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A longstanding computational challenge is the accurate simulation of many-body particle systems. Especially for deriving key characteristics of high-impact but complex systems such as battery materials and high entropy alloys (HEA). While simple models allow for simulations of the required scale, these methods often fail to capture the complex dynamics that determine the characteristics. A long-theorized approach is to use quantum computers for this purpose, which allows for a more efficient encoding of quantum mechanical systems. In recent years, the field of quantum computing has become significantly more mature. Furthermore, the rise in integration of machine learning with quantum computing further pushes to a near-term advantage. In this work we aim to improve the well-established quantum computing method for calculating the inter-atomic potential, the variational quantum eigensolver, by presenting an auto-encoded VQE with neural-network predictions: NN-AE-VQE. We apply a quantum autoencoder for a compressed quantum state representation of the atomic system, to which a naive circuit ansatz is applied. This reduces the number of circuit parameters to optimize, while still minimal reduction in accuracy. Additionally, we train a classical neural network to predict the circuit parameters to avoid computationally expensive parameter optimization. We demonstrate these methods on a $H_2$ molecule, achieving chemical accuracy. We believe this method shows promise of efficiently capturing highly accurate systems while omitting current bottlenecks of variational quantum algorithms. Finally, we explore options for exploiting the algorithm structure and further algorithm improvements.

We, the QAIMS lab lab at the Aerospace Faculty of TU Delft, participated as finalists in the Airbus/BMW Quantum Computing Challenge 2024. Stacking sequence retrieval, a complex combinatorial task within a bi-level optimization framework, is crucial for designing laminated composites that meet aerospace requirements for weight, strength, and stiffness. This document presents the scientifically relevant sections of our submission, which builds on our prior research on applying quantum computation to this challenging design problem. For the competition, we expanded our previous work in several significant ways. First, we incorporated a full set of manufacturing constraints into our algorithmic framework, including those previously established theoretically but not yet demonstrated, thereby aligning our approach more closely with real-world manufacturing demands. We implemented the F-VQE algorithm, which enhances the probability shaping of optimal solutions, improving on simpler variational quantum algorithms. Our approach also demonstrates flexibility by accommodating diverse objectives as well as finer ply-angle increments alongside the previously demonstrated conventional ply angles. Scalability was tested using the DMRG algorithm, which, despite limitations in entanglement representation, enabled simulations with up to 200 plies. Results were directly compared to conventional stacking sequence retrieval algorithms with DMRG showing high competitiveness. Given DMRG's limited entanglement capabilities, it serves as a conservative baseline, suggesting potential for even greater performance on fully realized quantum systems. This document serves to make our competition results publicly available as we prepare a formal publication on these findings and their implications for aerospace materials design optimization., Comment: Scientifically relevant sections of a submission to 2024 Airbus/BMW Quantum Computing Challenge. 26 pages, 10 figures, 3 tables

QAOA is a quantum algorithm for solving combinatorial optimization problems. It is capable of searching for the minimizing solution vector $x$ of a QUBO problem $x^TQx$. The number of two-qubit CNOT gates in the QAOA circuit scales linearly in the number of non-zero couplings of $Q$ and the depth of the circuit scales accordingly. Since CNOT operations have high error rates it is crucial to develop algorithms for reducing their number. We, therefore, present the concept of \textit{semi-symmetries} in QUBO matrices and an algorithm for identifying and factoring them out into ancilla qubits. \textit{Semi-symmetries} are prevalent in QUBO matrices of many well-known optimization problems like \textit{Maximum Clique}, \textit{Hamilton Cycles}, \textit{Graph Coloring}, \textit{Vertex Cover} and \textit{Graph Isomorphism}, among others. We theoretically show that our modified QUBO matrix $Q_{mod}$ describes the same energy spectrum as the original $Q$. Experiments conducted on the five optimization problems mentioned above demonstrate that our algorithm achieved reductions in the number of couplings by up to $49\%$ and in circuit depth by up to $41\%$.

