arXiv subjects

Ingo Roth

Publications and source records attributed to Ingo Roth.

At least 19 recordsLinked to original sources

arXiv2026

Estimating the generator of matrix exponential time-series

The achievable precision in estimating the spectrum of a time-series signal that is promised to be sparse in Fourier space deteriorates rapidly as the spectral peaks get closer together, as soon as we introduce noise. Here, we study the related task of generator estimation: estimating the generator of a matrix exponential time-series and its eigenvalues. We obtain rigorous non-asymptotic precision guarantees on genESPRIT, a practical algorithm solving generator estimation, and show that this task can be solved with precision independent of the spectral spacing. The guarantees are complemented by a Cramér--Rao analysis of a relaxation of the problem. In particular, in the case of unitary data with bounded additive noise with effective entrywise variance $σ^2$, we show that genESPRIT estimates the associated propagator matrix in Frobenius norm with precision scaling as $\tilde{\mathcal{O}}(σNL^{-\frac12})$ in the length of the time-series $L$ and matrix dimension $N$, matching the corresponding spectrum-independent Cramér--Rao standard deviation scaling up to logarithmic factors. We prove that the matching distance error in the spectrum estimated by genESPRIT scales as $\tilde{\mathcal{O}} (σ^2 N^3 L^{-1} + σN^{\frac32} L^{-\frac32} )$, which we compare to the lower bound on the corresponding Cramér--Rao bound with the asymptotic standard deviation scaling $\mathcal{O}(σL^{-\frac32})$. These guarantees provide the first rigorous bounds on solving the generator estimation problem. As the matrix exponential time-series can be obtained from linearly independent vector time-series by concatenation, this work opens up a new direction in spectral estimation, which circumvents the problem of crowded spectra, under the additional assumption of linear independence.

cs.IT↗

arXiv2026

Scalable Determination of Penalization Weights for Constrained Optimizations on Approximate Solvers

Quadratic unconstrained binary optimization (QUBO) provides problem formulations for various computational problems that can be solved with dedicated QUBO solvers, based on classical or quantum computation. A common approach to constrained combinatorial optimization problems is to enforce the constraints in the QUBO formulation by adding penalization terms. Penalization introduces an additional hyperparameter that significantly affects the solver's efficacy: the relative weight between the objective terms and the penalization terms. Here we study the problem of a priori determining suitable penalization weights from a foundational and practical perspective. We formally establish that finding its optimal value for Gibbs solvers is $\mathsf{NP}$-hard even approximately and $\#\mathsf{P}$-hard exactly. This serves us as a motivation to develop a widely applicable heuristic strategy for determining suitable penalization weights, with provable guarantees for Gibbs solvers, and polynomial complexity for broad problem classes. Experiments across diverse problems and solver architectures, including large-scale instances on Fujitsu's Digital Annealer, show robust performance and order-of-magnitude speedups over existing heuristics. We further extend the strategy to quantum approximate optimization and demonstrate its performance on Quantinuum's H2-2 trapped-ion processor.

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arXiv2026

Quickly extracting fidelity decay rates in random circuit benchmarking experiments

Randomized benchmarking (RB) with structured circuits is experimentally scalable, but gives biased short-depth fidelity estimates because incomplete ensemble mixing introduces transient modes. Waiting for these transients to decay in deeper circuits can push the signal below the noise floor. This is a well-established obstacle, e.g. in linear cross-entropy benchmarking (LinXEB). Here we overcome this obstacle solely through classical post-processing. We introduce a one-parameter family of estimators that interpolate between the standard LinXEB-type post-processing and a new post-processing technique we call the trace filter function. Under practical assumptions, the trace filter function provably suppresses transient modes, exposing an interpretable fidelity decay at short depth, with theoretical guarantees comparable to standard RB, at the cost of an increased variance. We bound the variance, analyze the evaluation complexity of the new estimators, and develop practical post-processing algorithms. Experiments on a Rigetti superconducting processor validate the method for one-dimensional circuits of up to 12 qubits: where the standard estimator requires depth beyond a 40-layer experimental window, the trace filter function yields consistent estimates below 10 layers. Trace-filtered randomized benchmarking therefore extends reliable fidelity characterization to relevant structured circuit ensembles and short-depth regimes that are inaccessible to conventional estimators.

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arXiv2026

Efficient certification of time-reversal symmetry requires entanglement

Time-reversal symmetry is a fundamental principle of physics describing the invariance of physical laws under reversal of the direction of time. We formulate a Bell-inequality-like test of this antiunitary symmetry using only forward access and trusted quantum operations: entanglement converts temporal input--output relations into measurable spatial exchange symmetry. For $n$-qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires $Ω(\min\{2^{n/2},2^{n-e}\})$ queries for any classically adaptive protocol. Here, $e=\min\{e_{\mathrm s},e_{\mathrm m}\}$ with $e_{\mathrm s}$ and $e_{\mathrm m}$ representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.

