arXiv subjects

Manuel Endres

Publications and source records attributed to Manuel Endres.

At least 19 recordsLinked to original sources

arXiv2026

Detuning- and Stark-robust Rydberg gates

Rydberg entangling gates driven by a two-photon transition in alkali atoms suffer from an adverse scaling of light-shift-induced errors. Robustness to such detuning errors is known to be impossible to achieve in the design of conventional Rydberg gate protocols, where only one of the qubit states is coupled to the Rydberg state. Here, we show that in a more general framework, in which both qubit states take part in the gate, full or partial robustness to these errors can be realized. We present two gate constructions, which either cancel the errors outright or convert them into single-qubit errors that can be corrected locally. We map the regimes -- in terms of light-shift strength, intensity inhomogeneity, and Rydberg decay rate -- in which these protocols outperform the widely used time-optimal Rydberg gate, and find that they already include the conditions of state-of-the-art experiments. Finally, we show the existence of a Rydberg `fly-by' entangling gate, an important primitive for an emerging class of neutral-atom quantum computing architectures.

quant-ph↗

arXiv2026

Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits

Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance and practical relevance to cryptography. However, due to the high overhead of quantum error correction, optimized resource estimates for cryptographically relevant instances of Shor's algorithm require millions of physical qubits. Here, by leveraging advances in high-rate quantum error-correcting codes, efficient logical instruction sets, and circuit design, we show that Shor's algorithm can be executed at cryptographically relevant scales with as few as 10,000 reconfigurable atomic qubits. Increasing the number of physical qubits improves time efficiency by enabling greater parallelism; under plausible assumptions, the runtime for discrete logarithms on the P-256 elliptic curve could be just a few days for a system with 26,000 physical qubits, while the runtime for factoring RSA-2048 integers is one to two orders of magnitude longer. Recent neutral-atom experiments have demonstrated universal fault-tolerant operations below the error-correction threshold, computation on arrays of hundreds of qubits, and trapping arrays with more than 6,000 highly coherent qubits. Although substantial engineering challenges remain, our theoretical analysis indicates that an appropriately designed neutral-atom architecture could support quantum computation at cryptographically relevant scales. More broadly, these results highlight the capability of neutral atoms for fault-tolerant quantum computing with wide-ranging scientific and technological applications.

quant-ph↗

arXiv2026

Gate-based Readout and Cooling of Neutral Atoms

Neutral atom arrays have seen tremendous progress in quantum simulation, quantum metrology, and fault-tolerant quantum computing. However, hardware constraints such as atom loss and heating remain significant challenges. In this work, we introduce a comprehensive ancilla-based toolbox for optical tweezer experiments that utilizes high-fidelity Rydberg entangling gates and ancilla atoms to mitigate these physical limitations. First, we demonstrate repeated ancilla-based atom readout, achieving improved detection fidelity over multiple rounds with minimal perturbation to data atoms. Second, leveraging the quantized motional states in tweezer-trapped strontium atoms, we transduce quantum information from the electronic to the motional manifold. This enables us to perform mid-circuit ancilla-based atom loss detection in a coherence-preserving fashion. Finally, we demonstrate algorithmic cooling, a circuit-based sequence that deterministically cools data atoms by transferring their motional entropy to the electronic states of ancilla atoms. We observe a marked reduction in the atomic temperature of data atoms. These tools offer a pathway to continuous operation in tweezer clocks and complement recent developments in continuous reloading experiments.

quant-ph↗

arXiv2026

Experimental observation of conformal field theory spectra

Conformal field theories (CFTs) feature prominently in high-energy physics, statistical mechanics, and condensed matter. For example, CFTs govern emergent universal properties of systems tuned to quantum phase transitions, including their entanglement, correlations, and low-energy excitation spectra. Much of the rich structure predicted by CFTs nevertheless remains unobserved in experiment. Here we directly observe the energy excitation spectra of emergent CFTs at quantum phase transitions -- recovering universal energy ratios characteristic of the underlying field theories. Specifically, we develop and implement a modulation technique to resolve a Rydberg chain's finite-size spectra, variably tuned to quantum phase transitions described by either Ising or tricritical Ising CFTs. We also employ local control to distinguish parities of excitations under reflection and, in the tricritical Ising chain, to induce transitions between distinct CFT spectra associated with changing boundary conditions. By utilizing a variant of the modulation technique, we furthermore study the dynamical structure factor of the critical system, which is closely related to the correlation of an underlying Ising conformal field. Our work not only probes the emergence of CFT features in a quantum simulator, but also provides a technique for diagnosing a priori unknown universality classes in future experiments.

