Noisy Intermediate-scale Quantum Research Articles

Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction

The variational quantum eigensolver (VQE) is a leading strategy that exploits noisy intermediate-scale quantum (NISQ) machines to tackle chemical problems. It is expected to demonstrate quantum advantage when handling a large number of qubits, where the density matrix cannot be processed efficiently on classical computers. To gain such computational advantages on large-scale problems, a feasible solution is the QUantum DIstributed Optimization (QUDIO) scheme, which partitions the original problem into K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{K}$$\\end{document} subproblems and allocates them to K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{K}$$\\end{document} quantum machines followed by the parallel optimization. Despite the provable acceleration ratio, the efficiency of QUDIO may heavily degrade by the synchronization operation. To conquer this issue, here we propose Shuffle-QUDIO to involve shuffle operations into local Hamiltonians during the quantum distributed optimization. Compared with QUDIO, Shuffle-QUDIO significantly reduces the communication frequency among quantum processors and simultaneously achieves better trainability. Particularly, we prove that Shuffle-QUDIO enables a faster convergence rate over QUDIO. Extensive numerical experiments are conducted to verify that Shuffle-QUDIO allows both a wall-clock time speedup and low approximation error in the tasks of estimating the ground state energy of a molecule. We empirically demonstrate that our proposal can be seamlessly integrated with other acceleration techniques, such as operator grouping, to further improve the efficacy of VQE.

Optimizing Variational Quantum Neural Networks Based on Collective Intelligence

Quantum machine learning stands out as one of the most promising applications of quantum computing, widely believed to possess potential quantum advantages. In the era of noisy intermediate-scale quantum, the scale and quality of quantum computers are limited, and quantum algorithms based on fault-tolerant quantum computing paradigms cannot be experimentally verified in the short term. The variational quantum algorithm design paradigm can better adapt to the practical characteristics of noisy quantum hardware and is currently one of the most promising solutions. However, variational quantum algorithms, due to their highly entangled nature, encounter the phenomenon known as the “barren plateau” during the optimization and training processes, making effective optimization challenging. This paper addresses this challenging issue by researching a variational quantum neural network optimization method based on collective intelligence algorithms. The aim is to overcome optimization difficulties encountered by traditional methods such as gradient descent. We study two typical applications of using quantum neural networks: random 2D Hamiltonian ground state solving and quantum phase recognition. We find that the collective intelligence algorithm shows a better optimization compared to gradient descent. The solution accuracy of ground energy and phase classification is enhanced, and the optimization iterations are also reduced. We highlight that the collective intelligence algorithm has great potential in tackling the optimization of variational quantum algorithms.

Non‐Markovian Cost Function for Quantum Error Mitigation

Non‐Markovian Cost Function for Quantum Error Mitigation

Parameter-setting heuristic for the quantum alternating operator ansatz

The quantum alternating operator ansatz (QAOA) is a generalized approach for solving challenging optimization problems that builds on the alternating structure of the quantum approximate optimization algorithm. Finding high-quality parameters efficiently for QAOA remains a major challenge in practice. In this work, we introduce a classical strategy for parameter setting, suitable for cases in which the number of distinct cost values grows only polynomially with the problem size, such as is common for constraint-satisfaction problems. The crux of our strategy is that we replace the cost function expectation value step of QAOA with a classical model that can be efficiently evaluated classically and has parameters which play an analogous role to the QAOA parameters. This model is based on empirical observations that, in some QAOA states, variable configurations with the same cost have the same amplitudes from step to step. We define this class of states as homogeneous states. For problems with particular symmetries, QAOA states are guaranteed to be homogeneous. More generally, high overlaps between QAOA states and homogeneous states have been empirically observed in a number of settings. Building on this idea, we define a classical homogeneous proxy for QAOA in which this property holds exactly and which yields information describing both states and expectation values. We then classically determine high-quality parameters for this proxy and then use these parameters in QAOA, an approach we label the homogeneous heuristic for parameter setting. We numerically examine this heuristic for MaxCut on unweighted Erdős-Rényi random graphs. For up to three QAOA levels we demonstrate that the heuristic is easily able to find parameters that match approximation ratios corresponding to previously found globally optimized approaches. For levels up to 20 we obtain parameters using our heuristic with approximation ratios monotonically increasing with depth, while a strategy that uses parameter transfer instead fails to converge with comparable classical resources. These results suggest that our heuristic may find good parameters in regimes that are intractable with noisy intermediate-scale quantum devices. Finally, we outline how our heuristic may be applied to wider classes of problems. Published by the American Physical Society 2024

Low-cost nonlocal Toffoli gate in a linear quantum network topology

Although a Toffoli gate can be equivalently implemented using several single-qubit and two-qubit gates, it will consume much resource, two of which are nonlocal controlled-NOT (CNOT) gates acting on two non-adjacent nodes, especially in distributed quantum computation (DQC). We, for the first time, employ an ancillary qubit to construct a nonlocal Toffoli gate for DQC in linear network topology. The ancillary-qubit-based scheme needs fewer qubits, quantum gates, and entanglement states than that based on quantum teleportation scheme and the entanglement swapping scheme. We also analyze the performance of the three proposed schemes under different application scenarios, and present their pros and cons. Our work will help to implement DQC in noisy intermediate-scale quantum (NISQ) era.