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. We empirically demonstrate the Pareto optimality 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. We find 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, we illustrate the correlation between the Bloch sphere path length and the energetic cost., Comment: 19 pages, 11 figures

Quantum error correction (QEC) is a crucial prerequisite for future large-scale quantum computation. Finding and analyzing new QEC codes, along with efficient decoding and fault-tolerance protocols, is central to this effort. Holographic codes are a recent class of QEC subsystem codes derived from holographic bulk/boundary dualities. In addition to exploring the physics of such dualities, these codes possess useful QEC properties such as tunable encoding rates, distance scaling competitive with topological codes, and excellent recovery thresholds. To allow for a comprehensive analysis of holographic code constructions, we introduce LEGO_HQEC, a software package utilizing the quantum LEGO formalism. This package constructs holographic codes on regular hyperbolic tilings and generates their stabilizer generators and logical operators for a specified number of seed codes and layers. Three decoders are included: an erasure decoder based on Gaussian elimination; an integer-optimization decoder; and a tensor-network decoder. With these tools, LEGO_HQEC thus enables future systematic studies regarding the utility of holographic codes for practical quantum computing.

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 x 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)x(n+m)-dimensional QUBO representations of MAX-3SAT instances is ineffective.

Several recent techniques for modifying topological codes with single-qubit Clifford operators have shown high resilience against pure Pauli noise. Paramount to these findings has been the demonstration that several variants exhibit error thresholds often attaining or exceeding the zero-rate hashing bound, a known benchmark for code-capacity noise channels, for biased noise. Additionally, direct comparison with the hashing bound has shown that several topological codes outperform the hashing bound at points of finite Pauli noise biases. Motivated by these observations, we study zero-rate holographic quantum error correction codes, discovering very high threshold values under diverse and finitely-biased noise channels using a tensor-network decoding approach. Our results establish that all codes tested achieve or surpass the hashing bound at various points, ranging from pure 2-Pauli noise ($\eta = 0$) to pure 1-Pauli noise ($\eta = +\infty$), thereby demonstrating that holographic codes exhibit excellent error tolerance in the code-capacity picture. Such findings imply the existence of a structured and systematic method for constructing high-threshold codes suitable for realistically motivated noise channels. To our knowledge, this work is also the first instance of such remarkable threshold behavior in stabilizer quantum codes for the pure 2-Pauli noise regime, as well as for finitely-biased noise channels., Comment: 8 pages, 5 figures, 2 tables

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 and universal architectural features that provide optimal performance across the examined circuits. Our work demonstrates that the synergy between DSE methodologies and optimization algorithms can effectively be deployed to provide useful suggestions to quantum processor designers., Comment: 21 pages, 4 figures, 6 tables

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 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 gate dependency graphs, 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.

We introduce a new class of qubit codes that we call Evenbly codes, building on a previous proposal of hyperinvariant tensor networks. Its tensor network description consists of local, non-perfect tensors describing CSS codes interspersed with Hadamard gates, placed on a hyperbolic $\{p,q\}$ geometry with even $q\geq 4$, yielding an infinitely large class of subsystem codes. We construct an example for a $\{5,4\}$ manifold and describe strategies of logical gauge fixing that lead to different rates $k/n$ and distances $d$, which we calculate analytically, finding distances which range from $d=2$ to $d \sim n^{2/3}$ in the ungauged case. Investigating threshold performance under erasure, depolarizing, and pure Pauli noise channels, we find that the code exhibits a depolarizing noise threshold of about $19.1\%$ in the code-capacity model and $50\%$ for pure Pauli and erasure channels under suitable gauges. We also test a constant-rate version with $k/n = 0.125$, finding excellent error resilience (about $40\%$) under the erasure channel. Recovery rates for these and other settings are studied both under an optimal decoder as well as a more efficient but non-optimal greedy decoder. We also consider generalizations beyond the CSS tensor construction, compute error rates and thresholds for other hyperbolic geometries, and discuss the relationship to holographic bulk/boundary dualities. Our work indicates that Evenbly codes may show promise for practical quantum computing applications., Comment: 22 pages, 13 figures

