arXiv subjects

Simon Martiel

Publications and source records attributed to Simon Martiel.

At least 19 recordsLinked to original sources

arXiv2026

Sampling hard circuits with verifiably high fidelity

Sampling-based proposals are prominent candidates for demonstrating quantum computations beyond the reach of classical supercomputers. However, it has been difficult to combine their complexity-theoretic hardness with two capabilities needed for scalable quantum computing more generally: suppressing hardware errors, and verifying the quantum computation itself. Here we address both issues by introducing structured circuits, which, in addition to provable hardness guarantees, admit an encoding in a quantum code. This allows us to simultaneously reach high fidelities at high circuit depths, and to certify an experimental fidelity via the circuit structure and measurement of code syndromes. The resulting certificate is device dependent, but requires substantially weaker noise assumptions than existing fidelity proxy benchmarks. We demonstrate our proposal with a $64$-qubit, depth-$73$ Clifford circuit, doped with $314$ $T$ gates. We use a total of $76$ physical qubits to encode this computation in spacetime codes, effectively suppressing gate error rates by $10\times$ after syndrome post-selection, and yielding a state with a fidelity lower bound of $0.349$ with $95\%$ confidence. Our construction is a systematic method for promoting a stabilizer state to a magic state while keeping an error-detected fidelity certificate.

quant-ph↗

arXiv2026

Entanglement from Expansion: High Rank-Width in Deterministic Graphs

Entanglement in quantum graph states is intrinsically linked to rank-width, a graph complexity measure introduced by Oum and Seymour. In this work, we enable the preparation of maximally entangled deterministic graph states in constant depth by developing a general method to derive lower bounds on the rank-width of regular graphs from their edge expansion. By bridging edge-isoperimetric inequalities with the strong chromatic index and Jel\'inek's approach for lower bounding cut-rank, we systematically establish lower bounds for the rank-width of Cartesian products, including hypercubes, Hamming graphs, and grids. Extending this framework via Boolean function analysis, using a generalization of the Kahn-Kalai-Linial's Theorem, we strengthen the bounds for all Cartesian products by a non-trivial logarithmic factor. These methods result in the discovery of deterministic families of graphs on $n$ vertices with a provably maximum rank-width $\Theta(n)$. Our results fill the previous gap in the literature for deterministic graph families of rank-width greater than $\Theta(\sqrt{n})$.

cs.DM↗

arXiv2026

Graphical and algebraic methods for Boolean factoring

The problem of factoring Boolean polynomials has significant applications in both classical and quantum computing technology. In this paper we have developed novel algorithms for factoring both ESOP and SOP expressions. Our aim is to optimize the AND-count. The AND-count plays a key role in determining the number of AND and Toffoli gates required to implement a reversible function with classical and quantum circuits, respectively. The first type of algorithms that we develop, are graphical. We reduce the problem of Boolean factoring to covering a bipartite graph with bicliques, and so optimizing the number of bicliques required to cover the bipartite graph, leads to reduced number of factors, and hence AND-count. The second type of algorithm is algebraic, and is derived from multivariate Horner method. We have compared the performances of our algorithms with existing popular methods like EXORCISM-4 and EPOEM2, on random functions of up to 12 variables. We have observed that our multivariate Horner method is substantially faster, while our biclique-based method achieves the maximum AND-count reduction. In fact, compared to EXORCISM-4 our biclique based method achieves up to 5 times reduction in AND-count.

quant-ph↗

arXiv2026

Observation of Improved Accuracy over Classical Sparse Ground-State Solvers using a Quantum Computer

Demonstrating quantum advantage over classical algorithms for ground state energy problems is an outstanding open problem in quantum computation. We experimentally demonstrate that a quantum algorithm can outperform classical selected configuration interaction (SCI) methods, a key family of techniques used in computational chemistry and condensed matter physics. We construct a class of local Hamiltonian problems with sparse ground states, and show that SCI fails to find the ground state of a 49-qubit instance. We then show that sample-based Krylov quantum diagonalization, run on an IBM Heron R3 processor, succeeds at the same task. While the problem is solvable classically using iterative solvers designed to target our Hamiltonian construction, this work resolves the question of whether a sample-based quantum diagonalization algorithm can outperform standard SCI heuristics.

quant-ph↗

arXiv2025

Big cats: entanglement in 120 qubits and beyond

Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schr\"odinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.

quant-ph↗

arXiv2025

Low-overhead error detection with spacetime codes

We introduce a low-overhead approach for detecting errors in arbitrary Clifford circuits on arbitrary qubit connectivities. Our method is based on the framework of spacetime codes, and is particularly suited to near-term hardware since it has a much milder overhead in qubits and gates compared to error correction, while achieving a better sampling overhead than existing error mitigation methods. We present efficient algorithms for finding valid checks that are simultaneously low weight, satisfy connectivity constraints, and cover large detecting regions within the circuit. Using this approach, we experimentally demonstrate error detection on circuits of up to 50 logical qubits containing 2450 CZ gates, and show physical to logical fidelity gains of up to $236\times$. Furthermore, we show our algorithm can efficiently find checks in universal circuits, but the space of valid checks diminishes exponentially with the non-Cliffordness of the circuit. These theoretical and experimental results suggest that Clifford-dominated circuits are promising candidates for near-term quantum advantage.

