在有限可编程量子比特环境中探测级浴驰豫的扇节存储阻碍
Sector-memory obstruction to probe-level bath emergence in finite programmable qubit environments
AI总结：
研究有限量子环境中与可编程量子比特浴耦合的探测量子比特，通过表征扇节分辨晚期布居、扇节存储方差和全局吉布斯拟合误差来分析探测级浴的出现，用精确模拟和实验得出相关结果。
摘要：
有限量子环境可使局部探测器弛豫而无需充当标准浴。我们研究了在激发数守恒动力学下与（\(N\)）个量子比特的可编程浴耦合的探测量子比特的这种区别。守恒电荷将希尔伯特空间划分为扇区。我们使用扇区分辨晚期布居（\(p_e^{(q)}\)）、扇区存储方差（\(M_N\)）和全局吉布斯拟合误差（\(\Delta_G^{\mathrm{global}}\)）来表征探测级浴的出现。在每个完整固定电荷扇区中使用哈尔随机纯态进行精确模拟，得出与扇区相关的布居接近最大混合扇区基准（\(p_e^{(q)}=q/(N + 1)\)），产生非零的吉布斯阻碍。然后我们使用（\(R_z\)）相位和（\(XX + YY\)）交换门构建保电荷弗洛凯电路，用理想和有噪声的Qiskit模拟进行验证，并在IBM Fez上进行有限深度实验。对于（\(N = 4\)）和（\(\epsilon = 0\)），硬件数据给出（\(M_N \simeq 0.044\)），（\(\Delta_G^{\mathrm{global}} \simeq 0.558\)），并且在读出缓解后电荷保持接近0.90。使用浴（\(R_x(\epsilon)\)）旋转的配对对称破缺扫描减少了这两种诊断，同时增加了电荷泄漏，但在可及深度上没有消除扇区排序。这些结果表明，在受限扇区内的平衡不足以使探测器形成与扇区无关的单一吉布斯态。
英文摘要：
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.
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