In the standard circuit model of quantum computation, the number and quality of the quantum gates composing the circuit influence the runtime and fidelity of the computation. The fidelity of the decomposition of quantum algorithms, represented as unitary matrices, to bounded depth quantum circuits depends strongly on the set of gates available for the decomposition routine. To investigate this dependence, we explore the design space of discrete quantum gate sets and present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The evaluation is conditioned on a set of unitary transformations representing target use cases on the quantum processors. The cost function considers three key factors: (i) the statistical distribution of the decomposed circuits' depth, (ii) the statistical distribution of process fidelities for the approximate decomposition, and (iii) the relative novelty of a gate set compared to other gate sets in terms of the aforementioned properties. The developed software, YAQQ (Yet Another Quantum Quantizer), enables the discovery of an optimized set of quantum gates through this tunable joint cost function. To identify these gate sets, we use the novelty search algorithm, circuit decomposition techniques, and stochastic optimization to implement YAQQ within the Qiskit quantum simulator environment. YAQQ exploits reachability tradeoffs conceptually derived from quantum algorithmic information theory. Our results demonstrate the pragmatic application of identifying gate sets that are advantageous to popularly used quantum gate sets in representing quantum algorithms. Consequently, we demonstrate pragmatic use cases of YAQQ in comparing transversal logical gate sets in quantum error correction codes, designing optimal quantum instruction sets, and compiling to specific quantum processors.

A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO, which in itself is a potentially difficult and expensive task. State-of-the-art transformations from MAX-3SAT to QUBO currently 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, therefore, algorithmically inefficient, we see potential for including search-based optimization. In this paper, we propose two methods of using evolutionary algorithms to automatically create QUBO representations of MAX-3SAT problems. 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.

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 $3$ gates on a $1$ qubit system 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., Comment: 14 pages

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 of qubits, their scalability remains a significant challenge. Modular quantum computing architectures have emerged as a promising approach to scale up quantum computing systems. This paper 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 $4.9\times$ and $1.6\times$ 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., Comment: Accepted to ACM Transaction in Quantum Computing

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 $1,000$ qubits, showing an average improvement of up to $80\%$ in gate overhead and $54\%$ in depth overhead, and up to $8.33$ times faster routing times.

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., Comment: Accepted at the 40th IEEE International Conference on Data Engineering (ICDE 2024)

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.

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. To adapt this problem 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 state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval., Comment: 44 pages, 6 figures. Accompanying code repository: https://github.com/ArneWulff/ssr-with-qc-and-tn . Accompanying data repository: https://doi.org/10.4121/ae276609-55b0-4af1-88c0-1102b1b58990 . Changes: Minor revision

Efficiently mapping quantum circuits onto hardware is an integral part of the quantum compilation process, wherein a circuit is modified in accordance with the stringent architectural demands of a quantum processor. Many techniques exist for solving the quantum circuit mapping problem, in addition to several theoretical perspectives that relate quantum circuit mapping to problems in classical computer science. This work considers a novel perspective on quantum circuit mapping, in which the routing process of a simplified circuit is viewed as a composition of quantum operations acting on density matrices representing the quantum circuit and processor. Drawing on insight from recent advances in quantum circuit complexity and information geometry, we show that a minimal SWAP-gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states using the quantum Jensen-Shannon divergence, which we dub the lightcone bound. Additionally, we develop a novel initial placement algorithm based on a graph similarity search that selects the partition nearest to a graph isomorphism between interaction and coupling graphs. From these two ingredients, we construct an algorithm for calculating the lightcone bound, which is directly compared alongside the IBM Qiskit compiler for over $600$ realistic benchmark experiments, as well as against a brute-force method for smaller benchmarks. In our simulations, we unambiguously find that neither the brute-force method nor the Qiskit compiler surpasses our bound, signaling utility for estimating minimal overhead when realizing quantum algorithms on constrained quantum hardware. This work also constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing. We anticipate that this method may have diverse applicability outside of the scope of quantum information science.

