FA-91110 / Quantum circuit simulation / Member archive

Reduced density matrix reads the kept bit big-endian · case 05

Keeping qubit 0 of a product state returns the other qubit reduced state.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [n, amps, keep]; trace out every qubit except keep (0 = LSB) from the pure state and return {"rho": 2x2 matrix of [re, im] entries with rho[r][c] = sum psi_r psi_c^*, trace-normalized, "purity": sum |rho_rc|^2}, all rounded to 6 decimals.

Why this case matters

Reduced states quantify entanglement and are used in debugging subsystem behavior; index or conjugation slips give non-physical matrices.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: random reduction 13	`{"purity": 0.59206, "rho": [[[0.285454, 0.0], [0.0, 0.0]], [[0.0, 0.0], [0.714546, 0.0]]]}`	`{"purity": 0.575758, "rho": [[[0.336611, 0.0], [0.097864, 0.040067]], [[0.097864, -0.040067], [0.663389, 0.0]]]}`	Failed

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