Quantum computing (QC) in the current NISQ era is still limited in size and precision. Hybrid applications mitigating those shortcomings are prevalent to gain early insight and advantages. Hybrid quantum machine learning (QML) comprises both the application of QC to improve machine learning (ML) and ML to improve QC architectures. This work considers the latter, leveraging reinforcement learning (RL) to improve quantum circuit design (QCD), which we formalize by a set of generic objectives. Furthermore, we propose qcd-gym, a concrete framework formalized as a Markov decision process, to enable learning policies capable of controlling a universal set of continuously parameterized quantum gates. Finally, we provide benchmark comparisons to assess the shortcomings and strengths of current state-of-the-art RL algorithms.

In the fast-paced field of quantum computing, identifying the architectural characteristics that will enable quantum processors to achieve high performance across a diverse range of quantum algorithms continues to pose a significant challenge. Given the extensive and costly nature of experimentally testing different designs, this paper introduces the first Design Space Exploration (DSE) for quantum-dot spin-qubit architectures. Utilizing the upgraded SpinQ compilation framework, this study explores a substantial design space comprising 29,312 spin-qubit-based architectures and applies an innovative optimization tool, ArtA (Artificial Architect), to speed up the design space traversal. ArtA can leverage 17 optimization configurations, significantly reducing exploration times by up to 99.1% compared to a traditional brute force approach while maintaining the same result quality. After a comprehensive evaluation of best-matching optimization configurations per quantum circuit, ArtA suggests specific as well as universal architectural features that provide optimal performance across the examined circuits. Our work demonstrates that combining DSE methodologies with optimization algorithms can be effectively used to generate meaningful design insights for quantum processor development.

Quantum computing represents a paradigm shift in computation, offering the potential to solve complex problems intractable for classical computers. Although current quantum processors already consist of a few hundred qubits, their scalability remains a significant challenge. Modular quantum computing architectures have emerged as a promising approach to scale up quantum computing systems. This article delves into the critical aspects of distributed multi-core quantum computing, focusing on quantum circuit mapping, a fundamental task to successfully execute quantum algorithms across cores while minimizing inter-core communications. We derive the theoretical bounds on the number of non-local communications needed for random quantum circuits and introduce the Hungarian Qubit Assignment (HQA) algorithm, a multi-core mapping algorithm designed to optimize qubit assignments to cores with the aim of reducing inter-core communications. Our exhaustive evaluation of HQA against state-of-the-art circuit mapping algorithms for modular architectures reveals a 4.9× and 1.6× improvement in terms of execution time and non-local communications, respectively, compared to the best-performing algorithm. HQA emerges as a very promising scalable approach for mapping quantum circuits into multi-core architectures, positioning it as a valuable tool for harnessing the potential of quantum computing at scale.

Application-specific quantum computers offer the most efficient means to tackle problems intractable by classical computers. Realizing these architectures necessitates a deep understanding of quantum circuit properties and their relationship to execution outcomes on quantum devices. Our study aims to perform for the first time a rigorous examination of quantum circuits by introducing graph theory-based metrics extracted from their qubit interaction graph and gate dependency graph (GDG) alongside conventional parameters describing the circuit itself. This methodology facilitates a comprehensive analysis and clustering of quantum circuits. Furthermore, it uncovers a connection between parameters rooted in both qubit interaction and GDGs, and the performance metrics for quantum circuit mapping, across a range of established quantum device and mapping configurations. Among the various device configurations, we particularly emphasize modular (i.e. multi-core) quantum computing architectures due to their high potential as a viable solution for quantum device scalability. This thorough analysis will help us to: i) identify key attributes of quantum circuits that affect the quantum circuit mapping performance metrics; ii) predict the performance on a specific chip for similar circuit structures; iii) determine preferable combinations of mapping techniques and hardware setups for specific circuits; and iv) define representative benchmark sets by clustering similarly structured circuits.

Quantum computing is considered a promising future technology for addressing complex societal and technical challenges. However, it is still in an experimental early stage. This article takes a full-stack perspective and advocates for a community-driven, interdisciplinary development of quantum computing. First, the importance of close collaboration across different scientific and technical disciplines is emphasized. It is then shown that long-term scalable quantum computers can only be realized through distributed architectures, and the resulting technical and organizational requirements are discussed. Using concrete application examples from the fields of energy, logistics, mobility, and network analysis, the paper illustrates where quantum computing could create real societal value in the future. Finally, a roadmap is presented with short-, medium-, and long-term actions addressing technological, infrastructural, and educational aspects. At the core of this message is the idea that open communities, transparent standards, and interdisciplinary knowledge exchange are essential for the sustainable development and broad adoption of quantum-based technologies.

