Practical quantum advantage in quantum simulation

Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal and a quantum annealer

Relaxation dynamics of complex many-body quantum systems trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and energy-efficient memory devices. In this work, we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material using time-resolved scanning tunneling microscopy and unveil a crossover from temperature to noisy quantum fluctuation dominated dynamics. The process is modeled using a programmable superconducting quantum annealer in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment and quantum simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics.

Quantitative Analogue Simulation of Planar Molecules

Synthetic quantum systems provide a pathway for exploring the physics of complex quantum matter in a programmable fashion. This approach becomes particularly advantageous when it comes to systems that are thermodynamically unfavorable. By sculpting the potential landscape of Cu(111) surfaces with carbon monoxide quantum corrals in a cryogenic scanning tunneling microscope, we created analogue simulators of planar organic molecules, including antiaromatic and non-Kekulé species that are generally reactive or unstable. Spectroscopic imaging of such synthetic molecules reveals close replications of molecular orbitals obtained from ab initio calculations of the organic molecules. We further illustrate the quantitative nature of such analogue simulators by faithful extraction of bond orders and global aromaticity indices, which are otherwise technically daunting using real molecules. Our approach therefore sets the stage for new research frontiers pertaining to the quantum physics and chemistry of designer nanostructures.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Haplotype-resolved assembly of diploid and polyploid genomes using quantum computing

Precision medicine's emphasis on individual genetic variants highlights the importance of haplotype-resolved assembly, a computational challenge in bioinformatics given its combinatorial nature. While classical algorithms have made strides in addressing this issue, the potential of quantum computing remains largely untapped. Here, we present the vehicle routing problem (VRP) assembler: an approach that transforms this task into a vehicle routing problem, an optimization formulation solvable on a quantum computer. We demonstrate its potential and feasibility through a proof of concept on short synthetic diploid and triploid genomes using a D-Wave quantum annealer. To tackle larger-scale assembly problems, we integrate the VRP assembler with Google's OR-Tools, achieving a haplotype-resolved local assembly across the human major histocompatibility complex (MHC) region. Our results show encouraging performance compared to Hifiasm with phasing accuracy approaching the theoretical limit, underscoring the promising future of quantum computing in bioinformatics.

A Perspective on Protein Structure Prediction Using Quantum Computers

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Vibrational ADAPT-VQE: Critical points lead to problematic convergence

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.

Quantum simulation of the bosonic Kitaev chain

Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analog of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the in situ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.

Spontaneously Sliding Multipole Spin Density Waves in Cold Atoms

We report on the observation of spontaneously drifting coupled spin and quadrupolar density waves in the ground state of laser driven Rubidium atoms. These laser-cooled atomic ensembles exhibit spontaneous magnetism via light mediated interactions when submitted to optical feedback by a retroreflecting mirror. Drift direction and chirality of the waves arise from spontaneous symmetry breaking. The observations demonstrate a novel transport process in out-of-equilibrium magnetic systems.

Variational Quantum Simulation of Lindblad Dynamics via Quantum State Diffusion

Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements. We then apply variational quantum simulation (VQS) to efficiently capture the nonunitary evolution in QSD. We demonstrate our QSD-VQS algorithm by investigating the quantum dynamics in a two-level system subjected to an amplitude damping channel and a four-level transverse field Ising model within a dissipative environment including time-independent and periodic Hamiltonian cases. The results reveal its promising utility with upcoming hardware in the near future.

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2-5, and it remains unsolved how to estimate the actual entanglement content of experiments6. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2-5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Post-quantum cryptography and the quantum future of cybersecurity

We review the current status of efforts to develop and deploy post-quantum cryptography on the Internet. Then we suggest specific ways in which quantum technologies might be used to enhance cybersecurity in the near future and beyond. We focus on two goals: protecting the secret keys that are used in classical cryptography, and ensuring the trustworthiness of quantum computations. These goals may soon be within reach, thanks to recent progress in both theory and experiment. This progress includes interactive protocols for testing quantumness as well as for performing uncloneable cryptographic computations; and experimental demonstrations of device-independent random number generators, device-independent quantum key distribution, quantum memories, and analog quantum simulators.

Photonic Source of Heralded Greenberger-Horne-Zeilinger States

Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2  Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators

The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.

Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model

We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.

Accreditation of analogue quantum simulators

We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress toward the realization of programmable hybrid analogue-digital quantum simulators.