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., Comment: 11 pages, 4 figures, accepted for publication at the 2024 IEEE International Conference on Quantum Computing and Engineering (QCE)

Modular quantum processor architectures are envisioned as a promising solution for the scalability of quantum computing systems beyond the Noisy Intermediate Scale Quantum (NISQ) devices era. Based upon interconnecting tens to hundreds of quantum cores via a quantum intranet, this approach unravels the pressing limitations of densely qubit-packed monolithic processors, mainly by mitigating the requirements of qubit control and enhancing qubit isolation, and therefore enables executing large-scale algorithms on quantum computers. In order to optimize such architectures, it is crucial to analyze the quantum state transfers occurring via inter-core communication networks, referred to as inter-core qubit traffic. This would also provide insights to improve the software and hardware stack for multi-core quantum computers. To this aim, we present a pioneering characterization of the spatio-temporal inter-core qubit traffic in large-scale circuits. The programs are executed on an all-to-all connected multi-core architecture that supports up to around 1000 qubits. We characterize the qubit traffic based on multiple performance metrics to assess the computational process and the communication overhead. Based on the showcased results, we conclude on the scalability of the presented algorithms, provide a set of guidelines to improve mapping quantum circuits to multi-core processors, and lay the foundations of benchmarking large-scale multi-core architectures., Comment: 34 pages, 9 figures

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.

Many promising applications of quantum computing with a provable speedup center around the HHL algorithm. Due to restrictions on the hardware and its significant demand on qubits and gates in known implementations, its execution is prohibitive on near-term quantum computers. Aiming to facilitate such NISQ-implementations, we propose a novel circuit approximation technique that enhances the arithmetic subroutines in the HHL, which resemble a particularly resource-demanding component in small-scale settings. For this, we provide a description of the algorithmic implementation of space-efficient rotations of polynomial functions that do not demand explicit arithmetic calculations inside the quantum circuit. We show how these types of circuits can be reduced in depth by providing a simple and powerful approximation technique. Moreover, we provide an algorithm that converts lookup-tables for arbitrary function rotations into a structure that allows an application of the approximation technique. This allows implementing approximate rotation circuits for many polynomial and non-polynomial functions. Experimental results obtained for realistic early-application dimensions show significant improvements compared to the state-of-the-art, yielding small circuits while achieving good approximations.

The simulation of many industrially relevant physical processes can be executed up to exponentially faster using quantum algorithms. However, this speedup can only be leveraged if the data input and output of the simulation can be implemented efficiently. While we show that recent advancements for optimal state preparation can effectively solve the problem of data input at a moderate cost of ancillary qubits in many cases, the output problem can provably not be solved efficiently in general. By acknowledging that many simulation problems arise only as a subproblem of a larger optimization problem in many practical applications however, we identify and define a class of practically relevant problems that does not suffer from the output problem: Quantum Simulation-based Optimization (QuSO). QuSO represents optimization problems whose objective function and/or constraints depend on summary statistic information on the result of a simulation, i.e., information that can be efficiently extracted from a quantum state vector. In this article, we focus on the LinQuSO subclass of QuSO, which is characterized by the linearity of the simulation problem, i.e., the simulation problem can be formulated as a system of linear equations. By cleverly combining the quantum singular value transformation (QSVT) with the quantum approximate optimization algorithm (QAOA), we prove that a large subgroup of LinQuSO problems can be solved with up to exponential quantum speedups with regards to their simulation component. Finally, we present two practically relevant use cases that fall within this subgroup of QuSO problems., Comment: 24 pages, 12 figure, completely refactored and formalized version with key new isights

Modular quantum computing architectures are a promising alternative to monolithic QPU (Quantum Processing Unit) designs for scaling up quantum devices. They refer to a set of interconnected QPUs or cores consisting of tightly coupled quantum bits that can communicate via quantum-coherent and classical links. In multi-core architectures, it is crucial to minimize the amount of communication between cores when executing an algorithm. Therefore, mapping a quantum circuit onto a modular architecture involves finding an optimal assignment of logical qubits (qubits in the quantum circuit) to different cores with the aim to minimize the number of expensive inter-core operations while adhering to given hardware constraints. In this paper, we propose for the first time a Quadratic Unconstrained Binary Optimization (QUBO) technique to encode the problem and the solution for both qubit allocation and inter-core communication costs in binary decision variables. To this end, the quantum circuit is split into slices, and qubit assignment is formulated as a graph partitioning problem for each circuit slice. The costly inter-core communication is reduced by penalizing inter-core qubit communications. The final solution is obtained by minimizing the overall cost across all circuit slices. To evaluate the effectiveness of our approach, we conduct a detailed analysis using a representative set of benchmarks having a high number of qubits on two different multi-core architectures. Our method showed promising results and performed exceptionally well with very dense and highly-parallelized circuits that require on average 0.78 inter-core communications per two-qubit gate., Comment: Submitted to IEEE QCE 2023