This research investigates the possibility of using quantum optimal control techniques to co-optimize the energetic cost and the process fidelity of a quantum unitary gate. The energetic cost is theoretically defined, and thereby, the gradient of the energetic cost for pulse engineering is derived. The Pareto optimality is empirically demonstrated in the trade-off between process fidelity and energetic cost. Thereafter, two novel numerical quantum optimal control approaches are proposed: i) energy-optimized gradient ascent pulse engineering (EO-GRAPE) as an open-loop gradient-based method, and ii) energy-optimized deep reinforcement learning for pulse engineering (EO-DRLPE) as a closed-loop method. The performance of both methods is probed in the presence of increasing noise. It is found that the EO-GRAPE method performs better than the EO-DRLPE methods with and without a warm start for most experimental settings. Additionally, for one qubit unitary gate, the correlation between the Bloch sphere path length and the energetic cost is illustrated.

Quantum computing promises to execute some tasks exponentially faster than classical computers. Quantum compilation, which transforms algorithms into executable quantum circuits, involves solving the initial mapping problem, crucial for optimizing qubit assignment and minimizing gate error rates. This study explores Deep Reinforcement Learning (DRL) for initial mapping across various qubit topologies, considering fixed gate error rates. Previous DRL approaches have succeeded but didn’t account for fixed error rates, used only one algorithm (PPO), and focused on a single topology with 20 qubits. The trial-and-error nature of Reinforcement Learning makes it ideal for initial mapping. DRL agents, using multiple policy gradient algorithms (A2C, PPO with and without action masking, and TRPO), compute high-quality mappings for small- and medium-scale quantum architectures. While effective, their efficiency decreases with larger systems, necessitating further optimization. Fine-tuning hyperparameters and action masking prevent illegal actions and enhance accuracy. Although currently not surpassing tools like Qiskit or achieving scalability for larger systems, this study highlights DRL’s potential for initial mapping in quantum computing, encouraging further innovation and refinement.

Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These algorithms aim to minimize the objective function xTQx, where Q is a QUBO matrix. However, the number of two-qubit CNOT gates in QAOA circuits and the complexity of problem embeddings in Quantum Annealing scale linearly with the number of non-zero couplings in Q, contributing to significant computational and error-related challenges. To address this, we introduce the concept of semi symmetries in QUBO matrices and propose an algorithm for identifying and factoring these symmetries into ancilla qubits. Semi-symmetries frequently arise in optimization problems such as Maximum Clique, Hamilton Cycles, Graph Coloring, and Graph Isomorphism. We theoretically demonstrate that the modified QUBO ma trix Qmod retains the same energy spectrum as the original Q. Experimental evaluations on the aforementioned problems show that our algorithm reduces the number of couplings and QAOA circuit depth by up to 45%. For Quantum Annealing, these reductions also lead to sparser problem embeddings, shorter qubit chains and better performance. This work highlights the utility of exploiting QUBO matrix structure to optimize quantum algorithms, advancing their scalability and practical applicability to real-world combinatorial problems.

Quantum computation represents a promising frontier in the domain of high-performance computing, blending quantum information theory with practical applications to overcome the limitations of classical computation. This study investigates the challenges of manufacturing high-fidelity and scalable quantum processors. Quantum gate set tomography (QGST) is a critical method for characterizing quantum processors and understanding their operational capabilities and limitations. This paper introduces Ml4Qgst as a novel approach to QGST by integrating machine learning techniques, specifically utilizing a transformer neural network model. Adapting the transformer model for QGST addresses the computational complexity of modeling quantum systems. Advanced training strategies, including data grouping and curriculum learning, are employed to enhance model performance, demonstrating significant congruence with ground-truth values. We benchmark this training pipeline on the constructed learning model, to successfully perform QGST for 2 and 3 gates on single-qubit and two-qubit systems, with over-rotation error and depolarizing noise estimation with comparable accuracy to pyGSTi. This research marks a pioneering step in applying deep neural networks to the complex problem of quantum gate set tomography, showcasing the potential of machine learning to tackle nonlinear tomography challenges in quantum computing.

