[Paper Review] Many-body Hilbert space scarring on a superconducting processor

Pengfei Zhang, Hang Dong+22 more|arXiv (Cornell University)|Jan 10, 2022

Quantum Information and Cryptography4 citations

TL;DR

This paper demonstrates many-body Hilbert space scarring in a superconducting quantum processor using a tunable transverse-field Ising model with engineered interactions. By preparing a collective dimerized initial state, the system exhibits persistent revivals in fidelity and imbalance, with localized eigenstates dominating the dynamics—evidenced by high squared overlaps with specific eigenstates—confirming the existence of quantum many-body scars in a non-integrable, non-kicked system, offering a path to suppress thermalization in quantum devices.

ABSTRACT

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

Motivation & Objective

• To demonstrate quantum many-body scarring (QMBS) in a superconducting quantum processor beyond kinetically constrained models.
• To investigate whether QMBS can emerge in a non-integrable, tunable spin chain without emergent dynamical symmetries.
• To verify the existence of scarred eigenstates through experimental observation of revivals in fidelity, imbalance, and entanglement entropy.
• To characterize the robustness of scarring under varying interaction parameters and system sizes.
• To establish a platform for studying weak ergodicity breaking in near-term quantum hardware.

Proposed method

• Engineering a 1D transverse-field Ising model with alternating ferromagnetic (J_a) and antiferromagnetic (J_e) couplings on a superconducting processor with 12–30 qubits.
• Preparing a collective dimerized initial state |Π⟩ as a superposition of spin-ordered configurations to probe scar dynamics.
• Measuring time evolution of fidelity, spin imbalance, and four-qubit entanglement entropy to detect revivals and localization.
• Using randomized initial product states as control to contrast with the scar state dynamics.
• Analyzing squared overlaps between |Π⟩ and eigenstates |E_n⟩ to identify dominant scar-supporting eigenstates.
• Varying interaction strengths (J_a, J_e, J_x) and system sizes (L=12 to 30) to test robustness and scaling behavior.

Experimental results

Research questions

• RQ1 Can quantum many-body scars be experimentally realized in a non-integrable, non-kicked superconducting quantum processor?
• RQ2 Do scarred eigenstates dominate the dynamics of a collective dimerized initial state in the absence of emergent dynamical symmetries?
• RQ3 How do fidelity, imbalance, and entanglement entropy evolve over time for scar states compared to random initial states?
• RQ4 What is the scaling behavior of scar fidelity and overlap with eigenstates as system size increases?
• RQ5 How robust is the scar dynamics to variations in interaction parameters and disorder?

Key findings

• The collective dimerized state |Π⟩ exhibits persistent revivals in fidelity and imbalance up to 20 ms, with fidelity reaching ~0.8 at the first revival, indicating strong non-thermalization.
• Squared overlaps between |Π⟩ and specific eigenstates show sharp peaks at certain energy levels, confirming the presence of scarred eigenstates in the Hilbert space.
• Fidelity revivals for |Π⟩ are significantly stronger than for random initial states, with a 3–5× enhancement in revival amplitude.
• Entanglement entropy for |Π⟩ remains low (~1.2–1.5 ebits) over time, contrasting with the rapid growth seen in random states, indicating suppressed thermalization.
• The scar state fidelity scales inversely with Hilbert space dimension (1/D), with a power-law dependence on 1/L, consistent with theoretical predictions for scar states.
• Robustness is observed across system sizes from L=12 to L=30, with consistent revival patterns and overlap structures, suggesting scalability of the effect.