Variational quantum circuit learning-enabled robust optimization for AI data center energy control and decarbonization

As the demand for artificial intelligence (AI) models and applications continues to grow, data centers that handle AI workloads are experiencing a rise in energy consumption and associated carbon footprint. This work proposes a variational quantum computing-based robust optimization (VQC-RO) framework for control and energy management in large-scale data centers to address the computational challenges and overcome limitations of conventional model-based and model-free strategies. The VQC-RO framework integrates variational quantum circuits (VQCs) with classical optimization to enable efficient and uncertainty-aware control of energy systems in AI data centers. Quantum algorithms executed on noisy intermediate-scale quantum (NISQ) devices are used for value function estimation trained with Q-learning, leading to the formulation of a robust optimization problem with uncertain coefficients. The quantum computing-based robust control strategy is designed to address uncertainties associated with weather conditions and renewable energy generation while optimizing energy consumption in AI data centers. This work also outlines the computational experiments conducted at various AI data center locations in the United States to analyze the reduction in power consumption and carbon emission levels associated with the proposed quantum computing-based robust control framework. This work contributes a novel approach to energy-efficient and sustainable data center operation, promising to reduce carbon emissions and energy consumption in large-scale data centers handling AI workloads by 9.8 % and 12.5 %, respectively.

Error estimation in current noisy quantum computers

One of the main important features of the noisy intermediate-scale quantum (NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyse the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate a lower bound for the fidelity in the NISQ era, avoiding the necessity of comparing the quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the Ising model, 2) the Quantum-Phase Estimation (QPE), and 3) the Grover’s algorithm. For each model, the main quantities of interest are computed and benchmarked against the reference simulator’s results as a function of the error probability for a representative and statistically significant sample size. The analysis is satisfactory in more than the 99%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99\\%$$\\end{document} of the cases. In addition, we study how error mitigation techniques are able to eliminate the noise induced during the measurement. These results have been calculated for the IBM quantum computers, but both the tool and the analysis can be easily extended to any other quantum computer.

Non-Markovian quantum gate set tomography

Engineering quantum devices requires reliable characterization of the quantum system, including qubits, quantum operations (also known as instruments) and the quantum noise. Recently, quantum gate set tomography (GST) has emerged as a powerful technique for self-consistently describing quantum states, gates, and measurements. However, non-Markovian correlations between the quantum system and environment impact the reliability of GST. To address this, we propose a self-consistent operational framework called instrument set tomography (IST) for non-Markovian GST. Based on the stochastic quantum process, the instrument set describes instruments and system-environment (SE) correlations. We introduce a linear inversion IST (LIST) to describe instruments and SE correlations without physical constraints. The disharmony of linear relationships between instruments is detected. Furthermore, we propose a physically constrained statistical method based on the maximum likelihood estimation for IST (MLE-IST) with adjustable dimensions. MLE-IST shows significant flexibility in adapting to different types of devices, such as noisy intermediate-scale quantum (NISQ) devices, by adjusting the model and constraints. Experimental results demonstrate the effectiveness and necessity of simultaneously describing instruments and SE correlations. Specifically, the LIST and MLE-IST obtains significant improvement on average square error reduction in the imperfect implemented simulations by orders of −23.77 and −6.21, respectively, compared to their comparative methods. Remarkably, real-chip experiments indicate that a polynomial number of parameters with respect to the Markovian order are sufficient to characterize non-Markovian quantum noise in current NISQ devices. Consequently, IST provides an essential and self-consistent framework for characterizing, benchmarking, and developing quantum devices in terms of the instrument set.

Meta-optimization of resources on quantum computers

The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all information encoded in the calculation. Even if the technology advances fast within the next years, any use of quantum computers will be limited to short and simple tasks, serving as subroutines of more complex classical procedures. Even for these applications the resource efficiency, measured in the number of quantum computer runs, will be a key parameter. Here we suggest a general meta-optimization procedure for hybrid quantum-classical algorithms that allows finding the optimal approach with limited quantum resources. This method optimizes the usage of resources of an existing method by testing its capabilities and setting the optimal resource utilization. We demonstrate this procedure on a specific example of variational quantum algorithm used to find the ground state energy of a hydrogen molecule.