The design and benchmarking of quantum computer architectures traditionally rely on practical hardware restrictions, such as gate fidelities, control, and cooling. At the theoretical and software levels, numerous approaches have been proposed for benchmarking quantum devices, ranging from, inter alia, quantum volume to randomized benchmarking. In this work, we utilize the quantum information-theoretic properties of multipartite maximally entangled quantum states, in addition to their correspondence with quantum error-correction codes, permitting us to quantify the entanglement generated on near-term bilinear spin-qubit architectures. For this aim, we introduce four metrics that ascertain the quality of genuine multipartite quantum entanglement, along with circuit-level fidelity measures. As part of the task of executing a quantum circuit on a device, we devise simulations, which combine expected hardware characteristics of spin-qubit devices with appropriate compilation techniques; we then analyze three different architectural choices of varying lattice sizes for bilinear arrays, under three increasingly realistic noise models. We find that if the use of a compiler is assumed, sparsely connected spin-qubit lattices can approach comparable values of our metrics to those of the most highly connected device architecture. Even more surprisingly, by incorporating crosstalk into our last noise model, we find that, as error rates for crosstalk approach realistic values, the benefits of utilizing a bilinear array with advanced connectivity vanish. Our results highlight the limitations of adding local connectivity to near-term spin-qubit devices, and can be readily adapted to other qubit technologies. The framework developed here can be used for analyzing quantum entanglement on a device before fabrication, informing experimentalists on concomitant realistic expectations.

As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of Quadratic Unconstrained Binary Optimization (QUBO). In this work, we thus study whether systematically approximating QUBO representations of the MAX-3SAT problem can improve the solution quality when solved on contemporary quantum hardware, compared to using exact, non-approximated QUBO representations. For a MAX-3SAT instance consisting of a 3SAT formula with n variables and m clauses, we propose a method of systematically creating approximate QUBO representations of dimension (n× n), which is significantly smaller than the QUBO matrices of any exact, non-approximated MAX-3SAT QUBO transformation. In an empirical evaluation, we demonstrate that using our QUBO approximations for solving MAX-3SAT problems on D-Wave's quantum annealer Advantage_System6.4 can yield better results than using state-of-the-art exact QUBO transformations. Furthermore, we demonstrate that using naive QUBO approximation methods, based on removing values from exact (n+m)×(n+m)-dimensional QUBO representations of MAX-3SAT instances, is ineffective.

As quantum computing devices increase in size with respect to the number of qubits, two-qubit interactions become more challenging, necessitating innovative and scalable qubit routing solutions. In this work, we introduce beSnake, a novel algorithm specifically designed to address the intricate qubit routing challenges in scalable spin-qubit architectures. Unlike traditional methods in superconducting architectures that solely rely on swap operations, beSnake also incorporates the shuttle operation to optimize the execution time and fidelity of quantum circuits and achieves fast computation times of the routing task itself. Employing a simple breadth-first search approach, beSnake effectively manages the restrictions created by diverse topologies and qubit positions acting as obstacles for up to 72% qubit density. It also has the option to adjust the level of optimization and to dynamically tackle parallelized routing tasks, all the while maintaining noise awareness. Our simulations demonstrate beSnake's advantage over an existing routing solution on random circuits and real quantum algorithms with up to 1000 qubits, showing an average improvement of up to 80% in gate overhead, 54% in depth overhead, and up to 8.33 times faster routing times.

In this paper, we present an open-source Python framework, called satqubolib. This framework aims to provide all necessary tools for solving (MAX)-3SAT problems on quantum hardware systems via Quadratic Unconstrained Binary Optimization (QUBO). Our framework solves two major issues when solving (MAX)-3SAT instances in the context of quantum computing. Firstly, a common way of solving satisfiability instances with quantum methods is, to transform these instances into instances of QUBO, as QUBO is the input format for quantum annealers and the Quantum Approximate Optimization Algorithm (QAOA) on quantum gate systems. Studies have shown, that the choice of this transformation can significantly impact the solution quality of quantum hardware systems. Thus, our framework provides thousands of usable QUBO transformations for satisfiability problems. Doing so also enables practitioners from any domain to immediately explore and use quantum techniques as a potential solver for their domain-specific problems, as long as they can be encoded as satisfiability problems. As a second contribution, we created a dataset of 6000 practically hard and satisfiable SAT instances that are also small enough to be solved with current quantum(-hybrid) methods. This dataset enables meaningful benchmarking of new quantum, quantum-hybrid, and classical methods for solving satisfiability problems.