Scalable Bright and Pure Single Photon Sources by Droplet Epitaxy on InP Nanowire Arrays

High-quality quantum light sources are crucial components for the implementation of practical and reliable quantum technologies. The persistent challenge, however, is the lack of scalable and deterministic single photon sources that can be synthesized reproducibly. Here, we present a combination of droplet epitaxy with selective area epitaxy to realize the deterministic growth of single quantum dots in nanowire arrays. By optimization of the single quantum dot growth and the nanowire cavity design, single emissions are effectively coupled with the dominant mode of the nanowires to realize Purcell enhancement. The resonance-enhanced quantum emitter system boasts a brightness of millions of counts per second with nanowatt excitation power, a short radiation lifetime of 350 ± 5 ps, and a high single-photon purity with g(2)(0) value of 0.05 with continuous wave above-band excitation. Finite-difference time-domain (FDTD) simulation results show that the emissions of single quantum dots are coupled into the TM01 mode of the nanowires, giving a Purcell factor ≈ 3. Our technology can be used for creating on-chip scalable single photon sources for future quantum technology applications including quantum networks, quantum computation, and quantum imaging.

Quantum computing for chemistry and physics applications from a Monte Carlo perspective

This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.

Basis Set Generation and Optimization in the NISQ Era with Quiqbox.jl

In the noisy intermediate-scale quantum era, ab initio computation of electronic structure problems has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. Basis sets play a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of single-particle basis sets, we propose a framework for more customizable basis set generation and optimization. This framework allows composite basis sets to go beyond typical basis set frameworks, such as atomic basis sets, by introducing the concept of mixed-contracted Gaussian-type orbitals. These basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source software package named "Quiqbox" in the Julia programming language. We demonstrate various examples of using Quiqbox for basis set optimization and generation, ranging from optimizing atomic basis sets on the Hartree-Fock level, preparing the initial state for variational quantum eigensolver computation, and constructing basis sets with completely delocalized orbitals. We also include various benchmarks of Quiqbox for basis set optimization and ab initial electronic structure computation.

Evolution Operator Can Always Be Separated into the Product of Holonomy and Dynamic Operators

The geometric phase is a fundamental quantity characterizing the holonomic feature of quantum systems. It is well known that the evolution operator of a quantum system undergoing a cyclic evolution can be simply written as the product of holonomic and dynamical components for the three special cases concerning the Berry phase, adiabatic non-Abelian geometric phase, and nonadiabatic Abelian geometric phase. However, for the most general case concerning the nonadiabatic non-Abelian geometric phase, how to separate the evolution operator into holonomic and dynamical components is a long-standing open problem. In this Letter, we solve this open problem. We show that the evolution operator of a quantum system can always be separated into the product of holonomy and dynamic operators. Based on it, we further derive a matrix representation of this separation formula for cyclic evolution, and give a necessary and sufficient condition for a general evolution being purely holonomic. Our finding is not only of theoretical interest itself, but also of vital importance for the application of quantum holonomy. It unifies the representations of all four types of evolution concerning the adiabatic/nonadiabatic Abelian/non-Abelian geometric phase, and provides a general approach to realizing purely holonomic evolution.

Digital quantum simulation of NMR experiments

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

Machine Learning-Guided Protein Engineering

Recent progress in engineering highly promising biocatalysts has increasingly involved machine learning methods. These methods leverage existing experimental and simulation data to aid in the discovery and annotation of promising enzymes, as well as in suggesting beneficial mutations for improving known targets. The field of machine learning for protein engineering is gathering steam, driven by recent success stories and notable progress in other areas. It already encompasses ambitious tasks such as understanding and predicting protein structure and function, catalytic efficiency, enantioselectivity, protein dynamics, stability, solubility, aggregation, and more. Nonetheless, the field is still evolving, with many challenges to overcome and questions to address. In this Perspective, we provide an overview of ongoing trends in this domain, highlight recent case studies, and examine the current limitations of machine learning-based methods. We emphasize the crucial importance of thorough experimental validation of emerging models before their use for rational protein design. We present our opinions on the fundamental problems and outline the potential directions for future research.