Modeling the performance of early fault-tolerant quantum algorithms

Progress in fault-tolerant quantum computation (FTQC) has driven the pursuit of practical applications with (EFTQC). These devices, limited in their qubit counts and fault-tolerance capabilities, require algorithms that can accommodate some degrees of error, which are known as EFTQC algorithms. To predict the onset of early quantum advantage, a comprehensive methodology is needed to develop and analyze EFTQC algorithms, drawing insights from both the methodologies of noisy intermediate-scale quantum and traditional FTQC. To address this need, we propose such a methodology for modeling algorithm performance on EFTQC devices under varying degrees of error. As a case study, we apply our methodology to analyze the performance of randomized Fourier estimation (RFE) [Kshirsagar, Katabarwa, and Johnson, ], an EFTQC algorithm for phase estimation. We investigate the runtime performance and the fault-tolerant overhead of RFE in comparison to the traditional quantum phase estimation algorithm. Our analysis reveals that RFE achieves significant savings in physical qubit counts while having a much higher runtime upper bound. We anticipate even greater physical qubit savings when considering more realistic assumptions about the performance of EFTQC devices. By providing insights into the performance trade-offs and resource requirements of EFTQC algorithms, our work contributes to the development of practical and efficient quantum computing solutions on the path to quantum advantage. Published by the American Physical Society 2024

Observing Majorana Fermion dynamic properties on a NISQ computer

Majorana particles are of particular interest due to their profound property of being their own anti-particles and potential applications for quantum computers. However, studying the dynamics of Majorana particles experimentally has proven to be challenging, with many unanswered questions about their behaviors. In this paper, we demonstrate that an improved discrete-time quantum walks (DTQW) on a Noisy Intermediate-Scale Quantum (NISQ) computer can be used to construct a well-defined Majorana fermion. Through this approach, we can observe the behaviors of Majorana particle propagation both in (1+1)- and (3+1)-dimensions. A counter-intuitive dynamic behavior of the non-vanishing expectation value of velocity and position with zero expectation value of momentum from the superposition of positive and negative energy solution is observed for the first time in NISQ. Our findings provide a promising avenue for experimentally studying the dynamical properties of Majorana particles.

Implementation of a quantum division circuit on noisy intermediate-scale quantum devices using dynamic circuits and approximate computing

Implementation of a quantum division circuit on noisy intermediate-scale quantum devices using dynamic circuits and approximate computing

Resource analysis for quantum-aided Byzantine agreement with the four-qubit singlet state

In distributed computing, a Byzantine fault is a condition where a component behaves inconsistently, showing different symptoms to different components of the system. Consensus among the correct components can be reached by appropriately crafted communication protocols even in the presence of byzantine faults. Quantum-aided protocols built upon distributed entangled quantum states are worth considering, as they are more resilient than traditional ones. Based on earlier ideas, here we establish a parameter-dependent family of quantum-aided weak broadcast protocols. We compute upper bounds on the failure probability of the protocol, and define and illustrate a procedure that minimizes the quantum resource requirements. Following earlier work demonstrating the suitability of noisy intermediate scale quantum (NISQ) devices for the study of quantum networks, we experimentally create our resource quantum state on publicly available quantum computers. Our work highlights important engineering aspects of the future deployment of quantum communication protocols with multi-qubit entangled states.

Warm-Starting and Quantum Computing: A Systematic Mapping Study

Due to low numbers of qubits and their error-proneness, Noisy Intermediate-Scale Quantum (NISQ) computers impose constraints on the size of quantum algorithms they can successfully execute. State-of-the-art research introduces various techniques addressing these limitations by utilizing known or inexpensively generated approximations, solutions, or models as a starting point to approach a task instead of starting from scratch. These so-called warm-starting techniques aim to reduce quantum resource consumption, thus facilitating the design of algorithms suiting the capabilities of NISQ computers. In this work, we collect and analyze scientific literature on warm-starting techniques in the quantum computing domain. In particular, we (i) create a systematic map of state-of-the-art research on warm-starting techniques using established guidelines for systematic mapping studies, (ii) identify relevant properties of such techniques, and (iii) based on these properties classify the techniques identified in the literature in an extensible classification scheme. Our results provide insights into the research field and aim to help quantum software engineers to categorize warm-starting techniques and apply them in practice. Moreover, our contributions may serve as a starting point for further research on the warm-starting topic since they provide an overview of existing work and facilitate the identification of research gaps.

