Curator's Take
This article shows that even when a small programmable qubit bath equilibrates within charge‑conserving sectors, the probe qubit does not settle into a true Gibbs state, revealing a “sector‑memory” obstruction that challenges common assumptions about thermalization in finite quantum simulators. By combining exact Haar‑random simulations with Floquet circuits on IBM hardware, the authors demonstrate a concrete diagnostic framework (sector‑resolved populations, memory variance and global Gibbs error) that can be used to benchmark how well near‑term devices emulate open‑system dynamics. The findings underscore that preserving symmetries in engineered environments may limit their usefulness for realistic bath engineering, a point that will shape future designs of quantum simulators and error‑mitigation strategies.
— Mark Eatherly
Summary
Finite quantum environments can relax local probes without acting as canonical baths. We study this distinction for a probe qubit coupled to a programmable bath of ($N$) qubits under excitation-number-conserving dynamics. The conserved charge partitions the Hilbert space into sectors. We characterize probe-level bath emergence using the sector-resolved late-time population ($p_e^{(q)}$), the sector-memory variance ($M_N$), and a global Gibbs-fit error ($Δ_G^{\mathrm{global}}$). Exact simulations with Haar-random pure states in each complete fixed-charge sector yield sector-dependent populations close to the maximally mixed-sector benchmark ($p_e^{(q)}=q/(N+1)$), producing a nonzero Gibbs obstruction. We then construct charge-preserving Floquet circuits using ($R_z$) phases and ($XX+YY$) exchange gates, validate them with ideal and noisy Qiskit simulations, and implement finite-depth experiments on IBM Fez. For ($N=4$) and ($ε=0$), the hardware data give ($M_N \simeq 0.044$), ($Δ_G^{\mathrm{global}} \simeq 0.558$), and charge preservation near 0.90 after readout mitigation. A paired symmetry-breaking scan using bath ($R_x(ε)$) rotations reduces both diagnostics while increasing charge leakage, but does not erase sector ordering over the accessible depths. These results show that equilibration within constrained sectors is insufficient to produce a single sector-independent Gibbs state for the probe.