Quantum Advantage Research Articles

Platinum-based catalysts for oxygen reduction reaction simulated with a quantum computer

Hydrogen has emerged as a promising energy source for low-carbon and sustainable mobility purposes. However, its applications are still limited by modest conversion efficiency in the electrocatalytic oxygen reduction reaction (ORR) within fuel cells. The complex nature of the ORR and the presence of strong electronic correlations present challenges to atomistic modelling using classical computers. This scenario opens new avenues for the implementation of novel quantum computing workflows. Here, we present a state-of-the-art study that combines classical and quantum computational approaches to investigate ORR on platinum-based surfaces. Our research demonstrates, for the first time, the feasibility of implementing this workflow on the H1-series trapped-ion quantum computer and identify the challenges of the quantum chemistry modelling of this reaction. The results highlight the great potentiality of quantum computers in solving notoriously difficult systems with strongly correlated electronic structures and suggest platinum/cobalt as ideal candidate for showcasing quantum advantage in future applications.

Mathematical comparison of classical and quantum mechanisms in optimization under local differential privacy

Abstract Differential privacy (DP) is an influential method of protecting private data, and is a condition for a conditional probability distribution. Since we can regard DP as a condition for a tuple of probability vectors, it is natural to consider a similar condition for a tuple of density matrices as a quantum version of DP. This condition is called classical-quantum DP (CQ-DP) because it is considered in converting classical data to quantum states. In the study of DP (including CQ-DP), a positive parameter ε represents the privacy level to be guaranteed. In this paper, we show that CQ-DP has a quantum advantage in certain optimization problems. Moreover, we compare classical DP and CQ-DP mathematically to clarify a relation between privacy level and quantum advantage.

Properties and Applications of the Kirkwood–Dirac Distribution

Abstract There are several mathematical formulations of quantum mechanics. The Schrödinger picture expresses quantum states in terms of wavefunctions over, e.g., position or momentum. Alternatively, phase-space formulations represent states with quasi-probability distributions over, e.g., position and momentum. A quasi-probability distribution resembles a probability distribution but may have negative and non-real entries. The most famous quasi-probability distribution, the Wigner function, has played a pivotal role in the development of a continuous-variable quantum theory that has clear analogues of position and momentum. However, the Wigner function is ill-suited for much modern quantum-information research, which is focused on finite-dimensional systems and general observables. Instead, recent years have seen the Kirkwood–Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summarise the KD distribution’s extensive usage in the study or development of measurement disturbance; quantum metrology; weak values; direct measurements of quantum states; quantum thermodynamics; quantum scrambling and out-of-time-ordered correlators; and the foundations of quantum mechanics, including Leggett–Garg inequalities, the consistent-histories interpretation, and contextuality. We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities. Third, we delve into the KD distribution’s mathematical structure. We summarise the current knowledge regarding the geometry of KD-positive states (the states for which the KD distribution is a classical probability distribution), describe how to witness and quantify KD non-positivity, and outline relationships between KD non-positivity, coherence and observables’ incompatibility.

Quantum Advantages in (n, d) →1 Random Access Codes

Abstract A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider (n, d)-RACs constituting an n-length string, constructed from a d size set of letters, and send an encoding of the string in a single d-level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, the so-called majority-encoding-identity-decoding, is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of (n, d)→1 RACs.

Initial State Preparation for Quantum Chemistry on Quantum Computers

Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground-state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that and the quality of initial states, accomplishing the latter with a new metric—the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates: such an improvement can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage. Published by the American Physical Society 2024

Single-qubit gate teleportation provides a quantum advantage

Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work \cite{TerhalDiVincenzo04}, Terhal and DiVincenzo have shown that these circuits elude simulation by efficient classical algorithms under plausible complexity-theoretic assumptions. Here we consider possibilistic simulation \cite{wang2021possibilistic}, a particularly weak form of this task where the goal is to output any string appearing with non-zero probability in the output distribution of the circuit. We show that even for single-qubit Clifford-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates. Our results are unconditional and are obtained by a reduction to the problem of computing the parity, a well-studied problem in classical circuit complexity.