Qubit Efficient Quantum Algorithms for the Vehicle Routing Problem on Noisy Intermediate‐Scale Quantum Processors

AbstractThe vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, the use of a previously‐introduced qubit encoding scheme is explored to reduce the number of qubits, to evaluate the effectiveness of Noisy Intermediate‐Scale Quantum (NISQ) devices when applied to industry relevant optimization problems. A quantum variational approach is applied to a testbed of multiple VRPTW instances ranging from 11 to 3964 routes. These intances are formulated as quadratic unconstrained binary optimization (QUBO) problems based on realistic shipping scenarios. The results are compared with standard binary‐to‐qubit mappings after executing on simulators as well as various quantum hardware platforms, including IBMQ, AWS (Rigetti), and IonQ. These results are benchmarked against the classical solver, Gurobi. The approach can find approximate solutions to the VRPTW comparable to those obtained from quantum algorithms using the full encoding, despite the reduction in qubits required. These results suggest that using the encoding scheme to fit larger problem sizes into fewer qubits is a promising step in using NISQ devices to find approximate solutions for industry‐based optimization problems, although additional resources are still required to eke out the performance from larger problem sizes.

Simulation of a spin-boson model by iterative optimization of a parametrized quantum circuit

Time evolution of the populations of spin states coupled with bosons, which can be a model of photosynthetic excitation energy transfer of dye molecules surrounded by proteins, is simulated using the projected-variational quantum dynamics algorithm. By a transformation of the Hamiltonian describing the spin-boson model into the one-dimensional nearest-neighbor form, it is shown that the spin-boson model can be simulated using the sequential ansatz even if a quantum computer has limited connectivity. The optimization of the parametrized quantum circuits is performed by the gradient descent method on a classical computer using the automatic differentiation, and the population of the spins is simulated on a noisy intermediate-scale quantum computer. The error originating from the quantum computing is mitigated by the Clifford data regression, in which the noise channel is estimated using the data obtained from all the time steps.

A quantum moving target segmentation algorithm for grayscale video based on background difference method

The classical moving target segmentation (MTS) algorithm in a video can segment the moving targets out by calculating frame by frame, but the algorithm encounters a real-time problem as the data increases. Recently, the benefits of quantum computing in video processing have been demonstrated, but it is still scarce for MTS. In this paper, a quantum moving target segmentation algorithm for grayscale video based on background difference method is proposed, which can simultaneously model the background of all frames and perform background difference to segment the moving targets. In addition, a feasible quantum subtractor is designed to perform the background difference operation. Then, several quantum units, including quantum cyclic shift transformation, quantum background modeling, quantum background difference, and quantum binarization, are designed in detail to establish the complete quantum circuit. For a video containing 2m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$2^{m}$\\end{document} frames (every frame is a 2n×2n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$2^{n} \ imes 2^{n}$\\end{document} image with q grayscale levels), the complexity of our algorithm is O(n+q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(n+q)$\\end{document}. This is an exponential speedup over the classical algorithm and also outperforms the existing quantum algorithms. Finally, the experiment on IBM Q demonstrates the feasibility of our algorithm in this noisy intermediate-scale quantum (NISQ) era.

Implementation and measurement of quantum entanglement using IBM quantum platforms

The use of quantum entanglement has garnered increasing attention among researchers in recent years due to its wide range of applications, not only revolutionizing the field of information processing but also enhancing quantum-safe communications. Identifying the degree of entanglement present in quantum states is a crucial focus, and designing an algorithm capable of feasibly measuring entanglement is imperative. While theoretical calculations hold high regard, the ease of implementing these algorithms in a laboratory setting is essential to gauge their efficiency.In this context, IBM quantum computers stand out as discrete value NISQ (Noisy Intermediate-Scale Quantum) platforms These platforms are based on superconducting qubits, providing an opportunity to test our algorithms without the need for extravagant laboratory equipment. This paper proposes an algorithm designed to measure entanglement in a bipartite system. We will execute the algorithm on IBM’s 127-qubit backends to compare our calculations with real-world results. Furthermore, we aim to address and mitigate errors inherent in these devices by utilizing local mitigation technique available in the IBM Experiments Python package, aiming for more accurate and reliable outcomes.

Probabilistic Interpolation of Quantum Rotation Angles.

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of B bits of resolution, i.e., it might support only 2^{B} possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher B can greatly complexify hardware. Here, we explore an alternative: probabilistic angle interpolation (PAI). This effectively implements any desired, continuously parametrized rotation by randomly choosing one of three discretized gate settings and postprocessing individual circuit outputs. The approach is particularly relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that (a)the approach is optimal in the sense that PAI achieves the least possible overhead and (b)the overhead is remarkably modest even with thousands of parametrized gates and only seven bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers where even 5-6bits of resolution may suffice and, as we demonstrate, the approach is many orders of magnitude more efficient than prior techniques. Moreover we conclude that, even for more mature late noisy intermediate-scale quantum era hardware, no more than nine bits will be necessary.

Quantum homogenization as a quantum steady-state protocol on noisy intermediate-scale quantum hardware

Quantum homogenization as a quantum steady-state protocol on noisy intermediate-scale quantum hardware