Entanglement entropy matches predictions on IBM processor

Researchers from the University of the Bundeswehr Munich and collaborating institutions have demonstrated that entropies measured on an IBM superconducting processor closely follow theoretical predictions without any fitted parameters. The work details how stochastic resetting, applying resets to qubits mid-circuit, creates unique, stable quantum states, and examines the resulting entanglement when reset histories are either tracked or averaged.

These two diagnostics respond differently because they read different components of the same reconstructed state, and a depolarizing model captures the concurrence suppression with one fitted parameter. The difference between the two entropies, i. e., the Jensen gap, equals the Holevo information that a subsystem retains about the time since the last reset, growing with chain length across the sizes studied.

Stochastic Resetting Drives Nonequilibrium Stationary States

Phase matching between energy eigenstates generates resonances within the stationary states created by stochastic resetting, and the visibility of these resonances is directly linked to the symmetry of the reset state itself. Researchers from the University of the Bundeswehr Munich and collaborating institutions derived closed-form results for two qubits, revealing this connection between reset state symmetry and resonance visibility, a detail not achievable through uninterrupted quantum evolution.

These theoretical findings demonstrate that the application of resets mid-circuit establishes unique, stable quantum states impossible to reach with standard unitary processes. This level of agreement is notable given the inherent challenges of calibrating and adjusting real-world quantum hardware to match theoretical models. It validates the approach to achieving nonequilibrium stationary states. However, the same experiments revealed a discrepancy. Concurrence, another measure of entanglement, consistently fell below predictions across most hardware measurements.

This difference in behavior between entanglement entropy and concurrence indicates that these diagnostics respond to different components of the reconstructed quantum state, highlighting the nuances of entanglement manifestation on the IBM processor. A depolarizing model successfully captured the suppression of concurrence with only one fitted parameter, suggesting that environmental noise plays a significant role in reducing the observed entanglement. With a Bell-state reset, this information grows with chain length, without visible saturation across the sizes studied, suggesting a potential for increasing information retention in larger systems.

Transverse-Field Ising Chain Analyzed with Up To 12 Qubits

Calculations of the transverse-field Ising chain extended to 12 qubits demonstrate the model’s capacity to simulate increasingly complex quantum systems. This level of analytical rigor, applied to a system undergoing stochastic resetting, reveals how entanglement characteristics depend on whether the history of these resets is fully accounted for or averaged. Analysis of the reset stationary state extended to chains, revealing a resonance structure mirroring the two-qubit system.

Phase Matching Resonances in Two-Qubit Systems

The work reveals that the symmetry of the reset state, the method used to return qubits to a known condition, influences which resonant features are observable. Researchers derived these insights by analyzing both a two-qubit system with closed-form results and chains extending to 12 qubits through exact evaluation.

The difference between two entanglement entropy measurements, termed the Jensen gap, directly quantifies information a quantum subsystem retains about the time elapsed since its last reset. Calculations reveal this gap equals the Holevo information, a theoretical bound on how much reset age a measurement on the subsystem can reveal. Analysis of quantum chains shows the Jensen gap for a half-chain subsystem grows with chain length using a tiled-Bell reset, with no sign of saturation.

Averaged-state entropy, measuring mixedness in the stationary state, increases due to the uncertainty of reset age. “The Jensen gap of a subsystem A bounds the information about the age that any measurement on An alone can extract,” the researchers write, emphasizing the fundamental limit on information retrieval.

Researchers calculated trajectory-averaged entropy and averaged-state entropy to assess entanglement, alongside the Wootters concurrence, a measure of entanglement for mixed states, to compare with hardware results.

Depolarizing Model Corrects Concurrence Suppression

Entanglement entropy measurements on an IBM superconducting processor closely aligned with theoretical predictions, requiring no fitted parameters, while concurrence, a separate measure of entanglement, deviated from those same predictions across most experimental conditions. This discrepancy highlights that different entanglement diagnostics can reveal distinct aspects of a quantum state, even when assessing the same system undergoing stochastic resetting. Researchers found that a depolarizing model, incorporating a single fitted parameter, successfully captured the observed suppression of concurrence.

Bell-State Reset Increases Information with Chain Length

The ability of a quantum system to retain information about the timing of a reset operation increases as the system grows, according to new analysis of entangled qubits. Calculations reveal a distinct response between single-site and half-chain subsystems. The single-site Jensen gap remains limited to one bit of information. Conversely, the half-chain Jensen gap grows with increasing chain length for a tiled-Bell reset, a pattern observed across a range of reset probabilities. These finite-size results demonstrate how reset history influences entanglement characteristics. The differing behavior of entanglement entropy and concurrence, two methods for characterizing quantum entanglement, further illuminates these dynamics.

Trajectory-Averaged Entropy Avoids Postselection

This method obtains the trajectory-averaged entropy without postselection by sampling and recording reset times classically, unlike circuits that require exponentially rare measurement records. Calculations demonstrate that this trajectory-averaged entropy, and its associated Jensen gap, is sensitive to phase-matching conditions invisible when examining only the averaged density matrix. The researchers verified these theoretical findings by evaluating equations for two qubits and simulating chains, achieving exact solutions for the system.

Resonance Condition: Eigenvalue Coincidence Marks Entropies

“For two qubits, a coherence between energy eigenstates i and j survives the averaging unchanged when (E_i-E_j)T ∈ 2πZ, provided the reset state overlaps with both eigenstates,” the researchers write, detailing the conditions for sustained coherence. These findings highlight the complex interplay between reset strategies, energy spectra and the resulting entanglement properties in driven quantum systems.

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