arXiv subjects

James R. Seddon

Publications and source records attributed to James R. Seddon.

6 recordsLinked to original sources

arXiv2026

Optimal and improved gate decompositions for accelerated classical simulation of near-Gaussian fermionic circuits

Fermionic Gaussian circuits can be simulated efficiently on a classical computer, but become universal when supplemented with non-Gaussian operations. Similar to stabilizer circuits augmented with non-stabilizer resources, these non-Gaussian circuits can be simulated classically using rank- or extent-based methods. These methods decompose non-Gaussian states or operations into Gaussian ones, with runtimes that scale polynomially with measures of non-Gaussianity such as the rank and the extent -- quantities that typically grow exponentially with the number of non-Gaussian resources. Current fermionic rank- and extent-based simulators are limited to Gaussian circuits with magic-state injection. Extending them to mixed states and non-unitary channels has been hindered by the lack of known extent-optimized decompositions for physically relevant gates and noisy channels. In this work, we address this gap. First, we derive analytic decompositions for key non-Gaussian gates and channels, including decompositions for arbitrary two-qubit fermionic gates which are provably optimal for diagonal gates or those acting on Jordan-Wigner-adjacent qubit pairs. Second, we show that stochastic Pauli noise can reduce the effective extent of non-Gaussian rotation gates, but that fermionic magic is substantially more robust to such noise than stabilizer magic. Finally, we demonstrate how these decompositions can accelerate classical sampling from the output distribution of a quantum circuit. This involves a generalization of existing sparsification methods, previously limited to convex-unitary channels, to circuits involving intermediate measurements and feed-forward. Our decompositions also yield speedups for emulating noisy Pauli rotations with quasiprobability simulators in the large-angle/arbitrary-strength-noise and small-angle/low-noise parameter regimes.

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arXiv2025

Fermionic dynamics on a trapped-ion quantum computer beyond exact classical simulation

Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and chemical synthesis. However, the performance of all previous digital quantum simulations of fermions has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. Here, we implement an efficient quantum simulation algorithm on Quantinuum's System Model H2 trapped-ion quantum computer for the time dynamics of a 56-qubit system that is too complex for exact classical simulation. We focus on the periodic spinful 2D Fermi-Hubbard model and present evidence of spin-charge separation, where the elementary electron's charge and spin decouple. In the limited cases where ground truth is available through exact classical simulation, we find that it agrees with the results we obtain from the quantum device. Employing long-range Wilson operators to study deconfinement of the effective gauge field between spinons and the effective potential between charge carriers, we find behaviour that differs from predictions made by classical tensor network methods. Our results herald the use of quantum computing for simulating strongly correlated electronic systems beyond the capacity of classical computing.

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arXiv2025

Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits

Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to ${6\times 6}$ using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.

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arXiv2025

Robust Lindbladian Estimation for Quantum Dynamics

We revisit the problem of fitting Lindbladian models to the outputs of quantum process tomography. A sequence of prior theoretical works approached the problem by considering whether there exists a Lindbladian generator close to a matrix logarithm of the tomographically estimated transfer matrix. This technique must take into account the non-uniqueness of the matrix logarithm, so that in general multiple branches of the logarithm must be checked. In contrast, all practical demonstrations of Lindbladian fitting on real experimental data have to our knowledge eschewed logarithm search, instead adopting direct numerical optimisation or ad-hoc approaches tailored to a particular experimental realisation. In our work, we introduce algorithmic improvements to logarithm search, demonstrating that it can be applied in practice to settings relevant for current quantum computing hardware. We additionally augment the task of Lindbladian fitting with techniques from gate set tomography to improve robustness against state preparation and measurement (SPAM) errors, which can otherwise obfuscate estimates of the model underlying the process of interest. We benchmark our techniques extensively using simulated tomographic data employing a range of realistic error models, before demonstrating their application to tomographic data collected from real superconducting-qubit hardware.

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arXiv2021

Quantifying quantum speedups: improved classical simulation from tighter magic monotones

Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm's performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators' performance scaling. Furthermore, our monotones establish several asymptotic and non-asymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence.

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arXiv2019

Quantifying magic for multi-qubit operations

The development of a framework for quantifying "non-stabiliserness" of quantum operations is motivated by the magic state model of fault-tolerant quantum computation, and by the need to estimate classical simulation cost for noisy intermediate-scale quantum (NISQ) devices. The robustness of magic was recently proposed as a well-behaved magic monotone for multi-qubit states and quantifies the simulation overhead of circuits composed of Clifford+T gates, or circuits using other gates from the Clifford hierarchy. Here we present a general theory of the "non-stabiliserness" of quantum operations rather than states, which are useful for classical simulation of more general circuits. We introduce two magic monotones, called channel robustness and magic capacity, which are well-defined for general n-qubit channels and treat all stabiliser-preserving CPTP maps as free operations. We present two complementary Monte Carlo-type classical simulation algorithms with sample complexity given by these quantities and provide examples of channels where the complexity of our algorithms is exponentially better than previous known simulators. We present additional techniques that ease the difficulty of calculating our monotones for special classes of channels.

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