3SAT instances need to be transformed into instances of Quadratic Unconstrained Binary Optimization (QUBO) to be solved on a quantum annealer. Although it has been shown that the choice of the 3SAT-to-QUBO transformation can impact the solution quality of quantum annealing significantly, currently only a few 3SAT-to-QUBO transformations are known. Additionally, all of the known 3SAT-to-QUBO transformations were created manually (and not procedurally) by an expert using reasoning, which is a rather slow and limiting process. In this paper, we will introduce the name Pattern QUBO for a concept that has been used implicitly in the construction of 3SAT-to-QUBO transformations before. We will provide an in-depth explanation for the idea behind Pattern QUBOs and show its importance by proposing an algorithmic method that uses Pattern QUBOs to create new 3SAT-to-QUBO transformations automatically. As an additional application of Pattern QUBOs and our proposed algorithmic method, we introduce approximate 3SAT-to-QUBO transformations. These transformations sacrifice optimality but use significantly fewer variables (and thus physical qubits on quantum hardware) than non-approximate 3SAT-to-QUBO transformations. We will show that approximate 3SAT-to-QUBO transformations can nevertheless be very effective in some cases.

To solve 3SAT instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3SAT problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.

Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit overhead, which is typically much smaller than in other approaches. However, as in most fault-tolerance protocols, the advantages of flag-style error correction come with a tradeoff: fault tolerance can be guaranteed, but such protocols involve high-depth circuits, due to the need for repeated stabilizer measurements. Here, we demonstrate that a dynamic choice of stabilizer measurements, based on past syndromes, and the utilization of elements from the full stabilizer group, leads to flag protocols with lower-depth syndrome-extraction circuits for the [[5,1,3]] code, as well as for the Steane code when compared to the standard methods in flag fault tolerance. We methodically prove that our new protocols yield fault-tolerant lookup tables, and demonstrate them with a pseudothreshold simulation, showcasing large improvements for all protocols when compared to previously-established methods. This work opens the dialogue on exploiting the properties of the full stabilizer group for reducing circuit overhead in fault-tolerant quantum-error correction., Comment: submitted to IEEE International Conference on Quantum Computing and Engineering (QCE23)

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections., Comment: 10 pages, 7 figures

Current monolithic quantum computer architectures have limited scalability. One promising approach for scaling them up is to use a modular or multi-core architecture, in which different quantum processors (cores) are connected via quantum and classical links. This new architectural design poses new challenges such as the expensive inter-core communication. To reduce these movements when executing a quantum algorithm, an efficient mapping technique is required. In this paper, a detailed critical discussion of the quantum circuit mapping problem for multi-core quantum computing architectures is provided. In addition, we further explore the performance of a mapping method, which is formulated as a partitioning over time graph problem, by performing an architectural scalability analysis.

We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach requires fewer couplings and fewer physical qubits than the current state-of-the-art, which results in higher solution quality. We verified the practical applicability of the approach by testing it on a D-Wave quantum annealer.

We have implemented a gated-based quantum version of a restricted Boltzmann machine for approximating the ground state of a Pauli-decomposed qubit Hamiltonian. During the implementation and evaluation, we have noticed a variety of unexpected topics. It starts from limitations due to the structure of the algorithm itself and continues with constraints induced by specific quantum software development kits, which did not (yet) support necessary features for an efficient implementation. In this paper we systematically summarize our findings and categorize them according to their relevance for the implementation of similar quantum algorithms. We also discuss the feasibility of executing such implementations on current NISQ devices., Comment: 6 pages