quant-ph↗

arXiv2025

Observation of ballistic plasma and memory in high-energy gauge theory dynamics

Gauge theories describe the fundamental forces of nature. However, high-energy dynamics, such as the formation of quark-gluon plasmas, is notoriously difficult to model with classical methods. Quantum simulation offers a promising alternative in this regime, yet experiments have mainly probed low energies. Here, we observe the formation of a ballistic plasma and long-time memory effects in high-energy gauge theory dynamics on a high-precision quantum simulator. Both observations are unexpected, as the initial state - fully filled with particle-antiparticle pairs - was thought to rapidly thermalize. Instead, we find correlations spreading ballistically to long distances and a memory of charge clusters. Our observations cannot be explained by many-body scars, but are captured by a new theory of plasma oscillations between electric field and current operators, persisting all the way to the continuum limit of the (1+1)D Schwinger model, of which we simulate a lattice version. Adapting techniques from quantum optics, we visualize plasma oscillations as rotations of Wigner distributions, leading to a novel set of predictions which we test in experiment and numerics. The new framework encompasses both our scenario and scars, which show up as coherent states of the plasma. The experimental surprises we observe in the high-energy dynamics of a simple gauge theory point to the potential of high-precision quantum simulations of gauge theories for general scientific discovery.

quant-ph↗

arXiv2025

A three-dimensional acousto-optic deflector

Acousto-optic deflectors (AODs) are widely used across physics, microscopy, neuroscience, and laser engineering, providing fast, precise, and non-mechanical control of light. While conventional AODs naturally support multiplexing in one and two dimensions, no analogous device has existed for three-dimensional control, leaving a critical gap in rapid focus tuning and 3D beam shaping. Here we demonstrate a three-dimensional AOD system capable of multiplexed axial and lateral beam control with high speed and large dynamic range. We achieve this by combining a double-pass AOD with a diffraction grating in the Littrow configuration to realize a compact frequency-tunable lens with multiplexing capability. Our device enables axial scanning over more than twenty Rayleigh ranges with switching rates up to 100 kHz, while simultaneous multi-tone driving produces arbitrary multi-focal beam profiles. By integrating the axial module with lateral deflection, we generate reconfigurable 3D optical patterns. This approach establishes a broadly applicable platform for multiplexed 3D beam control, with potential applications from high-resolution microscopy and laser processing to scalable neutral-atom quantum technologies.

physics.optics↗

arXiv2025

Extending the dynamic range in quantum frequency estimation with sequential weak measurements

Quantum metrology explores optimal quantum protocols for parameter estimation. In the context of optical atomic clocks, conventional protocols focus on optimal input states and measurements to achieve enhanced sensitivities. However, such protocols are typically limited by phase slip errors inflicted due to the decoherence of the local oscillator. Here, we study schemes to extend the dynamic range and overcome phase slip noise through weak measurements with ancilla qubits. Using coherent spin states, we find optimal weak measurements protocols: we identify optimal measurement strength for any given interrogation time and number of atoms. Then, we combine weak and projective measurements to construct a protocol that asymptotically saturates the noiseless precision limits, and outperforms previously proposed methods for phase slip noise suppression.

quant-ph↗

arXiv2025

Practical roadmap to measurement-altered criticality in Rydberg arrays

Weak measurements have been predicted to dramatically alter universal properties of quantum critical wavefunctions, though experimental validation remains an open problem. Here we devise a practical scheme for realizing measurement-altered criticality in a chain of Rydberg atoms tuned to Ising and tricritical Ising phase transitions. In particular, we show that projectively measuring a periodic subset of atoms alters quantum critical correlations in distinct ways that one can control via the choice of measured sites and the measurement outcomes. While our protocol relies on post-selection, the measurement outcomes yielding the most dramatic consequences occur with surprisingly large probabilities: O(10%) with chains featuring O(100) sites. Characterizing the proposed post-measurement states requires only an adjustment in the post-process averaging of outcomes used to characterize unmeasured critical states, resulting in minimal additional experimental overhead for demonstrating measurement-altered criticality.