Quantum-inspired encoding enhances stochastic sampling of soft matter systems

Quantum advantage in solving physical problems is still hard to assess due to hardware limitations. However, algorithms designed for quantum computers may engender transformative frameworks for modeling and simulating paradigmatically hard systems. Here, we show that the quadratic unconstrained binary optimization encoding enables tackling classical many-body systems that are challenging for conventional Monte Carlo. Specifically, in self-assembled melts of rigid lattice ring polymers, the combination of high density, chain stiffness, and topological constraints results in divergent autocorrelation times for real-space Monte Carlo. Our quantum-inspired encoding overcomes this problem and enables sampling melts of lattice rings with fixed curvature and compactness, unveiling counterintuitive topological effects. Tackling the same problems with the D-Wave quantum annealer leads to substantial performance improvements and advantageous scaling of sampling computational cost with the size of the self-assembled ring melts.

Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories

Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical spin-network algorithms for q-deformed gauge theories. To be explicit, we focus on SU(2)_{k} gauge theories with k∈N that are controlled by the deformation parameter q=e^{2πi/(k+2)}, a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)_{k} plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.

Quantum computing and machine learning for Arabic language sentiment classification in social media

With the increasing amount of digital data generated by Arabic speakers, the need for effective and efficient document classification techniques is more important than ever. In recent years, both quantum computing and machine learning have shown great promise in the field of document classification. However, there is a lack of research investigating the performance of these techniques on the Arabic language. This paper presents a comparative study of quantum computing and machine learning for two datasets of Arabic language document classification. In the first dataset of 213,465 Arabic tweets, both classic machine learning (ML) and quantum computing approaches achieve high accuracy in sentiment analysis, with quantum computing slightly outperforming classic ML. Quantum computing completes the task in approximately 59 min, slightly faster than classic ML, which takes around 1 h. The precision, recall, and F1 score metrics indicate the effectiveness of both approaches in predicting sentiment in Arabic tweets. Classic ML achieves precision, recall, and F1 score values of 0.8215, 0.8175, and 0.8121, respectively, while quantum computing achieves values of 0.8239, 0.8199, and 0.8147, respectively. In the second dataset of 44,000 tweets, both classic ML (using the Random Forest algorithm) and quantum computing demonstrate significantly reduced processing times compared to the first dataset, with no substantial difference between them. Classic ML completes the analysis in approximately 2 min, while quantum computing takes approximately 1 min and 53 s. The accuracy of classic ML is higher at 0.9241 compared to 0.9205 for quantum computing. However, both approaches achieve high precision, recall, and F1 scores, indicating their effectiveness in accurately predicting sentiment in the dataset. Classic ML achieves precision, recall, and F1 score values of 0.9286, 0.9241, and 0.9249, respectively, while quantum computing achieves values of 0.92456, 0.9205, and 0.9214, respectively. The analysis of the metrics indicates that quantum computing approaches are effective in identifying positive instances and capturing relevant sentiment information in large datasets. On the other hand, traditional machine learning techniques exhibit faster processing times when dealing with smaller dataset sizes. This study provides valuable insights into the strengths and limitations of quantum computing and machine learning for Arabic document classification, emphasizing the potential of quantum computing in achieving high accuracy, particularly in scenarios where traditional machine learning techniques may encounter difficulties. These findings contribute to the development of more accurate and efficient document classification systems for Arabic data.

Thermodynamics of Quantum Trajectories on a Quantum Computer

Quantum computers have recently become available as noisy intermediate-scale quantum devices. Already these machines yield a useful environment for research on quantum systems and dynamics. Building on this opportunity, we investigate open-system dynamics that are simulated on a quantum computer by coupling a system of interest to an ancilla. After each interaction the ancilla is measured, and the sequence of measurements defines a quantum trajectory. Using a thermodynamic analogy, which identifies trajectories as microstates, we show how to bias the dynamics of the open system in order to enhance the probability of quantum trajectories with desired properties, e.g., particular measurement patterns or temporal correlations. We discuss how such a biased-generally non-Markovian-dynamics can be implemented on a unitary, gate-based quantum computer and show proof-of-principle results on the publicly accessible ibmq_jakarta machine. While our analysis is solely conducted on small systems, it highlights the challenges in controlling complex aspects of open-system dynamics on digital quantum computers.

Future Potential of Quantum Computing and Simulations in Biological Science

The review article presents the recent progress in quantum computing and simulation within the field of biological sciences. The article is designed mainly into two portions: quantum computing and quantum simulation. In the first part, significant aspects of quantum computing was illustrated, such as quantum hardware, quantum RAM and big data, modern quantum processors, qubit, superposition effect in quantum computation, quantum interference, quantum entanglement, and quantum logic gates. Simultaneously, in the second part, vital features of the quantum simulation was illustrated, such as the quantum simulator, algorithms used in quantum simulations, and the use of quantum simulation in biological science. Finally, the review provides exceptional views to future researchers about different aspects of quantum simulation in biological science.

