Noisy Intermediate-Scale Quantum Era Research Articles

Space-efficient binary optimization for variational quantum computing

In the era of Noisy Intermediate-Scale Quantum (NISQ) computers it is crucial to design quantum algorithms which do not require many qubits or deep circuits. Unfortunately, most of the well-known quantum algorithms are too demanding to be run on currently available quantum devices. Moreover, even the state-of-the-art algorithms developed for the NISQ era often suffer from high space complexity requirements for particular problem classes. In this paper, we show that it is possible to greatly reduce the number of qubits needed for the Travelling Salesman Problem (TSP), a paradigmatic optimization task, at the cost of having deeper variational circuits. While the focus is on this particular problem, we claim that the approach can be generalized for other problems where the standard bit-encoding is highly inefficient. Finally, we also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models. All the proposed encodings have the same volume up to polylogarithmic factors and remain efficient to implement within the Quantum Approximate Optimization Algorithm framework.

Variational Quantum-Neural Hybrid Eigensolver.

The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-scale quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the ground-state simulations of some nontrivial Hamiltonians. However, short quantum coherence time and limited availability of quantum hardware resources in the NISQ hardware strongly restrain the capacity and expressiveness of VQEs. In this Letter, we introduce the variational quantum-neural hybrid eigensolver (VQNHE) in which the shallow-circuit quantum Ansatz can be further enhanced by classical post-processing with neural networks. We show that the VQNHE consistently and significantly outperforms the VQE in simulating ground-state energies of quantum spins and molecules given the same amount of quantum resources. More importantly, we demonstrate that, for arbitrary postprocessing neural functions, the VQNHE only incurs a polynomial overhead of processing time and represents the first scalable method to exponentially accelerate the VQE with nonunitary postprocessing that can be efficiently implemented in the NISQ era.

Any-To-Any Connected Cavity-Mediated Architecture for Quantum Computing with Trapped Ions or Rydberg Arrays

We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity. The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity. Heralding enables high-fidelity entanglement even for a cavity of moderate quality. For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few μs, increasing the interchain entanglement rate over 2 orders of magnitude beyond current methods and eliminating a major bottleneck for scaling trapped-ion systems. For one realistic scenario, we outline how to achieve the any-to-any entanglement of 20 ion chains containing a total of 500 qubits in 200μs, with both fidelities and rates limited only by local operations and ion readout. For processors composed of Rydberg atoms, our method fully connects a large array of thousands of neutral atoms. The connectivity afforded by our architecture is extendable to tens of thousands of qubits using multiple overlapping cavities, expanding capabilities for noisy intermediate-scale quantum era algorithms and Hamiltonian simulations, as well as enabling more robust high-dimensional error-correcting schemes.Received 21 September 2021Accepted 18 January 2022DOI:https://doi.org/10.1103/PRXQuantum.3.010344Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum gatesQuantum information architectures & platformsQuantum information processingQuantum simulationPhysical SystemsAtomsTechniquesAtom & ion coolingCavity resonatorsJaynes-Cummings modelQuantum InformationAtomic, Molecular & Optical

Variational quantum linear solver with a dynamic ansatz

Variational quantum algorithms have found success in the noisy intermediate-scale quantum era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our paper, we introduce the dynamic ansatz in the variational quantum linear solver for a system of linear algebraic equations. In this improved algorithm, the number of layers in the hardware efficient ansatz circuit is evolved, starting from a small and gradually increasing until convergence of the solution is reached. We demonstrate the algorithm advantage in comparison to the standard static ansatz by utilizing fewer quantum resources and with a smaller quantum depth on average in the presence and absence of quantum noise and in cases when the number of qubits or condition number of the system matrices are increased. The numbers of iterations and layers can be altered by a switching parameter. The performance of the algorithm in using quantum resources is quantified by a newly defined metric.