Unconditional quantum magic advantage in shallow circuit computation

Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of “magic” states—the secret sauce to establish universal quantum computation. However, it is still questionable whether magic indeed brings the believed quantum advantage, ridding unproven complexity assumptions or black-box oracles. In this work, we demonstrate the first unconditional magic advantage: a separation between the power of generic constant-depth or shallow quantum circuits and magic-free counterparts. For this purpose, we link the shallow circuit computation with the strongest form of quantum nonlocality—quantum pseudo-telepathy, where distant non-communicating observers generate perfectly synchronous statistics. We prove quantum magic is indispensable for such correlated statistics in a specific nonlocal game inspired by the linear binary constraint system. Then, we translate generating quantum pseudo-telepathy into computational tasks, where magic is necessary for a shallow circuit to meet the target. As a by-product, we provide an efficient algorithm to solve a general linear binary constraint system over the Pauli group, in contrast to the broad undecidability in constraint systems. We anticipate our results will enlighten the final establishment of the unconditional advantage of universal quantum computation.

Quantum-enhanced interferometry with unbalanced entangled coherent states

Abstract We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs), generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.

Tensor quantum programming

Abstract Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. In this article, we propose a novel approach called Tensor Quantum Programming, which leverages tensor networks (TNs) for hybrid quantum computing. Our key insight is that the primary challenge of algorithms based on TNs lies in their high ranks (bond dimensions). Quantum computing offers a potential solution to this challenge, as an ideal quantum computer can represent tensors with arbitrarily high ranks in contrast to classical counterparts, which indicates the way towards quantum advantage. While tensor-based vector-encoding and state-readout are known procedures, the matrix-encoding required for performing matrix-vector multiplications directly on quantum devices is much less studied. We introduce an algorithm that encodes matrix product operators into quantum circuits with a depth that scales linearly with the number of qubits. We demonstrate the algorithm’s performance for matrices commonly encountered in differential equations, optimization problems, and quantum chemistry, for systems involving up to 50 qubits.

Atom cavity encoding for NP-complete problems

We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we present encoding schemes for numerous nondeterministic polynomial-time complete (NP-complete) problems, encompassing the majority of Karp’s 21 NP-complete problems. We find a number of such computation problems can be encoded by the atom-cavity system at a linear cost of atom number. There are still certain problems that cannot be encoded by the atom-cavity as efficiently, such as quadratic unconstrained binary optimization (QUBO), and the Hamiltonian cycle. For these problems, we provide encoding schemes with a quadratic or quartic cost in the atom number. We expect this work to provide important guidance to search for the practical quantum advantage of the atom-cavity system in solving NP-complete problems. Moreover, the encoding schemes we develop here may also be adopted in other optical systems for solving NP-complete problems, where a similar form of Mattis-type spin glass Hamiltonian as in the atom-cavity system can be implemented.

Classification Analysis of Transition Metal Compounds Using Quantum Machine Learning

AbstractQuantum machine learning (QML) leverages the potential of machine learning (ML) to explore the subtle patterns in huge datasets of complex nature with quantum advantages. QML accelerates materials research with active screening of chemical space, identifying novel materials for practical applications, and classifying structurally diverse materials given their measured properties. This study analyzes the performance of three efficient quantum machine learning algorithms viz., variational quantum classifier (VQC), quantum support vector classifier (QSVC), and quantum neural networks (QNN) for distinguishing transition metal chalcogenides (TMCs) from transitional metal oxides (TMOs). By employing feature selection, classical machine learning achieves 100% accuracy whereas QML achieves the highest performance of 99% and 98% for test and train data respectively on QSVC. Further, to extend the QML models for structural and functional analysis of materials that cannot be inferred directly from the formula, stability analysis, and magnetic nature analysis on 1000 and 500 materials are performed, respectively. The stability analysis achieves 78% accuracy with QSVC and the magnetic nature analysis achieves 88% with QNN establishing the competence of QML models. This study proves that QML models are remarkable in materials classification and analysis which fuels the task of materials discovery in the future.