Quantum Simulation of Topological Zero Modes on a 41-Qubit Superconducting Processor

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-André-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.

Scalable Multipartite Entanglement Created by Spin Exchange in an Optical Lattice

Ultracold atoms in optical lattices form a competitive candidate for quantum computation owing to the excellent coherence properties, the highly parallel operations over spins, and the ultralow entropy achieved in qubit arrays. For this, a massive number of parallel entangled atom pairs have been realized in superlattices. However, the more formidable challenge is to scale up and detect multipartite entanglement, the basic resource for quantum computation, due to the lack of manipulations over local atomic spins in retroreflected bichromatic superlattices. In this Letter, we realize the functional building blocks in quantum-gate-based architecture by developing a cross-angle spin-dependent optical superlattice for implementing layers of quantum gates over moderately separated atoms incorporated with a quantum gas microscope for single-atom manipulation and detection. Bell states with a fidelity of 95.6(5)% and a lifetime of 2.20±0.13  s are prepared in parallel, and then connected to multipartite entangled states of one-dimensional ten-atom chains and two-dimensional plaquettes of 2×4 atoms. The multipartite entanglement is further verified with full bipartite nonseparability criteria. This offers a new platform toward scalable quantum computation and simulation.

Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models

We study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.

Optimizing the number of measurements for vibrational structure on quantum computers: coordinates and measurement schemes

One of the primary challenges prohibiting demonstrations of practical quantum advantages for near-term devices amounts to excessive measurement overheads for estimating relevant physical quantities such as ground state energies. However, with major differences between the electronic and vibrational structures of molecules, the question of how the resource requirements of computing anharmonic, vibrational states can be reduced remains relatively unexplored compared to its electronic counterpart. Importantly, bosonic commutation relations, distinguishable Hilbert spaces and vibrational coordinates allow manipulations of the vibrational system that can be exploited to minimize resource requirements. In this work, we investigate the impact of different coordinate systems and measurement schemes on the number of measurements needed to estimate anharmonic, vibrational states for a variety of three-mode (six-mode) molecules. We demonstrate an average of 3-fold (1.5-fold), with up to 7-fold (2.5-fold), reduction in the number of measurements required by employing appropriate coordinate transformations, based on an automized construction of qubit Hamiltonians from a conventional vibrational structure program.

Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions

The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration τ. Recent work suggested that DQS is typically characterized by a sharp Trotter transition: when τ is increased beyond a threshold value, approximation errors become uncontrolled at large times due to the onset of quantum chaos. Here, we contrast this picture with the case of integrable DQS. We focus on a simple quench from a spin-wave state in the prototypical XXZ Heisenberg spin chain, and study its integrable Trotterized evolution as a function of τ. Because of its exact local conservation laws, the system does not heat up to infinite temperature and the late-time properties of the dynamics are captured by a discrete generalized Gibbs ensemble (dGGE). By means of exact calculations we find that, for small τ, the dGGE depends analytically on the Trotter step, implying that discretization errors remain bounded even at infinite times. Conversely, the dGGE changes abruptly at a threshold value τ_{th}, signaling a novel type of Trotter transition. We show that the latter can be detected locally, as it is associated with the appearance of a nonzero staggered magnetization with a subtle dependence on τ. We highlight the differences between continuous and discrete GGEs, suggesting the latter as novel interesting nonequilibrium states exclusive to digital platforms.

Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole

Hawking radiation is one of the quantum features of a black hole that can be understood as a quantum tunneling across the event horizon of the black hole, but it is quite difficult to directly observe the Hawking radiation of an astrophysical black hole. Here, we report a fermionic lattice-model-type realization of an analogue black hole by using a chain of 10 superconducting transmon qubits with interactions mediated by 9 transmon-type tunable couplers. The quantum walks of quasi-particle in the curved spacetime reflect the gravitational effect near the black hole, resulting in the behaviour of stimulated Hawking radiation, which is verified by the state tomography measurement of all 7 qubits outside the horizon. In addition, the dynamics of entanglement in the curved spacetime is directly measured. Our results would stimulate more interests to explore the related features of black holes using the programmable superconducting processor with tunable couplers.