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arXiv2026

Anticoncentration is (almost) all you need

Until very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anticoncentration of random quantum circuits, mainly because it was shown that the latter anticoncentrate in logarithmic depth, while the former generally need linear depth circuits. This belief was disproven by recent results which show that so-called relative-error approximate unitary designs can, in fact, be generated in logarithmic depth, implying anticoncentration. Their result does however not apply to ordinary local random circuits, a gap which we close in this letter, at least for 2-designs. More precisely, we show that anticoncentration of local random quantum circuits already implies that they form relative-error approximate state 2-designs, making them equivalent properties for these ensembles. Our result holds more generally for any random circuit which is invariant under local (single-qubit) unitaries, independent of the architecture.

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arXiv2026

Fermionic quantum error correction is never free

Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, however, they require quantum error correction. In this work, we prove that any exact and sufficiently accurate approximate fermionic quantum error correction necessarily requires non-Gaussian operations, beyond the free-fermion regime of quadratic dynamics. This is in sharp contrast to the qubit setting, where the efficiently classically simulable stabilizer operations form the standard framework for quantum error correction. Specifically, we show that the logical space of any non-trivial fermionic error-correcting code contains no pure fermionic Gaussian state, utilizing a fundamental incompatibility between fermionic error correction and Wick's theorem. We further show that the required number of bounded-weight non-Gaussian gates for unitary codeword preparation grows at least linearly with both the code distance and the number of encoded modes, revealing an intrinsic resource overhead that increases simultaneously with error-protection strength and logical capacity. Furthermore, we analyze the performance of fermionic Gaussian operations in entanglement distillation, revealing a distinction from their bosonic counterparts. Our results reveal fundamental difficulties for fermionic error correction from the perspectives of both physical implementation and classical simulation, suggesting connections to fermionic phases of matter and state preparation complexity.

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arXiv2026

Qibocal: an open-source framework for calibration of self-hosted quantum devices

Calibration of quantum devices is fundamental to successfully deploy quantum algorithms on current available quantum hardware. We present Qibocal, an open-source software library to perform calibration and characterization of superconducting quantum devices within the Qibo framework. Qibocal completes the Qibo middleware framework by providing all necessary tools to easily (re)calibrate self-hosted quantum platforms. After presenting the layout and the features of the library, we give an overview on some of the protocols implemented to perform single and two-qubit gates calibration. Finally, we present applications involving recalibration and monitoring of superconducting platforms.

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arXiv2026

Witness expansion: A unified framework for analytical and measurable mixed-state resource detection

Quantum information science aims to harness different kinds of quantum resources to accomplish specific information-processing tasks. These resources also play an increasingly important role in addressing fundamental questions concerning quantum phases and dynamics. Therefore, developing powerful and practical methods for identifying and detecting quantum resources is of great significance, with applications ranging from benchmarking quantum devices to understanding the fundamental structure of quantum theory. In this work, we propose witness expansion, a unified framework for constructing nonlinear criteria for detecting quantum resources that are associated with a well-defined group of free unitaries. These criteria apply to both pure and mixed quantum states and are based on polynomial functions of the target state, which can be estimated experimentally using multiple copies of the state and evaluated analytically in certain physical models. We show how several well-known resource-detection quantities naturally emerge from our framework, including the $l_2$ norm of coherence, partial-transpose moments for entanglement, stabilizer entropy for nonstabilizerness (quantum magic), and fermionic antiflatness for fermionic non-Gaussianity. Beyond recovering these existing structures, our framework also yields new criteria for detecting qubit and qudit magic states, substantially enhancing witness-based detection capabilities. In addition, it gives, to the best of our knowledge, the first analytical criterion for detecting mixed-state fermionic non-Gaussianity with respect to the convex hull of pure fermionic Gaussian states that remains nontrivial for arbitrary numbers of qubits, demonstrating the broad applicability and conceptual unifying power of the framework.

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arXiv2026

Local robust shadows on a trapped ion computer -- a case study

We experimentally demonstrate local robust shadows on a trapped-ion quantum computing system, a protocol developed to counteract measurement errors. We alternate between a calibration stage and the shadow estimation stage and also introduce Pauli-X-twirling before measurements in both stages to symmetrize error rates. We then demonstrate the protocol on a trapped-ion quantum computer with artificially shortened measurement pulse duration. This yields faster experiments at the cost of increased error rates which are subsequently mitigated by the robust shadow protocol. We benchmark this approach on three exemplary quantum states: a local Haar random state, as well as standard and Pauli-correlation-encoded QAOA states. In all three cases, the local robust shadow protocol succeeds at mitigating the increased error rates hailing from shorter measurement pulse durations.

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arXiv2026

Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection

We introduce a mixed-state magic criterion, the Triangle Criterion, which plays a role for magic analogous to the Positive Partial Transposition (PPT) Criterion for entanglement: it combines strong detection capability, a clear geometric interpretation, and an operational link to magic distillation. Using this criterion, we uncover several new features of multi-qubit magic distillation and detection. We prove that genuinely multi-qubit magic distillation protocols are strictly more powerful than all single-qubit schemes by showing that the Triangle Criterion is not stable under tensor products. Moreover, we show that, with overwhelming probability, multi-qubit magic states with relatively low rank cannot be distilled by any single-qubit distillation protocol. We derive an upper bound on the minimal purity of magic states, which is conjectured to be tight with both numerical and constructive evidences. Using this minimal-purity result, we predict the existence of unfaithful magic states, namely states that cannot be detected by any fidelity-based magic witness, and reveal fundamental limitations of mixed-state magic detection in any single-copy scheme.

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arXiv2026

Blind calibration of a quantum computer

The calibration of quantum measurements is limited by the ability to accurately prepare quantum states under unknown device errors. We develop an accurate calibration protocol for the measurement apparatus of a quantum computer that is `blind' to the state preparation. Blind calibration quantifies and corrects measurement errors from simple tomographic data on a noisy quantum state. Importantly, it calibrates multiple error mechanisms in a single experiment, eliminating the need for bespoke, separate calibration experiments. Using a trapped-ion quantum computer, we systematically demonstrate the accuracy of the method. We use blind calibration to estimate the native calibration parameters of the experimental system. The recovered calibrations are consistent with directly measured values and perform similarly in predicting the state properties.

quant-ph↗

arXiv2026

Optimal randomized measurements for a family of non-linear quantum properties

Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal sample complexity for specific tasks like state purity estimation, generalizing these protocols to estimate broader classes of non-linear properties without sacrificing optimality remains an open problem. In this work, we introduce the observable-driven randomized measurement (ORM) protocol enabling the estimation of ${\rm Tr}(Oρ^2)$ for an arbitrary observable $O$ -- an essential quantity in quantum computing and many-body physics. We establish an upper bound for ORM's sample complexity and show its optimality for observables with a large trace-norm, including Pauli and local observables, closing a gap in the literature. For these observables, ORM admits an efficient implementation with Clifford circuits. Numerical experiments validate that ORM requires substantially fewer state samples to achieve the same precision compared to classical shadows. Additionally, we introduce a braiding randomized measurement protocol for multiple low-rank non-linear observables, reducing circuit complexities in practical applications.

quant-ph↗

arXiv2025

Alleviating the quantum Big-$M$ problem

A major obstacle for quantum optimizers is the reformulation of constraints as a quadratic unconstrained binary optimization (QUBO). Current QUBO translators exaggerate the weight $M$ of the penalty terms. Classically known as the "Big-$M$" problem, the issue becomes even more daunting for quantum solvers, since it affects the physical energy scale. We take a systematic, encompassing look at the quantum big-$M$ problem, revealing NP-hardness in finding the optimal $M$ and establishing bounds on the Hamiltonian spectral gap $Δ$, inversely related to the expected run-time of quantum solvers. We propose a practical translation algorithm, based on SDP relaxation, that outperforms previous methods in numerical benchmarks. Our algorithm gives values of $Δ$ orders of magnitude greater, e.g. for portfolio optimization instances. Solving such instances with an adiabatic algorithm on 6-qubits of an IonQ device, we observe significant advantages in time to solution and average solution quality. Our findings are relevant to quantum and quantum-inspired solvers alike.

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arXiv2025

Robust ultra-shallow shadows

We present a robust shadow estimation protocol for wide classes of low-depth measurement circuits that mitigates noise as long as the effective measurement map including noise is locally unitarily invariant. This is in practice an excellent approximation, encompassing for instance the case of ideal single-qubit Clifford gates composing the first circuit layer of an otherwise arbitrary circuit architecture and even non-Markovian, gate-dependent noise in the rest of the circuit. We argue that for weakly-correlated local noise, the measurement channel has an efficient matrix-product representation, and show how to estimate this directly from experimental data using tensor-network tools, eliminating the need for analytical or numeric calculations. We illustrate the relevance of our method with both numerics and proof-of-principle experiments on an IBM Quantum device. Numerically, we show that unmitigated shallow shadows with noisy circuits become more biased as the depth increases. In contrast, using the same number of samples, robust ultra-shallow shadows become more precise with increasing depth for relevant parameter regimes. The gain in sample efficiency is still limited by the noise per gate, resulting in an optimal circuit depth per noise level. Experimentally, we observe improved precision in two simple fidelity estimation tasks using five-qubit circuits with up to two layers of entangling gates, by about an order of magnitude. Under the practical constraints of current and near-term noisy quantum devices, our method maximally realizes the potential of shadow estimation with global rotations and identifies its fundamental limitations in the presence of noise.

