Andreas Elben

We develop a framework for extracting nonpolynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic continuation (SAC), is its robustness to statistical noise arising from finite repetitions of a quantum experiment, making it well suited to realistic quantum hardware. As a demonstration, we use SAC to estimate the von Neumann entanglement entropy of a numerically simulated quenched N\'eel state from R\'enyi entropies estimated via the randomized measurement protocol. We then apply the method to experimental R\'enyi data from a trapped-ion quantum simulator experiment, extracting subsystem von Neumann entropies at different evolution times. Finally, we briefly note that the SAC framework is readily generalizable to obtain other nonlinear diagnostics, such as the logarithmic negativity and R\'enyi relative entropies.

We introduce RandomMeas.jl , a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a powerful framework for extracting properties of quantum states and processes such as expectation values, entanglement, and fidelities using simple experimental procedures combined with classical post-processing, most prominently via the classical shadow formalism. RandomMeas.jl covers the full randomized measurement workflow, from the generation of measurement settings for use on a quantum computer, the optional classical simulation of randomized measurements with tensor networks, to a suite of estimators for physical properties based on classical shadows. The package includes advanced features such as robust and shallow shadow techniques, batch estimators, and built-in statistical uncertainty estimation. Its unified, composable design enables the scalable application and further development of randomized measurements protocols across theoretical and experimental contexts.

Quantum learning encounters fundamental challenges when estimating nonlinear 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 nonlinear properties without sacrificing optimality remains an open problem. In this work, we introduce the observable-driven randomized measurement (ORM) protocol enabling the estimation of Tr ( O ρ 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 nonlinear observables, reducing circuit complexities in practical applications.

Quantum-enhanced sensors, which surpass the standard quantum limit (SQL) and approach the fundamental precision limits dictated by quantum mechanics, are finding applications across a wide range of scientific fields. This quantum advantage becomes particularly significant when a large number of particles are included in the sensing circuit. Achieving such enhancement requires introducing and preserving entanglement among many particles, posing significant experimental challenges. In this work, we integrate concepts from Floquet theory and quantum information to design an entangler capable of generating the desired entanglement between two paths of a quantum interferometer. We demonstrate that our path-entangled states enable sensing beyond the SQL, reaching the fundamental Heisenberg limit (HL) of quantum mechanics. Moreover, we show that a decoding parity measurement maintains the HL when specific conditions from Floquet theory are satisfied—particularly those related to the periodic driving parameters that preserve entanglement during evolution. We address the effects of phase uncertainty, imperfect transmission, and other types of noises, showing that our method remains robust under realistic conditions. Finally, we propose a superconducting-circuit implementation of our sensor in the microwave regime, highlighting its potential for practical applications in high-precision measurements.

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators^1,2. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions³ in the XY model, as well as signatures of the classical Kosterlitz–Thouless phase transition⁴. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis^5–7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. Published by the American Physical Society 2024

We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state. This consists in performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multicopy observables and present performance guarantees in terms of variance bounds that depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through experimental and numerical examples detecting mixed-state entanglement, and estimating polynomial approximations of the von Neumann entropy and state fidelities. Published by the American Physical Society 2024

We provide an efficient randomized measurement protocol to estimate two- and four-point fermionic correlations in ultracold atom experiments. Our approach is based on combining random atomic beam splitter operations, which can be realized with programmable optical landscapes, with high-resolution imaging systems such as quantum gas microscopes. We illustrate our results in the context of the variational quantum eigensolver algorithm for solving quantum chemistry problems.

We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state of interest. This method involves performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multi-copy observables and present performance guarantees in terms of variance bounds which depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through numerical experiments estimating polynomial approximations of the von Neumann entropy and quantum state fidelities.