B8 — Operator Loschmidt echo

Source: examples/b8_ole/

The 56-qubit operator Loschmidt echo of arXiv:2607.25998 on ibm_boston, estimated by the paper's hybrid Pauli-propagation Monte Carlo (PP-MC), with caches that extend past one node through the MPI engine.

The circuit

The circuit is the Quantum Advantage Tracker’s operator_loschmidt_echo_56x1488: a CZ kicked-Ising Floquet echo U V_δ U† on a heavy-hex patch. Its 11 scattering qubits carry an rx angle shifted by η = 3πα/2. echo_half(L, η) rebuilds the measured half C for any depth and reproduces the six vendored tracker files gate for gate. The echo is S_δ = 2⁻ⁿ Tr(A V_δ† A V_δ), where A = C†OC, O = Z^{⊗12}, and V_δ = ⊗ e^{-iδX} on 35 qubits with δ = 0.3.

PP-MC

import ole
from paulistrings import truncation
policy = truncation.collapse_sample(cache=500_000_000, seed=s)
A = O.propagate(C, policy, direction="heisenberg")
S = ole.diagonal_echo(ole.anticommute_histogram(A, sites, "x"), 0.3)

• collapse_sample propagates exactly until a gate leaves more than cache strings.
• It then draws one string with probability b_P²/Σb² and restarts from it.
• The last block is kept whole.
• The diagonal estimator Σ b_P² cos(2δ)^{n_P} / Σ b² is the resummed moment series of the paper’s Eq. (C34).
• ole.rotated_overlap gives the exact echo of the same A, off-diagonal terms included.
• Both estimators are numpy over A.to_arrays(); under comm= each rank reads its result="local" share and comm.allreduce sums the values.
• collapse_sample draws the same string whatever the thread count.

Cost

One L = 6 trajectory at η = 9π/40 on 8 threads of ccqlin038 (Xeon Gold 6244):

For comparison, the paper’s Table VI reports about 8 minutes on 10 cores and 8–10 GB at cache 5e7. scripts/slurm/ole-ppmc-disbatch.sbatch runs the 800-trajectory sweep, and scripts/slurm/ole-mpi.sbatch runs caches beyond one node’s memory.