quant-ph↗

arXiv2024

Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos

Quantum many-body systems provide a unique platform for exploring the rich interplay between chaos, randomness, and complexity. In a recently proposed paradigm known as deep thermalization, random quantum states of system A are generated by performing projective measurements on system B following chaotic Hamiltonian evolution acting jointly on AB. In this scheme, the randomness of the projected state ensemble arises from the intrinsic randomness of the outcomes when B is measured. Here we propose a modified scheme, in which classical randomness injected during the protocol is converted by quantum chaos into quantum randomness of the resulting state ensemble. We show that for generic chaotic systems this conversion is optimal in that each bit of injected classical entropy generates as much additional quantum randomness as adding an extra qubit to B. This significantly enhances the randomness of the projected ensemble without imposing additional demands on the quantum hardware. Our scheme can be easily implemented on typical analog quantum simulators, providing a more scalable route for generating quantum randomness valuable for many applications. In particular, we demonstrate that the accuracy of a shadow tomography protocol can be substantially improved.

quant-ph↗

arXiv2024

Benchmarking and fidelity response theory of high-fidelity Rydberg entangling gates

The fidelity of entangling operations is a key figure of merit in quantum information processing, especially in the context of quantum error correction. High-fidelity entangling gates in neutral atoms have seen remarkable advancement recently. A full understanding of error sources and their respective contributions to gate infidelity will enable the prediction of fundamental limits on quantum gates in neutral atom platforms with realistic experimental constraints. In this work, we implement the time-optimal Rydberg CZ gate, design a circuit to benchmark its fidelity, and achieve a fidelity, averaged over symmetric input states, of 0.9971(5), downward-corrected for leakage error, which together with our recent work forms a new state-of-the-art for neutral atoms. The remaining infidelity is explained by an ab initio error model, consistent with our experimental results over a range of gate speeds, with varying contributions from different error sources. Further, we develop a fidelity response theory to efficiently predict infidelity from laser noise with non-trivial power spectral densities and derive scaling laws of infidelity with gate speed. Besides its capability of predicting gate fidelity, we also utilize the fidelity response theory to compare and optimize gate protocols, to learn laser frequency noise, and to study the noise response for quantum simulation tasks. Finally, we predict that a CZ gate fidelity of ${\gtrsim} 0.999$ is feasible with realistic experimental upgrades.

quant-ph↗

arXiv2024

Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits

Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop and analyze a scheme that achieves near-optimal precision up to a constant overhead for Bayesian phase estimation, using simple digital quantum circuits with depths scaling logarithmically with the number of qubits. We find that for Gaussian prior phase distributions with arbitrary widths, the optimal initial state can be approximated with products of Greenberger-Horne-Zeilinger states with varying number of qubits. Using local, adaptive measurements optimized for the prior distribution and the initial state, we show that Heisenberg scaling is achievable and that the proposed scheme outperforms known schemes in the literature that utilize a similar set of initial states. For an example prior width, we present a detailed comparison and find that is also possible to achieve Heisenberg scaling with a scheme that employs non-adaptive measurements, with the right allocation of copies per GHZ state and single-qubit rotations. We also propose an efficient phase unwinding protocol to extend the dynamic range of the proposed scheme, and show that it outperforms existing protocols by achieving an enhanced precision with a smaller number of additional atoms. Lastly, we discuss the impact of noise and imperfect gates.

quant-ph↗

arXiv2024

A tweezer array with 6100 highly coherent atomic qubits

Optical tweezer arrays have transformed atomic and molecular physics, now forming the backbone for a range of leading experiments in quantum computing, simulation, and metrology. Typical experiments trap tens to hundreds of atomic qubits, and recently systems with around one thousand atoms were realized without defining qubits or demonstrating coherent control. However, scaling to thousands of atomic qubits with long coherence times, low-loss, and high-fidelity imaging is an outstanding challenge and critical for progress in quantum science, particularly towards quantum error correction. Here, we experimentally realize an array of optical tweezers trapping over 6,100 neutral atoms in around 12,000 sites, simultaneously surpassing state-of-the-art performance for several metrics that underpin the success of the platform. Specifically, while scaling to such a large number of atoms, we demonstrate a coherence time of 12.6(1) seconds, a record for hyperfine qubits in an optical tweezer array. We show room-temperature trapping lifetimes of 23 minutes, enabling record-high imaging survival of 99.98952(1)% with an imaging fidelity of over 99.99%. We present a plan for zone-based quantum computing and demonstrate necessary coherence-preserving qubit transport and pick-up/drop-off operations on large spatial scales, characterized through interleaved randomized benchmarking. Our results, along with recent developments, indicate that universal quantum computing and quantum error correction with thousands to tens of thousands of physical qubits could be a near-term prospect.