quant-ph↗

arXiv2025

Stability of classical shadows under gate-dependent noise

Expectation values of observables are routinely estimated using so-called classical shadows$\unicode{x2014}$the outcomes of randomized bases measurements on a repeatedly prepared quantum state. In order to trust the accuracy of shadow estimation in practice, it is crucial to understand the behavior of the estimators under realistic noise. In this work, we prove that any shadow estimation protocol involving Clifford unitaries is stable under gate-dependent noise for observables with bounded stabilizer norm$\unicode{x2014}$originally introduced in the context of simulating Clifford circuits. In contrast, we demonstrate with concrete examples that estimation of `magic` observables can lead to highly misleading results in the presence of miscalibration errors and a worst case bias scaling exponentially in the system size. We further find that so-called robust shadows, aiming at mitigating noise, can introduce a large bias in the presence of gate-dependent noise compared to unmitigated classical shadows. Nevertheless, we guarantee the functioning of robust shadows for a more general noise setting than in previous works. On a technical level, we identify average noise channels that affect shadow estimators and allow for a more fine-grained control of noise-induced biases.

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arXiv2024

Bisparse Blind Deconvolution through Hierarchical Sparse Recovery

The hierarchical sparsity framework, and in particular the HiHTP algorithm, has been successfully applied to many relevant communication engineering problems recently, particularly when the signal space is hierarchically structured. In this paper, the applicability of the HiHTP algorithm for solving the bi-sparse blind deconvolution problem is studied. The bi-sparse blind deconvolution setting here consists of recovering $h$ and $b$ from the knowledge of $h*(Qb)$, where $Q$ is some linear operator, and both $b$ and $h$ are both assumed to be sparse. The approach rests upon lifting the problem to a linear one, and then applying HiHTP, through the \emph{hierarchical sparsity framework}. %In particular, the efficient HiHTP algorithm is proposed for performing the recovery. Then, for a Gaussian draw of the random matrix $Q$, it is theoretically shown that an $s$-sparse $h \in \mathbb{K}^μ$ and $σ$-sparse $b \in \mathbb{K}^n$ with high probability can be recovered when $μ\succcurlyeq s\log(s)^2\log(μ)\log(μn) + sσ\log(n)$.

cs.IT↗

arXiv2024

Benchmarking bosonic and fermionic dynamics

Analog quantum simulation allows for assessing static and dynamical properties of strongly correlated quantum systems to high precision. To perform simulations outside the reach of classical computers, accurate and reliable implementations of the anticipated Hamiltonians are required. To achieve those, characterization and benchmarking tools are a necessity. For digital quantum devices, randomized benchmarking can provide a benchmark on the average quality of the implementation of a gate set. In this work, we introduce a versatile framework for randomized analog benchmarking of bosonic and fermionic quantum devices implementing particle number preserving dynamics. The scheme makes use of the restricted operations which are native to analog simulators and other continuous variable systems. Importantly, like randomized benchmarking, it is robust against state preparation and measurement errors. We discuss the scheme's efficiency, derive theoretical performance guarantees and showcase the protocol with numerical examples.

quant-ph↗

arXiv2024

Robustly learning the Hamiltonian dynamics of a superconducting quantum processor

The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. The key to solving these issues are precise means of characterizing analog quantum simulators. Here, we robustly estimate the free Hamiltonian parameters of bosonic excitations in a superconducting-qubit analog quantum simulator from measured time-series of single-mode canonical coordinates. We achieve high levels of precision in estimating the Hamiltonian parameters by exploiting a priori knowledge, making it robust against noise and state-preparation and measurement (SPAM) errors. Importantly, we are also able to obtain tomographic information about those SPAM errors from the same data, crucial for the experimental applicability of Hamiltonian learning in dynamical quantum-quench experiments. Our learning algorithm is scalable both in terms of the required amounts of data and post-processing. To achieve this, we develop a new super-resolution technique coined tensorESPRIT for frequency extraction from matrix time-series. The algorithm then combines tensorESPRIT with constrained manifold optimization for the eigenspace reconstruction with pre- and post-processing stages. For up to 14 coupled superconducting qubits on two Sycamore processors, we identify the Hamiltonian parameters -- verifying the implementation on one of them up to sub-MHz precision -- and construct a spatial implementation error map for a grid of 27 qubits. Our results constitute an accurate implementation of a dynamical quantum simulation that is characterized using a new diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.

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