Despite NISQ devices being severely constrained, hardware- and algorithm-aware quantum circuit mapping techniques have been developed to enable successful algorithm executions. Not so much attention has been paid to mapping and compilation implementations for spin-qubit quantum processors due to the scarce availability of experimental devices and their small sizes. However, based on their high scalability potential and their rapid progress it is timely to start exploring solutions on such devices. In this work, we discuss the unique mapping challenges of a scalable crossbar architecture with shared control and introduce SpinQ, the first native compilation framework for scalable spin-qubit architectures. At the core of SpinQ is the Integrated Strategy that addresses the unique operational constraints of the crossbar while considering compilation scalability and obtaining a O(n) computational complexity. To evaluate the performance of SpinQ on this novel architecture, we compiled a broad set of well-defined quantum circuits and performed an in-depth analysis based on multiple metrics such as gate overhead, depth overhead, and estimated success probability, which in turn allowed us to create unique mapping and architectural insights. Finally, we propose novel mapping techniques that could increase algorithm success rates on this architecture and potentially inspire further research on quantum circuit mapping for other scalable spin-qubit architectures., Comment: 18 pages, 16 figures

The analysis of network structure is essential to many scientific areas, ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO based approach that only needs number-of-nodes many qubits and is represented by a QUBO-matrix as sparse as the input graph's adjacency matrix. The substantial improvement on the sparsity of the QUBO-matrix, which is typically very dense in related work, is achieved through the novel concept of separation-nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which -- upon its removal from the graph -- yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept. This work hence displays a promising approach to NISQ ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large scale, real world problem instances.

To execute quantum circuits on a quantum processor, they must be modified to meet the physical constraints of the quantum device. This process, called quantum circuit mapping, results in a gate/circuit depth overhead that depends on both the circuit properties and the hardware constraints, being the limited qubit connectivity a crucial restriction. In this paper, we propose to extend the characterization of quantum circuits by including qubit interaction graph properties using graph theory-based metrics in addition to previously used circuit-describing parameters. This approach allows for in-depth analysis and clustering of quantum circuits and a comparison of performance when run on different quantum processors, aiding in developing better mapping techniques. Our study reveals a correlation between interaction graph-based parameters and mapping performance metrics for various existing configurations of quantum devices. We also provide a comprehensive collection of quantum circuits and algorithms for benchmarking future compilation techniques and quantum devices.

Quantum many-core processors are envisioned as the ultimate solution for the scalability of quantum computers. Based upon Noisy Intermediate-Scale Quantum (NISQ) chips interconnected in a sort of quantum intranet, they enable large algorithms to be executed on current and close future technology. In order to optimize such architectures, it is crucial to develop tools that allow specific design space explorations. To this aim, in this paper we present a technique to perform a spatio-temporal characterization of quantum circuits running in multi-chip quantum computers. Specifically, we focus on the analysis of the qubit traffic resulting from operations that involve qubits residing in different cores, and hence quantum communication across chips, while also giving importance to the amount of intra-core operations that occur in between those communications. Using specific multi-core performance metrics and a complete set of benchmarks, our analysis showcases the opportunities that the proposed approach may provide to guide the design of multi-core quantum computers and their interconnects., Comment: 7 pages, to be presented at the ACM NanoCom 2022

Black-box optimization (BBO) can be used to optimize functions whose analytic form is unknown. A common approach to realising BBO is to learn a surrogate model which approximates the target black-box function which can then be solved via white-box optimization methods. In this paper, we present our approach BOX-QUBO, where the surrogate model is a QUBO matrix. However, unlike in previous state-of-the-art approaches, this matrix is not trained entirely by regression, but mostly by classification between 'good' and 'bad' solutions. This better accounts for the low capacity of the QUBO matrix, resulting in significantly better solutions overall. We tested our approach against the state-of-the-art on four domains and in all of them BOX-QUBO showed better results. A second contribution of this paper is the idea to also solve white-box problems, i.e. problems which could be directly formulated as QUBO, by means of black-box optimization in order to reduce the size of the QUBOs to the information-theoretic minimum. Experiments show that this significantly improves the results for MAX-k-SAT.