The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers

The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor&#x2019;s work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical post-processing algorithm. The theoretical result corresponds the situation where a quantum device working with a medium number of qubits of very small errors can solve DLP. However, all the quantum devices that we can use have a limited number of noisy qubits, as of the noisy intermediate-scale quantum (NISQ) era. Thus, evaluating the instance size that the latest quantum device can solve, and give a future prediction of the size along the progress of quantum devices are emerging research topics. This paper contains two proposal to discuss the performance of quantum devices against DLP in the NISQ era. (1) A quantitative measure based on the success probability of the post-processing algorithm to determine whether an experiment on a quantum device (or a classical simulator) succeeded. (2) A procedure to modify bit strings observed from a Shor&#x2019;s circuit to increase the success probability of a lattice-based post-processing algorithm. We conducted our experiments with the <monospace>ibm_kawasaki</monospace> device and discovered that the simplest circuit (7 qubits) from a 2-bit DLP instance achieves a sufficiently high success probability to proclaim the experiment successful. Experiments on another circuit from a slightly harder 2-bit DLP instance, on the other hand, did not succeed, and we determined that reducing the noise level by half is required to achieve a successful experiment. Finally, we give a near-term prediction based on required noise levels to solve some selected small DLP and integer factoring instances.

Survey of NISQ Era Hybrid Quantum-Classical Machine Learning Research

Quantum computing is a rapidly growing field that has received a significant amount of support in the past decade in industry and academia. Several physical quantum computers are now freely available to use through cloud services, with some implementations supporting upwards of hundreds of qubits. These advances mark the beginning of the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing, paving the way for hybrid quantum-classical systems. This work provides an introductory overview of gate-model quantum computing through the Visual IoT/Robotics Programming Language Environment and a survey of recent applications of NISQ era quantum computers to hybrid quantum-classical machine learning.

Fast-forwarding with NISQ processors without feedback loop

Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for quantum simulation. Hybrid classical quantum algorithms such as the variational quantum algorithms have been proposed to effectively use current term quantum devices. One promising approach to quantum simulation in the noisy intermediate-scale quantum (NISQ) era is the diagonalisation based approach, with some of the promising examples being the subspace variational quantum simulator (SVQS), variational fast forwarding (VFF), fixed-state variational fast forwarding (fs-VFF), and the variational Hamiltonian diagonalisation (VHD) algorithms. However, these algorithms require a feedback loop between the classical and quantum computers, which can be a crucial bottleneck in practical application. Here, we present the classical quantum fast forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF shares some similarities with SVQS, VFF, fs-VFF and VHD but removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. The CQFF algorithm does not suffer from the barren plateau problem and the accuracy can be systematically increased. Furthermore, if the Hamiltonian to be simulated is expressed as a linear combination of tensored-Pauli matrices, the CQFF algorithm reduces to the task of sampling some many-body quantum state in a set of Pauli-rotated bases, which is easy to do in the NISQ era. We run the CQFF algorithm on existing quantum processors and demonstrate the promise of the CQFF algorithm for current-term quantum hardware. We compare CQFF with Trotterization for a XY spin chain model Hamiltonian and find that the CQFF algorithm can simulate the dynamics more than 105 times longer than Trotterization on current-term quantum hardware. This provides a 104 times improvement over the previous record.

Quantum computing: A taxonomy, systematic review and future directions

AbstractQuantum computing (QC) is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum‐mechanical principles such as entanglement and superposition. It is anticipated that this computational advantage of QC will help to solve many complex and computationally intractable problems in several application domains such as drug design, data science, clean energy, finance, industrial chemical development, secure communications, and quantum chemistry. In recent years, tremendous progress in both quantum hardware development and quantum software/algorithm has brought QC much closer to reality. Indeed, the demonstration of quantum supremacy marks a significant milestone in the Noisy Intermediate Scale Quantum (NISQ) era—the next logical step being the quantum advantage whereby quantum computers solve a real‐world problem much more efficiently than classical computing. As the quantum devices are expected to steadily scale up in the next few years, quantum decoherence and qubit interconnectivity are two of the major challenges to achieve quantum advantage in the NISQ era. QC is a highly topical and fast‐moving field of research with significant ongoing progress in all facets. A systematic review of the existing literature on QC will be invaluable to understand the state‐of‐the‐art of this emerging field and identify open challenges for the QC community to address in the coming years. This article presents a comprehensive review of QC literature and proposes taxonomy of QC. The proposed taxonomy is used to map various related studies to identify the research gaps. A detailed overview of quantum software tools and technologies, post‐quantum cryptography, and quantum computer hardware development captures the current state‐of‐the‐art in the respective areas. The article identifies and highlights various open challenges and promising future directions for research and innovation in QC.