quant-ph↗

arXiv2024

Experimental signatures of Hilbert-space ergodicity: Universal bitstring distributions and applications in noise learning

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently a strong notion of quantum ergodicity has been proposed, namely that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition exhibits universal properties on a quantitative level amongst a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. For an open system, where the environment is uncontrolled, we predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate between candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. This allows for computationally efficient experimental noise learning, and more broadly is a new avenue for quantitatively classifying the behavior of noisy quantum systems. Ultimately our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

quant-ph↗

arXiv2024

A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

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 formulae 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.

quant-ph↗

arXiv2024

Universal quantum operations and ancilla-based readout for tweezer clocks

Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in the field of quantum metrology. Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and readout strategies. Neutral atom optical clocks, leading systems for measuring time, have shown recent progress in terms of entanglement generation, but currently lack the control capabilities to realize such schemes. Here we show universal quantum operations and ancilla-based readout for ultranarrow optical transitions of neutral atoms. Our demonstration in a tweezer clock platform enables a circuit-based approach to quantum metrology with neutral atom optical clocks. To this end, we demonstrate two-qubit entangling gates with 99.62(3)% fidelity - averaged over symmetric input states - via Rydberg interactions and dynamical connectivity for optical clock qubits, which we combine with local addressing to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state, a cascade of Greenberger-Horne-Zeilinger (GHZ) states of different sizes, and perform dual-quadrature GHZ readout. We also show repeated fast phase detection with non-destructive conditional reset of clock qubits and minimal dead time between repetitions by implementing ancilla-based quantum logic spectroscopy (QLS) for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell state preparation. Our work lays the foundation for hybrid processor-clock devices with neutral atoms and more generally points to a future of practical applications for quantum processors linked with quantum sensors.

quant-ph↗

arXiv2023

Erasure-cooling, control, and hyper-entanglement of motion in optical tweezers

Coherently controlling the motion of single atoms in optical tweezers would enable new applications in quantum information science. To demonstrate this, we first prepare atoms in their motional ground state using a species-agnostic cooling mechanism that converts motional excitations into erasures -- errors with a known location. This cooling mechanism fundamentally outperforms idealized traditional sideband cooling, which we experimentally demonstrate. By coherently manipulating the resultant pure motional state, we perform mid-circuit readout and mid-circuit erasure detection via local shelving into motional superposition states. We finally entangle the motion of two atoms in separate tweezers and generate hyper-entanglement by preparing a simultaneous Bell state of motional and optical qubits, unlocking a large new class of quantum operations with neutral atoms.

quant-ph↗

arXiv2023

Benchmarking highly entangled states on a 60-atom analog quantum simulator

Quantum systems have entered a competitive regime where classical computers must make approximations to represent highly entangled quantum states. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices, and it remains unsolved how to estimate the actual entanglement content of experiments. Here we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analog Rydberg quantum simulator, reaching a high entanglement entropy regime where exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we employ. Our results enable a new paradigm for evaluating the ability of both analog and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

quant-ph↗

arXiv2023

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices and for the quest towards fault-tolerant quantum computation. Rydberg arrays have emerged as a prominent platform in this context with impressive system sizes and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution, a form of erasure error conversion. However, two-qubit entanglement fidelities in Rydberg atom arrays have lagged behind competitors and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator. We implement erasure conversion via fast imaging of alkaline-earth atoms, which leaves atoms in a metastable state unperturbed and yields additional information independent of the final qubit readout. When excising data with observed erasure errors, we achieve a lower-bound for the Bell state generation fidelity of ${\geq} 0.9971^{+10}_{-13}$, which improves to ${\geq}0.9985^{+7}_{-12}$ when correcting for remaining state preparation errors. We further demonstrate erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, where we explicitly differentiate erasure conversion of preparation and Rydberg decay errors. We unveil the otherwise hidden impact of these errors on the simulation outcome by evaluating correlations between erasures and the final readout as well as between erasures themselves. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the ${\sim} 0.999$ regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices.

quant-ph↗