The standard model of quantum computation is based on quantum circuits, where 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, called yet another quantum quantizer (YAQQ), 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 (like Solovay–Kitaev, Cartan, and quantum Shannon decomposition), 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 for YAQQ, including comparing transversal logical gate sets in quantum error correction codes and designing optimal quantum instruction sets for a benchmark suite of quantum algorithms.

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 ≥ 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 ∼ n²/³. 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.

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.

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.

Traditional methods for handling (inequality) constraints in the quantum approximate optimization algorithm (QAOA) typically rely on penalty terms and slack variables, which increase problem complexity and expand the search space. More sophisticated mixer-based QAOA variants restrict the search within the feasible assignments but often suffer from prohibitive circuit complexity. This paper presents a penalty-free formalism for incorporating inequality constraints into the cost function of QAOA using an oracle-based subroutine that evaluates constraint satisfaction in an additional register, subsequently called indicator function QAOA (IF-QAOA). Applied to the knapsack problem, we demonstrate in numerical simulations the superior performance of IF-QAOA over conventional penalty-based approaches. Using advanced QAOA simulation techniques, we find that IF-QAOA achieves significantly higher solution quality and a faster time to solution in 82% of our benchmark cases, even though circuit depth is approximately three times larger. Analysis of the scaling behavior shows favorable scaling of IF-QAOA compared to penalty-based methods. Also, benchmarks against the recently developed quantum tree generator QAOA for knapsack problems (P. Christiansen et al., arXiv:2411.00518) demonstrated higher solution quality for circuits of similar depth. Additionally, this paper introduces a method for approximating the indicator function when the number of ancillary qubits is limited or the constraint function is noninteger. With a specialized simulation algorithm based on projective measurements, we empirically demonstrate that this formalism can encode general inequality constraints using a fixed number of ancillary qubits.

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.

Advances in quantum algorithms as well as in control hardware designs are continuously being made. These quantum algorithms, expressed as quantum circuits, need to be translated to a set of instructions from a defined quantum instruction-set architecture (ISA), which are executed by the control hardware. These translations can be done by a compiler, targeting different qubit technologies. Specifically for diamond NV centers, no compiler exists to perform this translation. Therefore, in this paper we present a compiler designed for quantum computers utilizing diamond NV center specific instructions, such as direct carbon control and partial swaps, to reduce execution times and gate count. Additionally, our compiler adds on top of general compilers by allowing classical instructions to perform state tomography and measurement-based operations. The output of the compiler is tested in a diamond NV center specific simulator. Comparing a general compiler output with the diamond NV center specific output of our compiler while applying decoherence and depolarization noise showed reduced noise effects due to diamond specific decomposition. The compiler was also tested to perform state tomography and measurement-based operations, which showed to be functional. Our results show that we have successfully created a compiler with integrated classical and quantum instructions support, which can improve circuit execution fidelity by utilizing diamond specific optimizations.

Design space exploration (DSE) plays an important role in optimising quantum circuit execution by systematically evaluating different configurations of compilation strategies and hardware settings. In this paper, we conduct a comprehensive investigation into the impact of various layout methods, qubit routing techniques, and optimisation levels, as well as device-specific properties such as different variants and strengths of noise and imperfections, the topological structure of qubits, connectivity densities, and back-end sizes. By spanning through these dimensions, we aim to understand the interplay between compilation choices and hardware characteristics. A key question driving our exploration is whether the optimal selection of device parameters, mapping techniques, comprising of initial layout strategies and routing heuristics can mitigate device induced errors beyond standard error mitigation approaches. Our results show that carefully selecting software strategies (e.g., mapping and routing algorithms) and tailoring hardware characteristics (such as minimising noise and leveraging topology and connectivity density) significantly improve the fidelity of circuit execution outcomes, and thus the expected correctness or success probability of the computational result. We provide estimates based on key metrics such as circuit depth, gate count and expected fidelity. Our results highlight the importance of hardware–software co-design, particularly as quantum systems scale to larger dimensions, and along the way towards fully error corrected quantum systems: Our study is based on computationally noisy simulations, but considers various implementations of quantum error correction (QEC) using the same approach as for other algorithms. The observed sensitivity of circuit fidelity to noise and connectivity suggests that co-design principles will be equally critical when integrating QEC in future systems. Our exploration provides practical guidelines for co-optimising physical mapping, qubit routing, and hardware configurations in realistic quantum computing scenarios.

Quantum computers require large-scale error correction codes to circumvent the limited fidelity of physical qubits. However, current error decoders are either not scalable to practical code sizes or cannot meet the strict real-time decoding requirements. This work presents a novel decoder for stabilizer error correction codes that exploits hyperdimensional computing to offer an efficient hardware implementation for large-scale codes, thus achieving low latency and high throughput. Next to a universal approach for generating the necessary hypervectors, an efficient method specific to surface codes is devised. In this very first implementation, the proposed decoder outclasses popular graph-based decoders for small surface codes with depolarizing noise and efficiently scales to large codes, thus representing both a suitable solution for near-term real-time error correction and a promising alternative for future large-scale codes.

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.

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.

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.

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.