Quadratic unconstrained binary optimization (QUBO) can be seen as a generic language for optimization problems. QUBOs attract particular attention since they can be solved with quantum hardware, like quantum annealers or quantum gate computers running QAOA. In this paper, we present two novel QUBO formulations for $k$-SAT and Hamiltonian Cycles that scale significantly better than existing approaches. For $k$-SAT we reduce the growth of the QUBO matrix from $O(k)$ to $O(log(k))$. For Hamiltonian Cycles the matrix no longer grows quadratically in the number of nodes, as currently, but linearly in the number of edges and logarithmically in the number of nodes. We present these two formulations not as mathematical expressions, as most QUBO formulations are, but as meta-algorithms that facilitate the design of more complex QUBO formulations and allow easy reuse in larger and more complex QUBO formulations., Comment: Accepted at GECCO 2022

Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a toolkit of methods to transform almost arbitrary problems to QUBO by (i) approximating them as a polynomial and then (ii) translating any polynomial to QUBO. We showcase the usage of our approaches on two example problems (ratio cut and logistic regression).

The progress in developing quantum hardware with functional quantum processors integrating tens of noisy qubits, together with the availability of near-term quantum algorithms has led to the release of the first quantum computers. These quantum computing systems already integrate different software and hardware components of the so-called "full-stack", bridging quantum applications to quantum devices. In this paper, we will provide an overview on current full-stack quantum computing systems. We will emphasize the need for tight co-design among adjacent layers as well as vertical cross-layer design to extract the most from noisy intermediate-scale quantum (NISQ) processors which are both error-prone and severely constrained in resources. As an example of co-design, we will focus on the development of hardware-aware and algorithm-driven compilation techniques., Comment: Design, Automation and Test in Europe Conference (DATE 2022)

The qubit-mapping problem aims to assign and route qubits of a quantum circuit onto a NISQ device in an optimized fashion, with respect to some cost function. Finding an optimal solution to this problem is known to scale exponentially in computational complexity; as such, it is imperative to investigate scalable qubit-mapping solutions for NISQ computation. In this work, a noise-aware heuristic qubit-assignment algorithm (which assigns initial placements for qubits in a quantum algorithm to qubits on a NISQ device, but does not route qubits during the quantum algorithm's execution) is presented and compared against the optimal \textit{brute-force} solution, as well as a trivial qubit assignment, with the aim to quantify the performance of our heuristic qubit-assignment algorithm. We find that for small, connected-graph algorithms, our heuristic-assignment algorithm faithfully lies in between the effective upper and lower bounds given by the brute-force and trivial qubit-assignment algorithms. Additionally, we find that the topological-graph properties of quantum algorithms with over six qubits play an important role in our heuristic qubit-assignment algorithm's performance on NISQ devices. Finally, we investigate the scaling properties of our heuristic algorithm for quantum processors with up to 100 qubits; here, the algorithm was found to be scalable for quantum-algorithms which admit path-like graphs. Our findings show that as the size of the quantum processor in our simulation grows, so do the benefits from utilizing the heuristic qubit-assignment algorithm, under particular constraints for our heuristic algorithm. This work thus characterizes the performance of a heuristic qubit-assignment algorithm with respect to the topological-graph and scaling properties of a quantum algorithm which one may wish to run on a given NISQ device., Comment: Accepted for publication in IEEE Transactions on Quantum Engineering

The efficiency of Quantum Characterisation, Verification, and Validation (QCVV) protocols highly hinges on the agreement between the assumed noise model and the underlying error mechanisms. As a matter of fact, errors in Quantum Processing Units (QPUs) incorporate various aspects of context-dependability which are overlooked by the majority of the commonly used QCVV protocols. As QCVV protocols are indispensable when it comes to characterizing and evaluating quantum operations, there is a serious need for a detailed characterization taking into account such aspects. In this work, we address these shortcomings by designing a context-aware version of the gate set tomography (GST) protocol. Our experiment selection approach is based on a polynomial quantification of the accumulation of errors within the designed circuits. Using simulated QPUs, we show that this technique enables a characterization with an inaccuracy reaching $10^{-5}$. Furthermore, we use our proposed protocol to experimentally infer context-dependent errors, namely crosstalk and memory effects, in a publicly accessible cloud-based superconducting qubits platform. Our results show that when the GST is upgraded to include such features of context-awareness, a large coherence in the errors is observed. These findings open up possibilities of drastically reducing the errors within the currently demonstrated QPUs.

Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively and to avoid obstacles in a forward-looking way. The task of collision avoidance can be divided into a global and a local level. Regarding the global level, we propose an approach called "Predictive Collision Management Path Planning" (PCMP). At the local level, solutions for collision avoidance are used that prevent an inevitable collision. Therefore, the aim of PCMP is to avoid unnecessary local collision scenarios using predictive collision management. PCMP is a graph-based algorithm with a focus on the time dimension consisting of three parts: (1) movement prediction, (2) integration of movement prediction into a time-dependent graph, and (3) time and risk-dependent path planning. The algorithm combines the search for a shortest path with the question: is the detour worth avoiding a possible collision scenario? We evaluate the evasion behavior in different simulation scenarios and the results show that a risk-sensitive agent can avoid 47.3% of the collision scenarios while making a detour of 1.3%. A risk-averse agent avoids up to 97.3% of the collision scenarios with a detour of 39.1%. Thus, an agent's evasive behavior can be controlled actively and risk-dependent using PCMP., Comment: Extended version of the SIGSPATIAL '20 paper

Extracting a Construction Tree from potentially noisy point clouds is an important aspect of Reverse Engineering tasks in Computer Aided Design. Solutions based on algorithmic geometry impose constraints on usable model representations (e.g. quadric surfaces only) and noise robustness. Re-formulating the problem as a combinatorial optimization problem and solving it with an Evolutionary Algorithm can mitigate some of these constraints at the cost of increased computational complexity. This paper proposes a graph-based search space partitioning scheme that is able to accelerate Evolutionary Construction Tree extraction while exploiting parallelization capabilities of modern CPUs. The evaluation indicates a speed-up up to a factor of $46.6$ compared to the baseline approach while resulting tree sizes increased by $25.2\%$ to $88.6\%$., Comment: The 26th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision 2016 in co-operation with EUROGRAPHICS: University of West Bohemia, Plzen, Czech Republic May 28 - June 1 2018, p. 29-37

CSG trees are an intuitive, yet powerful technique for the representation of geometry using a combination of Boolean set-operations and geometric primitives. In general, there exists an infinite number of trees all describing the same 3D solid. However, some trees are optimal regarding the number of used operations, their shape or other attributes, like their suitability for intuitive, human-controlled editing. In this paper, we present a systematic comparison of newly developed and existing tree optimization methods and propose a flexible processing pipeline with a focus on tree editability. The pipeline uses a redundancy removal and decomposition stage for complexity reduction and different (meta-)heuristics for remaining tree optimization. We also introduce a new quantitative measure for CSG tree editability and show how it can be used as a constraint in the optimization process., Comment: The 28th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG) 2020, p. 79-88. Update: Enlarge some of the figures and move some of the figures to the end

We discuss the synergetic connection between quantum computing and artificial intelligence. After surveying current approaches to quantum artificial intelligence and relating them to a formal model for machine learning processes, we deduce four major challenges for the future of quantum artificial intelligence: (i) Replace iterative training with faster quantum algorithms, (ii) distill the experience of larger amounts of data into the training process, (iii) allow quantum and classical components to be easily combined and exchanged, and (iv) build tools to thoroughly analyze whether observed benefits really stem from quantum properties of the algorithm., Comment: 6 pages, 4 figures, accepted at the 1st International Workshop on Quantum Software Engineering (Q-SE 2020) at ICSE 2020 and to be published in the corresponding proceedings

Current hardware limitations restrict the potential when solving quadratic unconstrained binary optimization (QUBO) problems via the quantum approximate optimization algorithm (QAOA) or quantum annealing (QA). Thus, we consider training neural networks in this context. We first discuss QUBO problems that originate from translated instances of the traveling salesman problem (TSP): Analyzing this representation via autoencoders shows that there is way more information included than necessary to solve the original TSP. Then we show that neural networks can be used to solve TSP instances from both QUBO input and autoencoders' hiddenstate representation. We finally generalize the approach and successfully train neural networks to solve arbitrary QUBO problems, sketching means to use neuromorphic hardware as a simulator or an additional co-processor for quantum computing., Comment: 6 pages, 5 figures, accepted at the 1st International Workshop on Quantum Software Engineering (Q-SE 2020) at ICSE 2020 and to be published in the corresponding proceedings