quant-ph↗

arXiv2025

Pauli Network Circuit Synthesis with Reinforcement Learning

We introduce a Reinforcement Learning (RL)-based method for re-synthesis of quantum circuits containing arbitrary Pauli rotations alongside Clifford operations. By collapsing each sub-block to a compact representation and then synthesizing it step-by-step through a learned heuristic, we obtain circuits that are both shorter and compliant with hardware connectivity constraints. We find that the method is fast enough and good enough to work as an optimization procedure: in direct comparisons on 6-qubit random Pauli Networks against state-of-the-art heuristic methods, our RL approach yields over 2x reduction in two-qubit gate count, while executing in under 10 milliseconds per circuit. We further integrate the method into a collect-and-re-synthesize pipeline, applied as a Qiskit transpiler pass, where we observe average improvements of 20% in two-qubit gate count and depth, reaching up to 60% for many instances, across the Benchpress benchmark. These results highlight the potential of RL-driven synthesis to significantly improve circuit quality in realistic, large-scale quantum transpilation workloads.

quant-ph↗

arXiv2024

Circuit Depth Reduction for Executable Hamiltonian Dynamics of Covalent Inhibitor Reactivity on Quantum Hardware

Quantum chemistry applications in the noisy intermediate-scale quantum era require end-to-end approaches that balance algorithmic fidelity with practical executability on existing hardware. We present an end-to-end Hamiltonian dynamics case study for predicting the reactivity of pharmaceutically relevant covalent inhibitors containing sulfonyl fluoride warheads, using a quantum-centric data-driven research and development framework that combines Hamiltonian time evolution with classical machine learning. To make such simulations executable on current quantum processors, we introduce a systematic circuit reduction strategy based on Hamiltonian term truncation with observable error bounds, Clifford Decomposition and Transformation, and hardware-aware transpilation. Across representative molecular fragments, this approach achieves circuit depth reductions of up to 28.5x under all-to-all connectivity assumptions and up to 15.5x on IBM Heron-class architectures. For an eight-qubit Hamiltonian dynamics simulation, a transpiled instruction set architecture (ISA) circuit depth of 1330 is rendered executable through middleware-enabled circuit decomposition, enabling the execution of sub-circuits with depths up to 371 and containing up to 216 two-qubit gates on real hardware. We evaluate the impact of circuit reduction on downstream reactivity prediction accuracy and show that chemically meaningful predictions can be retained despite aggressive circuit simplifications, clarifying the trade-offs that govern practical quantum chemistry workflows on near-term quantum systems.

quant-ph↗

arXiv2024

Quantum computing with Qiskit

We describe Qiskit, a software development kit for quantum information science. We discuss the key design decisions that have shaped its development, and examine the software architecture and its core components. We demonstrate an end-to-end workflow for solving a problem in condensed matter physics on a quantum computer that serves to highlight some of Qiskit's capabilities, for example the representation and optimization of circuits at various abstraction levels, its scalability and retargetability to new gates, and the use of quantum-classical computations via dynamic circuits. Lastly, we discuss some of the ecosystem of tools and plugins that extend Qiskit for various tasks, and the future ahead.

quant-ph↗

arXiv2024

Chemistry Beyond the Scale of Exact Diagonalization on a Quantum-Centric Supercomputer

A universal quantum computer can simulate diverse quantum systems, with electronic structure for chemistry offering challenging problems for practical use cases around the hundred-qubit mark. While current quantum processors have reached this size, deep circuits and large number of measurements lead to prohibitive runtimes for quantum computers in isolation. Here, we demonstrate the use of classical distributed computing to offload all but an intrinsically quantum component of a workflow for electronic structure simulations. Using a Heron superconducting processor and the supercomputer Fugaku, we simulate the ground-state dissociation of N$_2$ and the [2Fe-2S] and [4Fe-4S] clusters, with circuits up to 77 qubits and 10,570 gates. The proposed algorithm processes quantum samples to produce upper bounds for the ground-state energy and sparse approximations to the ground-state wavefunctions. Our results suggest that, for current error rates, a quantum-centric supercomputing architecture can tackle challenging chemistry problems beyond sizes amenable to exact diagonalization.

quant-ph↗

arXiv2024

Faster and shorter synthesis of Hamiltonian simulation circuits

We devise greedy heuristics tailored for synthesizing quantum circuits that implement a specified set of Pauli rotations. Our heuristics are designed to minimize either the count of entangling gates or the depth of entangling gates, and they can be adjusted to either maintain or loosen the ordering of rotations. We present benchmark results demonstrating a depth reduction of up to a factor of 4 compared to the current state-of-the-art heuristics for synthesizing Hamiltonian simulation circuits. We also show that these heuristics can be used to optimize generic quantum circuits by decomposing and resynthesizing them.

