes solving complex problems whose solution lies well beyond the capacity of contemporary and even future supercomputers that are based on conventional computing technologies. As a foundation for future generations of computing and information processing, quantum computing represents an exciting area for developing new ideas in computer science and computational engineering.
97 MATHEMATICS AND COMPUTING↗
QuYBE - An Algebraic Compiler for Quantum Circuit Compression
QuYBE is an open-source algebraic compiler for the compression of quantum circuits. It has been applied for the efficient simulation of the Heisenberg Hamiltonian on quantum computers. Currently, it can simulate the time dynamics of one-dimensional chains. It includes modules to generate the quantum circuits for the above as well as produce the compressed circuits, which are independent of the time step. It utilizes the Yang-Baxter equation (YBE) to perform the compression. QuYBE enables users to seamlessly design, execute, and analyze the time dynamics of the Heisenberg Hamiltonian on quantum computers. QuYBE is the first step toward making the YBE technique available to a broader community of scientists from multiple domains. The QuYBE compiler is available at https://github.com/ZichangHe/QuYBE.
Gulania, Sahil↗