Quantum Processor Reveals Rényi-2 Entanglement and Symmetries in Random States
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Researchers are increasingly focused on understanding how complex quantum systems exhibit universal behaviours governed by fundamental symmetries. Jia-Nan Yang, Lata Kh Joshi, Filiberto Ares et al. from Zhejiang University and SISSA investigate this phenomenon by probing entanglement and symmetries within random quantum states generated on a superconducting quantum processor. Their work is significant because it experimentally verifies theoretical predictions about the ‘typical’ characteristics of these states, demonstrating agreement with the Haar-random state ensemble. By measuring entanglement entropy, asymmetry, and moments of reduced density matrices, the team reveal distinct entanglement phases and offer a new experimental perspective on the fundamental properties of complex quantum systems. Floquet dynamics generate Haar-random states for many-body system studies, offering a powerful simulation approach Scientists have demonstrated the experimental generation and characterisation of random quantum states, achieving a significant step towards understanding the universal features of complex many-body systems. The research team successfully created these states by evolving simple product states under ergodic Floquet models, a technique utilising periodic driving to induce quantum chaos. Crucially, the generated states exhibit strong agreement with theoretical predictions based on the Haar-random state ensemble, a benchmark for typical quantum behaviour. This work establishes a practical approach to studying entanglement and symmetries in these complex systems, bypassing the need for exponentially difficult direct generation of truly random states. The study employed a superconducting quantum processor to implement low-depth quantum circuits designed to produce approximate state k-designs, ensembles of states mimicking the statistical properties of Haar-random states. Beginning with a simple product state of L qubits, the researchers applied a Floquet circuit, repeating the process τ times to construct the desired random states. Measurements confirmed that the resulting states are largely independent of the specific dynamics used to generate them, validating the approach. Analysis of the generated states revealed an average fidelity converging towards the prediction for Haar-random ensembles, demonstrating the effectiveness of the method. Experiments focused on quantifying key characteristics of these random states, beginning with the measurement of the Rényi-2 entanglement entropy as a function of subsystem size.
The team observed the characteristic Page curve, a hallmark of Haar-random states, indicating the expected scaling of entanglement with system size. Further probing involved investigating subsystem symmetries using entanglement asymmetry, revealing non-trivial behaviour consistent with theoretical predictions. Finally, researchers measured the moments of partially transposed reduced density matrices, successfully identifying distinct entanglement phases within the generated ensembles.
This research extends beyond simply generating random states, offering a new experimental perspective on the typical entanglement and symmetries of many-body quantum systems. By harnessing the intrinsic quantum randomness of projective measurements and incorporating randomness into local potentials, the team has created a versatile platform for benchmarking quantum processors and exploring fundamental aspects of quantum many-body physics. The work opens avenues for applications in areas such as thermalisation, quantum information theory, complexity theory, quantum cryptography, and the simulation of ergodic quantum dynamics. Floquet engineering and random state generation on a superconducting lattice offer new avenues for quantum control Scientists investigated the entanglement and symmetries of random quantum states generated through ergodic Floquet models, finding strong agreement with predictions based on the Haar-random state ensemble. The research team engineered a periodically kicked spin-1/2 system to generate these random states, beginning with a product state |0⟩ and applying a Floquet time-evolution operator, V = e−iH(y)T/3e−iH(z)T/3e−iH(x)T/3, where T represents one Floquet cycle. This operator incorporates Hamiltonians H(x,y,z) describing nearest-neighbor interactions and disordered local fields, defined as H(x,y,z) = J L−1Σl=1 σ+l σ−l+1 + σ−l σ+l+1 + L Σl=1 h(x,y,z)l σ(x,y,z)l, with J denoting the coupling strength and h(x,y,z)l representing random values uniformly distributed between −J and J. Experiments employed a superconducting quantum processor with qubits arranged in a two-dimensional square lattice, setting the nearest-neighbor coupling to J/2π = −5MHz and the Floquet period to T = 90ns. Unitary evolution of the initial product state induces rapid scrambling of quantum information, and after a sufficient number of Floquet cycles τ, the resulting state Vτ|0⟩ closely approximates a state drawn from the Haar measure. The study demonstrated that for system sizes L = 5, 7, 9, and 11, only a few cycles were sufficient to generate an approximate state k-design, closely mirroring Haar-random behavior for k = 2, 3, and 4. To characterise the generated states, the team created an ensemble of states {ρr = |ψr⟩⟨ψr|} and estimated average fidelities between them, observing convergence towards the Haar-random prediction of 2−L after τ = 3 cycles for smaller systems. Subsequently, the researchers measured the Rényi-2 entanglement entropy as a function of subsystem size, successfully observing the Page curve, and probed subsystem symmetries using entanglement asymmetry. Further analysis involved measuring the moments of partially transposed reduced density matrices, revealing distinct entanglement phases and offering an experimental perspective on the typical entanglement and symmetries of random states. Entanglement scaling and symmetry transitions in ergodic Floquet random states reveal novel many-body phenomena Scientists have experimentally studied the entanglement and symmetries of random states generated using ergodic Floquet models, finding excellent agreement with predictions from the Haar-random state ensemble.
The team measured the Rényi-2 entanglement entropy as a function of subsystem size, successfully observing the characteristic Page curve, a key signature of random quantum states. This observation confirms theoretical predictions regarding the entanglement scaling in these systems. Researchers probed subsystem symmetries using entanglement asymmetry, revealing non-trivial behaviour consistent with Haar-random states. Measurements confirm a sharp transition from a symmetric to a non-symmetric state at half-system size, mirroring predictions related to black hole information recovery. The work demonstrates a practical approach to generating state k-designs by incorporating randomness into local potentials within the Floquet models. Experiments revealed that the generated random states are, on average, independent of the dynamics creating them, functioning as approximate state k-designs.
The team’s results closely follow predictions for Haar-random states for the initial values of k tested. Furthermore, scientists measured the moments of partially transposed reduced density matrices, obtained by tracing out part of the system, thereby revealing distinct entanglement phases within the generated ensembles. The study estimates these quantities using the classical shadow formalism, based on randomized measurements performed on a superconducting quantum processor. Measurements of the average fidelity between the generated random states, as a function of Floquet cycle depth τ, converged toward the predicted value of 2−L, where L represents the number of qubits. This convergence validates the effectiveness of the state preparation protocol. The breakthrough delivers an experimental perspective on the typical entanglement and symmetries of many-body quantum systems, opening avenues for benchmarking and characterising quantum devices. Floquet dynamics validate Haar randomness and reveal entanglement phases in driven systems Scientists have experimentally investigated the entanglement and symmetries of random quantum states generated using Floquet models. These states, created by evolving simple product states, demonstrate strong agreement with predictions based on the Haar-random state ensemble, a framework for understanding typical quantum behaviour. Researchers measured the Rényi-2 entanglement entropy and observed the expected Page curve, which describes how entanglement scales with subsystem size. Furthermore, the study probed subsystem symmetries using entanglement asymmetry and measured moments of partially transposed reduced density matrices, revealing distinct entanglement phases within the generated ensembles. The findings highlight the ability of superconducting quantum processors to study complex many-body quantum systems through randomised measurement protocols. Authors acknowledge limitations related to system size and computational complexity, necessitating larger systems and more efficient classical shadow methods for future exploration. Future research could extend this work by generating random states with specific global symmetries, allowing for investigations of chaotic dynamics under conservation laws and a deeper understanding of universal features in quantum systems. 👉 More information 🗞 Probing Entanglement and Symmetries in Random States Using a Superconducting Quantum Processor 🧠 ArXiv: https://arxiv.org/abs/2601.22224 Tags: