arXiv subjects

Ingo Roth

Publications and source records attributed to Ingo Roth.

At least 19 recordsLinked to original sources

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.

quant-ph↗

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, which can be 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. We develop a pre-computation strategy for determining 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.

quant-ph↗

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.

quant-ph↗

arXiv2025

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.

quant-ph↗

arXiv2025

Anti-concentration 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.

quant-ph↗

arXiv2025

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 ${\rm Tr}(O\rho^2)$ 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

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.

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arXiv2024

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.

quant-ph↗

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

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↗

arXiv2023

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.

quant-ph↗

arXiv2023

Qibolab: an open-source hybrid quantum operating system

We present Qibolab, an open-source software library for quantum hardware control integrated with the Qibo quantum computing middleware framework. Qibolab provides the software layer required to automatically execute circuit-based algorithms on custom self-hosted quantum hardware platforms. We introduce a set of objects designed to provide programmatic access to quantum control through pulses-oriented drivers for instruments, transpilers and optimization algorithms. Qibolab enables experimentalists and developers to delegate all complex aspects of hardware implementation to the library so they can standardize the deployment of quantum computing algorithms in a extensible hardware-agnostic way, using superconducting qubits as the first officially supported quantum technology. We first describe the status of all components of the library, then we show examples of control setup for superconducting qubits platforms. Finally, we present successful application results related to circuit-based algorithms.

quant-ph↗

arXiv2023

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 $\Delta$, 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 $\Delta$ 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.

quant-ph↗

arXiv2023

Towards an open-source framework to perform quantum calibration and characterization

In this proceedings we present Qibocal, an open-source software package for calibration and characterization of quantum processing units (QPUs) based on the Qibo framework. Qibocal is specifically designed for self-hosted QPUs and provides the groundwork to easily develop, deploy and distribute characterization and calibration routines for all levels of hardware abstraction. Qibocal is based on a modular QPU platform agnostic approach and it provides a general purpose toolkit for superconducting qubits with the possibility of extensions to other quantum technologies. After motivating the need for such a module, we explain the program's flow and show examples of actual use for QPU calibration. We also showcase additional features provided by the library including automatic report generation and live plotting.

quant-ph↗

arXiv2022

Randomized benchmarking with random quantum circuits

In its many variants, randomized benchmarking (RB) is a broadly used technique for assessing the quality of gate implementations on quantum computers. A detailed theoretical understanding and general guarantees exist for the functioning and interpretation of RB protocols if the gates under scrutiny are drawn uniformly at random from a compact group. In contrast, many practically attractive and scalable RB protocols implement random quantum circuits with local gates randomly drawn from some gate-set. Despite their abundance in practice, for those non-uniform RB protocols, general guarantees for gates from arbitrary compact groups under experimentally plausible assumptions are missing. In this work, we derive such guarantees for a large class of RB protocols for random circuits that we refer to as filtered RB. Prominent examples include linear cross-entropy benchmarking, character benchmarking, Pauli-noise tomography and variants of simultaneous RB. Building upon recent results for random circuits, we show that many relevant filtered RB schemes can be realized with random quantum circuits in linear depth, and we provide explicit small constants for common instances. We further derive general sample complexity bounds for filtered RB. We show filtered RB to be sample-efficient for several relevant groups, including protocols addressing higher-order cross-talk. Our theory for non-uniform filtered RB is, in principle, flexible enough to design new protocols for non-universal and analog quantum simulators.

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arXiv2022

Closed-form analytic expressions for shadow estimation with brickwork circuits

Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.

quant-ph↗

arXiv2022

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 $h \in \mathbb{K}^\mu$ and $\sigma$-sparse $b \in \mathbb{K}^n$ with high probability can be recovered when $\mu \succcurlyeq s\log(s)^2\log(\mu)\log(\mu n) + s\sigma \log(n)$.

cs.IT↗

arXiv2022

Scalably learning quantum many-body Hamiltonians from dynamical data

The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.

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