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. We numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Y. Ha and S. Shashaani also gratefully acknowledge the U.S. National Science Foundation Division of Civil, Mechanical and Manufacturing Innovation Grant CMMI-2226347 and the U.S. Office of Naval Research [Grant N000142412398]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0575 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0575 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Benchmarking quantum computer simulation software packages: State vector simulators

Rapid advances in quantum computing technology lead to an increasing need for software simulators that enable both algorithm design and the validation of results obtained from quantum hardware. This includes calculations that aim at probing regimes of quantum advantage, where a quantum computer outperforms a classical computer in the same task. High performance computing (HPC) platforms play a crucial role as today’s quantum devices already reach beyond the limits of what powerful workstations can model, but a systematic evaluation of the individual performance of the many offered simulation packages is lacking so far. In this Technical Review, we benchmark several software packages capable of simulating quantum dynamics with a special focus on HPC capabilities. We develop a containerized toolchain for benchmarking a large set of simulation packages on a local HPC cluster using different parallelisation capabilities, and compare the performance and system size-scaling for three paradigmatic quantum computing tasks. Our results can help finding the right package for a given simulation task and lay the foundation for a systematic community effort to benchmark and validate upcoming versions of existing and also newly developed simulation packages.

Counting collisions in random circuit sampling for benchmarking quantum computers

We show that counting the number of collisions (re-sampled bitstrings) when measuring a random quantum circuit provides a practical benchmark for the quality of a quantum computer and a quantitative noise characterization method. We analytically estimate the difference in the expected number of collisions when sampling bitstrings from a pure random state and when sampling from the classical uniform distribution. We show that this quantity, if properly normalized, can be used as a collision anomaly benchmark or as a collision volume test, which is similar to the well-known quantum volume test, with advantages (no classical computing cost) and disadvantages (high sampling cost). We also propose to count the number of cross-collisions between two independent quantum computers running the same random circuit in order to obtain a cross-validation test of the two devices. Finally, we quantify the sampling cost of quantum collision experiments. We find that the sampling cost for running a collision volume test on state-of-the-art processors (e.g., 20 effective clean qubits) is quite small: less than 105 shots. For large-scale experiments in the quantum supremacy regime, the required number of shots for observing a quantum signal in the observed number of collisions is currently infeasible (>1012), but not completely out of reach for near-future technology.

Quantum-inspired attribute selection algorithms

Abstract In this study, we propose the use of quantum information gain (QIG) and fidelity as quantum splitting criteria to construct an efficient and balanced quantum decision tree. QIG is a circuit-based criterion in which angle embedding is used to construct a quantum state, which utilizes quantum mutual information to compute the information between a feature and the class attribute. For the fidelity-based criterion, we construct a quantum state using the occurrence of random events in a feature and its corresponding class. We use the constructed state to further compute fidelity for determining the splitting attribute among all features. Using numerical analysis, our results clearly demonstrate that the fidelity-based criterion ensures the construction of a balanced tree. We further compare the efficiency of our quantum information gain and fidelity-based quantum splitting criteria with different classical splitting criteria on balanced and imbalanced datasets. Our analysis shows that the quantum splitting criteria lead to quantum advantage in comparison to classical splitting criteria for different evaluation metrics.

Sudden death of quantum advantage in correlation generations.

Quantum noise is one of the most profound obstacles to implementing large-scale quantum algorithms and schemes. In particular, the dynamical process by which quantum noise, varying in strength from 0 to critical levels, affects and destroys quantum advantage has not been well understood. Meanwhile, correlation generation serves as a precious theoretical model for information processing tasks, where quantum advantage can be precisely quantified. In this study, we show that this model provides valuable insights into the understanding of this dynamical process. We prove that, as the strength of quantum noise continuously increases from 0, the quantum advantage diminishes gradually and eventually vanishes. Unexpectedly, in some cases, we observe the phenomenon of a sudden death of quantum advantage: When the noise strength exceeds a certain threshold, the quantum advantage abruptly disappears from a substantial level. This phenomenon, once again, reveals the tremendous impact of noise on quantum information processing tasks.