As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters, which is typically the second phase in a common bi-level optimization procedure for minimizing the weight of composite structures. To adapt stacking sequence retrieval for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed numerical state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For the DMRG algorithm, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.

Quantum algorithms, represented as quantum circuits, can be used as benchmarks for assessing the performance of quantum systems. Existing datasets, widely utilized in the field, suffer from limitations in size and versatility, leading researchers to employ randomly generated circuits. Random circuits are, however, not representative benchmarks as they lack the inherent properties of real quantum algorithms for which the quantum systems are manufactured. This shortage of ‘useful’ quantum benchmarks poses a challenge to advancing the development and comparison of quantum compilers and hardware. This research aims to enhance the existing quantum circuit datasets by generating what we refer to as ‘realistic-looking’ circuits by employing the Transformer machine learning architecture. For this purpose, we introduce KetGPT, a tool that generates synthetic circuits in OpenQASM language, whose structure is based on quantum circuits derived from existing quantum algorithms and follows the typical patterns of human-written algorithm-based code (e.g., order of gates and qubits). Our three-fold verification process, involving manual inspection and Qiskit framework execution, transformer-based classification, and structural analysis, demonstrates the efficacy of KetGPT in producing large amounts of additional circuits that closely align with algorithm-based structures. Beyond benchmarking, we envision KetGPT contributing substantially to AI-driven quantum compilers and systems.

A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO. State-of-the-art transformations from MAX-3SAT to QUBO work by mapping clauses of a 3SAT formula associated with the MAX-3SAT instance to an instance of QUBO and combining the resulting QUBOs into a single QUBO instance representing the whole MAX-3SAT instance. As creating these transformations is currently done manually or via exhaustive search methods and is, therefore, algorithmically inefficient, we see potential for including search-based optimization. In this paper, we propose two methods of using evolutionary algorithms to create QUBO representations of MAX-3SAT problems automatically. We evaluate our created QUBOs on 500 and 1000-clause 3SAT formulae and find competitive performance to state-of-the-art baselines when using both classical and quantum annealing solvers.

Correction to: npj Quantum Informationhttps://doi.org/10.1038/s41534-024-00909-7, published online 09 November 2024 The original version of this Article contained an error in the caption of Fig. 5, which has now been replaced with the correct caption. Additionally, Affiliation 3, originally listed as "Computer Engineering Department, Technical University of Valencia, Valencia, Spain," was incorrect and has been updated to "Departamento de Informática de Sistemas y Computadores, Universitat Politècnica de València, 46022 València, Spain”. This has been corrected in both the PDF and HTML versions of the Article.

Efficiently mapping quantum circuits onto hardware is integral for the quantum compilation process, wherein a circuit is modified in accordance with a quantum processor’s connectivity. Many techniques currently exist for solving this problem, wherein SWAP-gate overhead is usually prioritized as a cost metric. We reconstitute quantum circuit mapping using tools from quantum information theory, showing that a lower bound, which we dub the lightcone bound, emerges for a circuit executed on hardware. We also develop an initial placement algorithm based on graph similarity search, aiding us in optimally placing circuit qubits onto a device. 600 realistic benchmarks using the IBM Qiskit compiler and a brute-force method are then tested against the lightcone bound, with results unambiguously verifying the veracity of the bound, while permitting trustworthy estimations of minimal overhead in near-term realizations of quantum algorithms. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing.

Quantum computing has emerged as a transformative tool for future data management. Classical problems in database domains, including query optimization, data integration, and transaction management, have recently been addressed using quantum computing techniques. This tutorial aims to establish the theoretical foundation essential for enhancing methodologies and practical implementations in this line of research. Moreover, this tutorial takes a forward-looking approach by delving into recent strides in quantum internet technologies and the nonlocality theory. We aim to shed light on the uncharted territory of future data systems tailored for the quantum internet.

Compiling a quantum circuit for specific quantum hardware is a challenging task. Moreover, current quantum computers have severe hardware limitations. To make the most use of the limited resources, the compilation process should be optimized. To improve currents methods, Reinforcement Learning (RL), a technique in which an agent interacts with an environment to learn complex policies to attain a specific goal, can be used. In this work, we present qgym, a software framework derived from the OpenAI gym, together with environments that are specifically tailored towards quantum compilation. The goal of qgym is to connect the research fields of Artificial Intelligence (AI) with quantum compilation by abstracting parts of the process that are irrelevant to either domain. It can be used to train and benchmark RL agents and algorithms in highly customizable environments.