arXiv subjects

Kristian Wold

Publications and source records attributed to Kristian Wold.

5 recordsLinked to original sources

arXiv2025

Spectra of noisy parameterized quantum circuits: Single-Ring universality

Random unitaries are an important resource for quantum information processing. While their universal properties have been thoroughly analyzed, it is not known what happens to these properties when the unitaries are sampled on the present-day noisy intermediate-scale quantum (NISQ) computers. We implement parameterized circuits, which have been proposed as a means to generate random unitaries, on an IBM Quantum processor and model these implementations as quantum maps. To retrieve the maps, a machine-learning assisted tomography is used. We find the spectrum of a map to be either an annulus or a disk depending on the circuit depth and detect an annulus-disk transition. By their spectral properties, the retrieved maps appear to be very similar to a recently introduced ensemble of random maps, for which spectral densities can be analytically evaluated. Our results establish, via Dissipative Quantum Chaos theory, a connection between intrinsic properties of present-day noisy intermediate-scale quantum (NISQ) computing platforms and non-Hermitian random matrix theory.

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arXiv2025

Experimental Detection of Dissipative Quantum Chaos

More than four decades of research on chaos in isolated quantum systems have led to the identification of universal signatures -- such as level repulsion and eigenstate thermalization -- that serve as cornerstones in our understanding of complex quantum dynamics. The emerging field of dissipative quantum chaos explores how these properties manifest in open quantum systems, where interactions with the environment play an essential role. We report the first experimental detection of dissipative quantum chaos and integrability by measuring the complex spacing ratios (CSRs) of open many-body quantum systems implemented on a high-fidelity superconducting quantum processor. Employing gradient-based tomography, we retrieve a ``donut-shaped'' CSR distribution for chaotic dissipative circuits, a hallmark of level repulsion in open quantum systems. For an integrable circuit, spectral correlations vanish, evidenced by a sharp peak at the origin in the CSR distribution. As we increase the depth of the integrable dissipative circuit, the CSR distribution undergoes an integrability-to-chaos crossover, demonstrating that intrinsic noise in the quantum processor is a dissipative chaotic process. Our results reveal the universal spectral features of dissipative many-body systems and establish present-day quantum computation platforms, which are predominantly used to run unitary simulations, as testbeds to explore dissipative many-body phenomena.

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arXiv2025

Dissipation-Induced Threshold on Integrability Footprints

The presence of a dissipative environment substantially disrupts unitary evolution. Nevertheless, key features of the evolution, such as its integrable or chaotic nature, are not immediately erased by dissipation. To understand this, we model environment-induced dissipation as a convex combination of unitary evolution and a random Kraus map, and examine how signatures of integrability gradually fade with increasing dissipation strength. Our analysis shows that in the weakly dissipative regime, the complex eigenvalue spectrum organizes into well-defined, high-density clusters. We estimate the critical dissipation threshold beyond which these clusters disappear, rendering the dynamics indistinguishable from chaotic evolution. This threshold depends only on the number of spectral clusters and the rank of the Kraus map. To characterize this transition, we introduce the eigenvalue angular velocity as a diagnostic of integrability loss. We illustrate our findings using several integrable quantum circuits, including the dissipative quantum Fourier transform. Our results provide a quantitative picture of how noise gradually erases the footprints of unitary integrability in open quantum systems.

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arXiv2025

Quantum Liouvillian Tomography

Characterization of near-term quantum computing platforms requires the ability to capture and quantify dissipative effects. This is an inherently challenging task, as these effects are multifaceted, spanning a broad spectrum from Markovian to strongly non-Markovian dynamics. We introduce Quantum Liouvillian Tomography (QLT), a protocol to capture and quantify non-Markovian effects in time-continuous quantum dynamics. The protocol leverages gradient-based quantum process tomography to reconstruct dynamical maps and utilizes regression over the derivatives of Pauli string probability distributions to extract the Liouvillian governing the dynamics. We benchmark the protocol using synthetic data and quantify its accuracy in recovering Hamiltonians, jump operators, and dissipation rates for two-qubit systems. Finally, we apply QLT to analyze the evolution of an idling two-qubit system implemented on a superconducting quantum platform to extract characteristics of Hamiltonian and dissipative components and, as a result, detect inherently non-Markovian dynamics. Our work introduces the first protocol capable of retrieving generators of generic open quantum evolution from experimental data, thus enabling more precise characterization of many-body non-Markovian effects in near-term quantum computing platforms.

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arXiv2025

Recursive Variational Quantum Compiling

Variational quantum compiling (VQC) algorithms aim to approximate deep quantum circuits with shallow parameterized ansatzes, making them more suitable for NISQ hardware. In this article a variant of VQC named the recursive variational quantum compiling (RVQC) algorithm is proposed. Existing VQC algorithms typically require coherently executing the full circuit during compilation. Under the influence of noise, sufficiently deep target circuits make compiling unfeasible using ordinary VQC. Since the compiling is often accomplished using a gradient-based quantum-classical approach, the quantum noise manifest as a noisy gradient during optimization, making convergence hard to obtain. On the other hand, RVQC can compile a circuit by first dividing it into $N$ shorter sub-circuits, then evaluate one sub-circuit at a time. As a result, the circuit depth required to implement RVQC is not dependent on the depth of the target circuit, but on the depth of the sub-circuits. Choosing a high enough $N$ thus ensures sufficiently shallow sub-circuit which can be successfully compiled individually. We show mathematical evidence of this property. RVQC was compared with VQC on a noise model of the IBM Santiago device with the goal of compiling several randomly generated five-qubit circuits of approximately depth 1000. It was shown that VQC was not able to converge within 500 iterations of optimization. On the other hand, RVQC was able to converge to a fidelity of $0.90 \pm 0.05$ within a total of 500 iterations when splitting the target circuits into $N = 5$ parts. We argue that this comes as a result of the mitigation of noise-induced barren plateaus.

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