arXiv subjects

Rick P. A. Simon

Publications and source records attributed to Rick P. A. Simon.

7 recordsLinked to original sources

arXiv2026

Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators

Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. A promising avenue is multi-copy schemes, where identical copies of a quantum state are measured jointly so that all Pauli operators within the considered observable can be simultaneously assessed. Here, we present a first implementation of such a two-copy scheme in a measurement protocol. Based on Bayesian statistics, it accurately estimates not only the average of the desired observable but also the error en route. This enables an adaptive shot-allocation algorithm that preferentially samples the most uncertain Pauli terms. In regimes with many non-commuting Pauli operators, this ``double'' scheme can outperform the state-of-the-art measurement protocol in minimizing total shots for a given precision. We also numerically confirm the finding in previous theoretical works that the two-copy scheme incurs an overhead due to the square-root relationship between the variance of measured quantities and the number of measurement shots.

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arXiv2026

Graph automorphisms to obtain Clifford symmetries in open and closed qudit models

In the recent article [arXiv:2605.18966], we demonstrated that finding Clifford symmetries can be mapped to a Graph Automorphism (GA) problem. Here, we provide an algorithm to obtain such symmetries on general qudit systems, that works on the principle of encoding Clifford invariants of a Hamiltonian onto properties of a graph. Labelling Hamiltonian terms as vertices, a permutation of such vertices that respects the Clifford invariants (a GA) is both a valid Clifford, and a symmetry up to phase correction checks. We test this on multiple physical models and discuss the scaling with respect to the number of qudits and Pauli strings, as well as various strategies for optimisation in different regimes. We further show that the graph automorphism representation of Clifford symmetries can be expanded to open quantum systems.

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arXiv2026

Attention-based optimizer for symmetry finding

Finding symmetries is crucial for understanding physical models. In this work, we present an optimization framework that searches Pauli symmetries of Hamiltonians, merging the fields of machine learning with automated symmetry finding. Built on a Set-Transformer architecture, our framework uses self-attention to encode the pairwise and higher-order correlations among the Pauli-Strings. The relations are then decoded as a candidate, which is further optimized with a custom commutation-based objective, and mapped to a symmetry of the input Hamiltonian. We apply our method to random Pauli Hamiltonians, periodic one and two dimensional transverse-field Ising model and the Toric code. We show that for physical Hamiltonians (Ising and Toric), our framework succeeds with near-deterministic probability while providing substantial advantage compared to state-of-the-art strategies. For random Pauli Hamiltonians, we estimate the required computational resources, specifically the number of parallel starts and the number of GPUs, to find a symmetry with high success probability under fixed design specifications.

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arXiv2026

Clifford symmetries in quantum many-body systems

Obtaining the symmetries of a model is a critical step towards developing an understanding and ultimately analytically or numerically solving the model. However, finding symmetries is generally extremely complicated, often being the result of insightful thinking. In this work, we complement human ingenuity with an algorithm. We leverage the classically efficient Clifford group to find symmetries for arbitrary many-body Hamiltonians via a graph representation. We demonstrate our method on random and physical Hamiltonians, with instances of up to one thousand qubits and demonstrate how our approach can provide deeper understanding of the model.

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arXiv2026

An Error-aware and Adaptive Method for the Estimation of Quantum Observables on Qudit-Based Quantum Computers

The accurate estimation of observables is a crucial task in quantum computing. Recent advances have highlighted the need for (a) specialized protocols for qudit-based devices, that include (b) error-aware strategies. Here, we present AQUIRE, the first protocol that can (a) accurately estimate both the mean and the error of an observable on qudit-based quantum computers. AQUIRE achieves this by constructing a Bayesian model to accommodate generalized Pauli operators. It is designed to continuously monitor the estimated average and the associated error of the observable, adjusting the subsequent measurements in real-time. Additionally, AQUIRE is (b) device- and experiment-specific error-aware, and accounts for hardware imperfections and experimental noise during the estimation process. We demonstrate AQUIRE's advantage via numerical simulations and showcase its ability to quantify the noise affecting the estimation by implementing it on a trapped-ion qudit quantum processor. By exploiting general commutation relations and overlap grouping measurements, our protocol is state-of-the-art when restricted to qubit-based quantum computers and extends this advantage to the qudit case.

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arXiv2025

Correlations enable lossless ergotropy transport

"A battery powers a device" can be read as "work stored in the battery is being transported to the device." In quantum batteries, the total amount of stored work can be measured by ergotropy, which is the maximal work extractable by unitary operations. Transporting ergotropy is fundamentally different from transporting energy, and here we find that ergotropy can be gained even when the transmission channel is strictly energy conserving. We show that, generically, ergotropy transport is lossy whenever the two systems start uncorrelated. In contrast, for a large class of correlated initial states, transport can be gainful. Furthermore, a single correlated state can be used multiple times, allowing to transport without losses an order of magnitude more work than the battery capacity. Correlations are thus a useful resource for ergotropy transport, and we quantify how this resource is consumed during gainful transport.

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arXiv2024

Concentration of ergotropy in many-body systems

Ergotropy -- the maximal amount of unitarily extractable work -- measures the ``charge level'' of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy of such systems is almost constant for almost all states sampled from the Hilbert--Schmidt measure. We establish this by first proving that ergotropy, as a function of the state, is Lipschitz-continuous with respect to the Bures distance, and then applying Levy's measure concentration lemma. In parallel, we showcase the analogous properties of von Neumann entropy, compiling and adapting known results about its continuity and concentration properties. Furthermore, we consider the situation with the least amount of prior information about the state. This corresponds to the quantum version of the Jeffreys prior distribution -- the Bures measure. In this case, there exist no analytical bounds guaranteeing exponential concentration of measure. Nonetheless, we provide numerical evidence that ergotropy, as well as von Neumann entropy, concentrate also in this case.

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