quant-ph↗

arXiv2024

Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences

The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of fault-tolerant quantum computing it is then crucial to minimize the number of $T$ gates. Many algorithms, yielding effective results, have been designed to address this problem. It has been demonstrated that performing a pre-processing step consisting of reducing the number of Hadamard gates in the circuit can help to exploit the full potential of these algorithms and thereby lead to a substantial $T$-count reduction. Moreover, minimizing the number of Hadamard gates also restrains the number of additional qubits and operations resulting from the gadgetization of Hadamard gates, a procedure used by some compilers to further reduce the number of $T$ gates. In this work we tackle the Hadamard gate reduction problem, and propose an algorithm for synthesizing a sequence of $π/4$ Pauli rotations with a minimal number of Hadamard gates. Based on this result, we present an algorithm which optimally minimizes the number of Hadamard gates lying between the first and the last $T$ gate of the circuit.

quant-ph↗

arXiv2023

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

quant-ph↗

arXiv2023

Anti-crossings occurrence as exponentially closing gaps in Quantum Annealing

This paper explores the phenomenon of avoided level crossings in quantum annealing, a promising framework for quantum computing that may provide a quantum advantage for certain tasks. Quantum annealing involves letting a quantum system evolve according to the Schrödinger equation, with the goal of obtaining the optimal solution to an optimization problem through measurements of the final state. However, the continuous nature of quantum annealing makes analytical analysis challenging, particularly with regard to the instantaneous eigenenergies. The adiabatic theorem provides a theoretical result for the annealing time required to obtain the optimal solution with high probability, which is inversely proportional to the square of the minimum spectral gap. Avoided level crossings can create exponentially closing gaps, which can lead to exponentially long running times for optimization problems. In this paper, we use a perturbative expansion to derive a condition for the occurrence of an avoided level crossing during the annealing process. We then apply this condition to the MaxCut problem on bipartite graphs. We show that no exponentially small gaps arise for regular bipartite graphs, implying that QA can efficiently solve MaxCut in that case. On the other hand, we show that irregularities in the vertex degrees can lead to the satisfaction of the avoided level crossing occurrence condition. We provide numerical evidence to support this theoretical development, and discuss the relation between the presence of exponentially closing gaps and the failure of quantum annealing.

quant-ph↗

arXiv2023

Tight Lieb-Robinson Bound for approximation ratio in Quantum Annealing

Quantum annealing (QA) holds promise for optimization problems in quantum computing, especially for combinatorial optimization. This analog framework attracts attention for its potential to address complex problems. Its gate-based homologous, QAOA with proven performance, has brought lots of attention to the NISQ era. Several numerical benchmarks try to classify these two metaheuristics however, classical computational power highly limits the performance insights. In this work, we introduce a new parametrized version of QA enabling a precise 1-local analysis of the algorithm. We develop a tight Lieb-Robinson bound for regular graphs, achieving the best-known numerical value to analyze QA locally. Studying MaxCut over cubic graph as a benchmark optimization problem, we show that a linear-schedule QA with a 1-local analysis achieves an approximation ratio over 0.7020, outperforming any known 1-local algorithms.

quant-ph↗

arXiv2023

Speeding up quantum circuits simulation using ZX-Calculus

We present a simple and efficient way to reduce the contraction cost of a tensor network to simulate a quantum circuit. We start by interpreting the circuit as a ZX-diagram. We then use simplification and local complementation rules to sparsify it. We find that optimizing graph-like ZX-diagrams improves existing state of the art contraction cost by several order of magnitude. In particular, we demonstrate an average contraction cost 1180 times better for Sycamore circuits of depth 20, and up to 4200 times better at peak performance.

quant-ph↗

arXiv2023

Shallower CNOT circuits on realistic quantum hardware

We focus on the depth optimization of CNOT circuits on hardwares with limited connectivity. We adapt the algorithm from Kutin et al. that implements any $n$-qubit CNOT circuit in depth at most $5n$ on a Linear Nearest Neighbour (LNN) architecture. Our proposal is a block version of Kutin et al.'s algorithm that is scalable with the number of interactions available in the hardware: the more interactions we have the less the depth. We derive better theoretical upper bounds and we provide a simple implementation of the algorithm. Overall, we achieve better depth complexity for CNOT circuits on some realistic quantum hardware like a grid or a ladder. For instance the execution of a $n$-qubit CNOT circuit on a grid can be done in depth $4n$.

quant-ph↗

arXiv2022

A graph-state based synthesis framework for Clifford isometries

We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford group and one equation of the symplectic group. We highlight the versatility of our framework by showing that several normal forms of the literature are natural corollaries. We recover the state of the art two-qubit gate depth necessary for the execution of a Clifford circuit on an LNN architecture, concomitantly with another work. We also propose practical synthesis algorithms for Clifford isometries with a focus on Clifford operators, graph states and codiagonalization of Pauli rotations. Benchmarks show that in all three cases we improve the 2-qubit gate count and depth of random instances compared to the state-of-the-art methods. We also improve the execution of practical quantum chemistry experiments.

quant-ph↗