Towards understanding the power of quantum kernels in the NISQ era

A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To this end, a crucial open question is: does the power of quantum kernels still hold under the NISQ setting? In this study, we fill this knowledge gap by exploiting the power of quantum kernels when the quantum system noise and sample error are considered. Concretely, we first prove that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise. With the aim of preserving the superiority of quantum kernels in the NISQ era, we further devise an effective method via indefinite kernel learning. Numerical simulations accord with our theoretical results. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.

Quantum-Enhanced Data Classification with a Variational Entangled Sensor Network

Variational quantum circuits (VQCs) built upon noisy intermediate-scale quantum (NISQ) hardware, in conjunction with classical processing, constitute a promising architecture for quantum simulations, classical optimization, and machine learning. However, the required VQC depth to demonstrate a quantum advantage over classical schemes is beyond the reach of available NISQ devices. Supervised learning assisted by an entangled sensor network (SLAEN) is a distinct paradigm that harnesses VQCs trained by classical machine-learning algorithms to tailor multipartite entanglement shared by sensors for solving practically useful data-processing problems. Here, we report the first experimental demonstration of SLAEN and show an entanglement-enabled reduction in the error probability for classification of multidimensional radio-frequency signals. Our work paves a new route for quantum-enhanced data processing and its applications in the NISQ era.

Quantum reservoir computing with a single nonlinear oscillator

Realizing the promise of quantum information processing remains a daunting task, given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term applications in the noisy intermediate-scale quantum era. Here, we propose continuous variable quantum reservoir computing in a single nonlinear oscillator. Through numerical simulation of our model we demonstrate quantum-classical performance improvement, and identify its likely source: the nonlinearity of quantum measurement. Beyond quantum reservoir computing, this result may impact the interpretation of results across quantum machine learning. We study how the performance of our quantum reservoir depends on Hilbert space dimension, how it is impacted by injected noise, and briefly comment on its experimental implementation. Our results show that quantum reservoir computing in a single nonlinear oscillator is an attractive modality for quantum computing on near-term hardware.

Simulation of wave-particle duality in multipath interferometers on a quantum computer

We present an architecture to investigate wave-particle duality in $N$-path interferometers on a universal quantum computer involving as low as $2\log N$ qubits and develop a measurement scheme which allows the efficient extraction of quantifiers of interference visibility and which-path information. We implement our algorithms for interferometers with up to $N=16$ paths in proof-of-principle experiments on a noisy intermediate-scale quantum (NISQ) device using down to $\mathcal{O}(\log N)$ gates and despite increasing noise consistently observe a complementary behavior between interference visibility and which-path information. Our results are in accordance with our current understanding of wave-particle duality and allow its investigation for interferometers with an exponentially growing number of paths on future quantum devices beyond the NISQ era.

The bitter truth about gate-based quantum algorithms in the NISQ era

Implementing a gate-based quantum algorithm on an noisy intermediate scale quantum (NISQ) device has several challenges that arise from the fact that such devices are noisy and have limited quantum resources. Thus, various factors contributing to the depth and width as well as to the noise of an implementation of a gate-based algorithm must be understood in order to assess whether an implementation will execute successfully on a given NISQ device. In this contribution, we discuss these factors and their impact on algorithm implementations. Especially, we will cover state preparation, oracle expansion, connectivity, circuit rewriting, and readout: these factors are very often ignored when presenting a gate-based algorithm but they are crucial when implementing such an algorithm on near-term quantum computers. Our contribution will help developers in charge of realizing gate-based algorithms on such machines in (i) achieving an executable implementation, and (ii) assessing the success of their implementation on a given machine.

Machine-Learning Quantum States in the NISQ Era

We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. We review recent techniques in reconstruction of a cold atom wavefunction, intended for use on experimental noisy intermediate-scale quantum (NISQ) devices. Finally, we discuss the outlook for future experimental state reconstruction using machine learning in the NISQ era and beyond.