Quantum versatility in PageRank

Quantum mechanics empowers the emergence of quantum advantages in various fields, including quantum algorithms. Quantum PageRank is a promising tool for a future quantum internet. Recently, arbitrary phase rotations (APRs) have been introduced in the underlying Szegedy's quantum walk of the quantum PageRank algorithm. In this work we thoroughly study the role APR plays in quantum PageRank. We discover the versatility resulting from quantumness. Specifically, we discover the emergence of a cluster phenomenon in rankings considering the rotation phases, i.e., the existence of similar clusters in the distribution of the rankings and their fidelity with the corresponding classical PageRanks, the ranking distribution variance, the coherence and entanglement of PageRank states, and the power-law parameter in the ranking distributions on a scale-free network concerning the two rotation phases. Furthermore, we propose an alternate quantum PageRank with APR which provides an extra tunnel for the analysis of PageRank. We also study the PageRank on the trackback graph of a scale-free graph for the investigation of network information traffic tracking. We demonstrate the rich cluster diversity formed in our alternate quantum PageRank, which offers a novel perspective on the quantum versatility of PageRank. Our results present the quantum-enabled perspective for PageRanking and shed light on the design and application of practical quantum PageRank algorithms. Published by the American Physical Society 2024

Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage.

We implement an experiment on a photonic quantum processor establishing efficacy of the elementary quantum system in classical information storage. The advantage is established by considering a class of simple bipartite games played with the communication resource qubit and classical bit (c bit), respectively. Conventional wisdom, supported by the no-go theorems of Holevo and Frenkel-Weiner, suggests that such a quantum advantage is unattainable when the sender and receiver share randomness or classical correlations. However, our results reveal a quantum advantage in a scenario devoid of any shared randomness. Our experiment involves the development of a variational triangular polarimeter, enabling the realization of positive operator value measurements crucial for establishing the targeted quantum advantage. Beyond showcasing a robust communication advantage with a single qubit, our work paves the way for immediate applications in near-term quantum technologies. It provides a semi-device-independent certification scheme for quantum encoding-decoding systems and offers an efficient method for information loading and transmission in quantum networks.

Clique Homology is QMA1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathsf{QMA}}}_{1}$$\\end{document}-hard

We address the long-standing question of the computational complexity of determining homology groups of simplicial complexes, a fundamental task in computational topology, posed by Kaibel and Pfetsch over twenty years ago. We show that decision problem is QMA1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathsf{QMA}}}_{1}$$\\end{document}-hard and the exact counting version is #BQP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\#{\\mathsf{BQP}}$$\\end{document}-hard. In fact, we strengthen this by showing that the problems remains hard in the case of clique complexes, a family of simplicial complexes specified by a graph which is relevant to the problem of topological data analysis. The proof combines a number of techniques from Hamiltonian complexity and algebraic topology. As we discuss, a version of the problems satisfying a suitable promise and certain constraints is contained in QMA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathsf{QMA}}$$\\end{document} and #BQP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\#{\\mathsf{BQP}}$$\\end{document}, respectively. This suggests that the seemingly classical problem may in fact be quantum mechanical. We discuss potential implications for the problem of quantum advantage in topological data analysis.

KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search

Quantum architecture Search (QAS) is a promising direction for optimization and automated design of quantum circuits towards quantum advantage. Recent techniques in QAS emphasize Multi-Layer Perceptron (MLP)-based deep Q-networks. However, their interpretability remains challenging due to the large number of learnable parameters and the complexities involved in selecting appropriate activation functions. In this work, to overcome these challenges, we utilize the Kolmogorov-Arnold Network (KAN) in the QAS algorithm, analyzing their efficiency in the task of quantum state preparation and quantum chemistry. In quantum state preparation, our results show that in a noiseless scenario, the probability of success is 2× to 5× higher than MLPs. In noisy environments, KAN outperforms MLPs in fidelity when approximating these states, showcasing its robustness against noise. In tackling quantum chemistry problems, we enhance the recently proposed QAS algorithm by integrating curriculum reinforcement learning with a KAN structure. This facilitates a more efficient design of parameterized quantum circuits by reducing the number of required 2-qubit gates and circuit depth. Further investigation reveals that KAN requires a significantly smaller number of learnable parameters compared to MLPs; however, the average time of executing each episode for KAN is higher.