def partial_trace_cupy(rho: cupy.ndarray, retain_qubits) -> cupy.ndarray:
"""
Compute the partial trace of rho.
Args:
rho: input rho
retain_qubits: the qubits which we want to keep after partial trace.
"""
if len(retain_qubits) == 0:
return trace(rho)
total_qb = int(math.log2(rho.shape[0]))
assert min(retain_qubits) >= 0 and max(retain_qubits) < total_qb
if total_qb == 1 or len(retain_qubits) == total_qb:
return rho
all_qbs = list(range(total_qb))
qbs_to_remove = list(filter(lambda x: x not in retain_qubits, all_qbs))
rho = rho.reshape([2] * (2 * total_qb))
for qid in reversed(qbs_to_remove):
rho = trace(rho, axis1=qid, axis2=qid + total_qb)
total_qb -= 1
# retain back to normal density matrix
newshape = 2 ** total_qb
return rho.reshape(newshape, newshape)
def partial_trace_wf_cupy(iwf: cupy.ndarray, retain_qubits):
nqb = int(math_log2(iwf.shape[0]))
if len(retain_qubits) == nqb:
return outer(iwf, iwf.conj())
iwf = iwf.reshape([2] * nqb, order="C")
retain_qubits = sorted(retain_qubits)
for idx in range(len(retain_qubits)):
r = retain_qubits[idx]
if idx != r:
iwf = iwf.swapaxes(idx, r)
iwf = iwf.reshape((2 ** nqb,))
return partial_trace_wf_keep_first_cupy(iwf, len(retain_qubits))
def partial_trace_1d_cupy(rho: cupy.ndarray, retain_qubit: int):
"""
Compute the partial trace of rho. Returns a reduced density matrix
in the Hilbert space of "retain_qubit"th qubit.
"""
total_qb = int(math.log2(rho.shape[0]))
if retain_qubit >= total_qb or retain_qubit < 0:
raise ValueError(retain_qubit)
if total_qb == 1:
return rho
all_qbs = list(range(total_qb))
qbs_to_remove = list(filter(lambda x: x != retain_qubit, all_qbs))
assert qbs_to_remove == list(sorted(qbs_to_remove))
rho = rho.reshape([2] * (2 * total_qb))
# ret = np.empty(shape=(2,2), dtype=complex)
ret = None
for qid in reversed(qbs_to_remove):
# remove the qubit with higher qubit count first, this is crucial
# otherwise we will have indexing problems.
if ret is None:
ret = trace(rho, axis1=qid, axis2=qid + total_qb)
total_qb -= 1 # removed one already
else:
ret = trace(ret, axis1=qid, axis2=qid + total_qb)
total_qb -= 1 # removed one already
assert ret.shape == (2, 2)
return ret