Accelerating Lattice Quantum Field Theory Calculations via Interpolator Optimization Using Noisy Intermediate-Scale Quantum Computing.

The only known way to study quantum field theories in nonperturbative regimes is using numerical calculations regulated on discrete space-time lattices. Such computations, however, are often faced with exponential signal-to-noise challenges that render key physics studies untenable even with next generation classical computing. Here, a method is presented by which the output of small-scale quantum computations on noisy intermediate-scale quantum era hardware can be used to accelerate larger-scale classical field theory calculations through the construction of optimized interpolating operators. The method is implemented and studied in the context of the 1+1-dimensional Schwinger model, a simple field theory which shares key features with the standard model of nuclear and particle physics.

A quantum solution for efficient use of symmetries in the simulation of many-body systems

A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a memory/computational bottleneck on classical computers during exact diagonalization. We apply Grover’s search in the form of a minimization procedure to solve this problem. Our quantum solution provides an exponential reduction in memory, and a quadratic speedup in time over classical methods. We discuss explicitly the full circuit implementation of Grover minimization as applied to this problem, finding that the oracle only scales as polylog in the size of the group, which acts as the search space. Further, we design an error mitigation scheme that, with no additional qubits, reduces the impact of bit-flip errors on the computation, with the magnitude of mitigation directly correlated with the error rate, improving the utility of the algorithm in the Noisy Intermediate Scale Quantum era.

A Hardware-Aware Heuristic for the Qubit Mapping Problem in the NISQ Era

Due to several physical limitations in the realisation of quantum hardware, today's quantum computers are qualified as Noisy Intermediate-Scale Quantum (NISQ) hardware. NISQ hardware is characterized by a small number of qubits (50 to a few hundred) and noisy operations. Moreover, current realisations of superconducting quantum chips do not have the ideal all-to-all connectivity between qubits but rather at most a nearest-neighbour connectivity. All these hardware restrictions add supplementary low-level requirements. They need to be addressed before submitting the quantum circuit to an actual chip. Satisfying these requirements is a tedious task for the programmer. Instead, the task of adapting the quantum circuit to a given hardware is left to the compiler. In this paper, we propose a Hardware-Aware mapping transition algorithm (HA) that takes the calibration data into account with the aim to improve the overall fidelity of the circuit. Evaluation results on IBM quantum hardware show that our HA approach can outperform the state of the art both in terms of the number of additional gates and circuit fidelity.

Neighborhood-history quantum walk

History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of the walk. We generalize this model to the neighborhood-history quantum walk (NHQW), in which the walk dynamics and the state of the memory qubits in a neighborhood of the particle’s position are interdependent. To demonstrate it, we construct an NHQW on a one-dimensional lattice, with a simple neighborhood. Several dynamically interesting history dependent QWs can be realized as single-particle sectors of quantum lattice gas automata. In contrast, the NHQW constructed in this paper is realized as a single-particle sector of the more general quantum cellular automaton. The complexity of the NHQW dynamics presents a promising avenue toward richer walk strategies and a potentially useful model of QWs for the Noisy Intermediate-Scale Quantum era of quantum computing. It also modifies QWs to conceivably allow for modeling fundamental physics incorporating quantum field interactions with particles.

Quantum Associative Memory in Hep Track Pattern Recognition

We have entered the Noisy Intermediate-Scale Quantum Era. A plethora of quantum processor prototypes allow evaluation of potential of the Quantum Computing paradigm in applications to pressing computational problems of the future. Growing data input rates and detector resolution foreseen in High-Energy LHC (2030s) experiments expose the often high time and/or space complexity of classical algorithms. Quantum algorithms can potentially become the lower-complexity alternatives in such cases. In this work we discuss the potential of Quantum Associative Memory (QuAM) in the context of LHC data triggering. We examine the practical limits of storage capacity, as well as store and recall errorless efficiency, from the viewpoints of the state-of-the-art IBM quantum processors and LHC real-time charged track pattern recognition requirements. We present a software prototype implementation of the QuAM protocols and analyze the topological limitations for porting the simplest QuAM instances to the public IBM 5Q and 14Q cloud-based superconducting chips.

Quantum Computing in the NISQ era and beyond

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.