Demonstration of Algorithmic Quantum Speedup

Despite the development of increasingly capable quantum computers, an experimental demonstration of a provable algorithmic quantum speedup employing today's non-fault-tolerant devices has remained elusive. Here, we unequivocally demonstrate such a speedup within the oracular model, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, using two different 27-qubit IBM Quantum superconducting processors. The speedup is observed on only one of the two processors when the quantum computation is protected by dynamical decoupling but not without it. The quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem in the setting of a game with an oracle and a verifier.

Generation of Pseudo-Random Quantum States on Actual Quantum Processors

The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of multipartite entanglement is nearly maximal. We argue that the method is optimal, and use it to benchmark actual superconducting (IBM's ibm_lagos) and ion trap (IonQ's Harmony) quantum processors. Despite the fact that ibm_lagos has lower single-qubit and two-qubit error rates, the overall performance of Harmony is better thanks to its low error rate in state preparation and measurement and to the all-to-all connectivity of qubits. Our result highlights the relevance of the qubits network architecture to generate highly entangled states.

Many-body bound states and induced interactions of charged impurities in a bosonic bath

Induced interactions and bound states of charge carriers immersed in a quantum medium are crucial for the investigation of quantum transport. Ultracold atom-ion systems can provide a convenient platform for studying this problem. Here, we investigate the static properties of one and two ionic impurities in a bosonic bath using quantum Monte Carlo methods. We identify three bipolaronic regimes depending on the strength of the atom-ion potential and the number of its two-body bound states: a perturbative regime resembling the situation of a pair of neutral impurities, a non-perturbative regime that loses the quasi-particle character of the former, and a many-body bound state regime that can arise only in the presence of a bound state in the two-body potential. We further reveal strong bath-induced interactions between the two ionic polarons. Our findings show that numerical simulations are indispensable for describing highly correlated impurity models.

Quantum-enabled millimetre wave to optical transduction using neutral atoms

Early experiments with transiting circular Rydberg atoms in a superconducting resonator laid the foundations of modern cavity and circuit quantum electrodynamics1, and helped explore the defining features of quantum mechanics such as entanglement. Whereas ultracold atoms and superconducting circuits have since taken rather independent paths in the exploration of new physics, taking advantage of their complementary strengths in an integrated system enables access to fundamentally new parameter regimes and device capabilities2,3. Here we report on such a system, coupling an ensemble of cold 85Rb atoms simultaneously to an, as far as we are aware, first-of-its-kind optically accessible, three-dimensional superconducting resonator4 and a vibration-suppressed optical cavity in a cryogenic (5 K) environment. To demonstrate the capabilities of this platform, and with an eye towards quantum networking5, we leverage the strong coupling between Rydberg atoms and the superconducting resonator to implement a quantum-enabled millimetre wave (mmwave) photon to optical photon transducer6. We measured an internal conversion efficiency of 58(11)%, a conversion bandwidth of 360(20) kHz and added thermal noise of 0.6 photons, in agreement with a parameter-free theory. Extensions of this technique will allow near-unity efficiency transduction in both the mmwave and microwave regimes. More broadly, our results open a new field of hybrid mmwave/optical quantum science, with prospects for operation deep in the strong coupling regime for efficient generation of metrologically or computationally useful entangled states7 and quantum simulation/computation with strong non-local interactions8.

Correcting Coherent Errors by Random Operation on Actual Quantum Hardware

Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve the performance of the next generation of quantum hardware. To investigate the importance of the different noise mechanisms affecting quantum computation, we performed a full quantum process tomography of single qubits in a real quantum processor in which echo experiments are implemented. In addition to the sources of error already included in the standard models, the obtained results show the dominant role of coherent errors, which we practically corrected by inserting random single-qubit unitaries in the quantum circuit, significantly increasing the circuit length over which quantum computations on actual quantum hardware produce reliable results.

Finite-size criticality in fully connected spin models on superconducting quantum hardware

The emergence of a collective behavior in a many-body system is responsible for the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different approaches to study quantum phase transitions. In this work, we exploit the new resources offered by quantum algorithms to detect the quantum critical behavior of fully connected spin-1/2 models. We define a suitable Hamiltonian depending on an internal anisotropy parameter γ that allows us to examine three paradigmatic examples of spin models, whose lattice is a fully connected graph. We propose a method based on variational algorithms run on superconducting transmon qubits to detect the critical behavior for systems of finite size. We evaluate the energy gap between the first excited state and the ground state, the magnetization along the easy axis of the system, and the spin-spin correlations. We finally report a discussion about the feasibility of scaling such approach on a real quantum device for a system having a dimension such that classical simulations start requiring significant resources.

Quantum algorithms for quantum dynamics

Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.