decompositions for multi-qubit gates when partials are impossible
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Daniel Tsvetkov
parent
92ccea6469
commit
09d9b78683
91
lib.py
91
lib.py
@ -602,8 +602,8 @@ class HermitianMatrix(SquareMatrix):
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class UnitaryOperator(LinearTransformation, UnitaryMatrix):
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def __init__(self, m: ListOrNdarray, name: str = '', partials=None, *args,
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**kwargs):
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def __init__(self, m: ListOrNdarray, name: str = '', partials=None,
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decomposition=None, *args, **kwargs):
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"""UnitaryOperator inherits from both LinearTransformation and a
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Unitary matrix
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It is used to act on a State vector by defining the operator to be
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@ -614,13 +614,15 @@ class UnitaryOperator(LinearTransformation, UnitaryMatrix):
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the list is the Nth partial that is used, i.e. for the first - |0><0|,
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for the second - |1><1|
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"""
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if np.shape(m) != (2, 2) and partials is None:
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raise Exception("Please define partials in a non-single operator")
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if np.shape(m) != (2, 2) and partials is None and decomposition is None:
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raise Exception("Please define partials or decomposition in "
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"a non-single operator")
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UnitaryMatrix.__init__(self, m=m, *args, **kwargs)
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LinearTransformation.__init__(self, m=m, func=self.operator_func, *args,
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**kwargs)
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self.name = name
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self.partials = partials
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self.decomposition = decomposition
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def operator_func(self, other, which_qbit=None):
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this_cols, other_rows = np.shape(self.m)[1], np.shape(other.m)[0]
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@ -631,6 +633,8 @@ class UnitaryOperator(LinearTransformation, UnitaryMatrix):
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"Please specify which_qubit to operate on".format(
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this_cols, other_rows))
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total_qbits = int(np.log2(other_rows))
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if type(which_qbit) is list and len(which_qbit) == 1:
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which_qbit = which_qbit[0]
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if type(which_qbit) is int:
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# single qubit-gate
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assert this_cols == 2
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@ -639,39 +643,40 @@ class UnitaryOperator(LinearTransformation, UnitaryMatrix):
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range(total_qbits)]
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new_m = np.prod(extended_m).m
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elif type(which_qbit) is list:
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# single or multiple qubit-gate
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assert 1 <= len(which_qbit) <= total_qbits
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assert len(which_qbit) == len(self.partials)
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assert all([q < total_qbits for q in which_qbit])
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this_gate_len = 2 ** (len(self.partials) - 1)
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bins = generate_bins(this_gate_len)
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extended_m, next_control = [[] for _ in bins], 0
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partial_mapping = dict(zip(which_qbit, self.partials))
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for qbit in range(total_qbits):
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if qbit not in partial_mapping:
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for i in range(this_gate_len):
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extended_m[i].append(I)
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else:
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this_partial = partial_mapping[qbit]
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# TODO: This works only with C_partial :(((
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if this_partial == C_partial:
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if self.decomposition:
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return self.decomposition(other, *which_qbit)
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else:
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# single or multiple qubit-gate
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assert 1 <= len(which_qbit) <= total_qbits
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assert len(which_qbit) == len(self.partials)
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assert all([q < total_qbits for q in which_qbit])
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this_gate_len = 2 ** (len(self.partials) - 1)
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bins = generate_bins(this_gate_len)
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extended_m, next_control = [[] for _ in bins], 0
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partial_mapping = dict(zip(which_qbit, self.partials))
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for qbit in range(total_qbits):
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if qbit not in partial_mapping:
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for i in range(this_gate_len):
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bin_dig = bins[i][next_control]
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extended_m[i].append(
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s("|" + bin_dig + "><" + bin_dig + "|"))
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next_control += 1
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else:
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for i in range(this_gate_len - 1):
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extended_m[i].append(I)
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extended_m[-1].append(this_partial)
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new_m = sum([np.prod(e).m for e in extended_m])
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else:
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this_partial = partial_mapping[qbit]
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# TODO: This works only with C_partial :(((
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if this_partial == C_partial:
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for i in range(this_gate_len):
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bin_dig = bins[i][next_control]
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extended_m[i].append(
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s("|" + bin_dig + "><" + bin_dig + "|"))
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next_control += 1
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else:
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for i in range(this_gate_len - 1):
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extended_m[i].append(I)
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extended_m[-1].append(this_partial)
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new_m = sum([np.prod(e).m for e in extended_m])
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else:
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raise Exception(
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"which_qubit needs to be either an int of N-th qubit or list")
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extended_op = UnitaryOperator(new_m, name=self.name,
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partials=self.partials)
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return State(np.dot(extended_op.m, other.m))
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return State(np.dot(new_m, other.m))
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def __repr__(self):
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if self.name:
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@ -836,8 +841,7 @@ T = lambda phi: Gate([[1, 0],
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#
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# Decomposed CNOT :
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# reverse engineered from
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# https://quantumcomputing.stackexchange.com/questions/4252/how-to-derive-the
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# -cnot-matrix-for-a-3-qbit-system-where-the-control-target-qbi
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# https://quantumcomputing.stackexchange.com/questions/4252/how-to-derive-the-cnot-matrix-for-a-3-qbit-system-where-the-control-target-qbi
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#
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# CNOT(q1, I, q2):
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# |0><0| x I_2 x I_2 + |1><1| x I_2 x X
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@ -874,13 +878,17 @@ CZ = Gate([
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[0, 0, 0, -1],
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], name="CZ", partials=[C_partial, z_partial])
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# TODO: These are not the correct partials
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# Can't do partials for SWAP, but can be decomposed
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# SWAP is decomposed into three CNOTs where the second one is flipped
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SWAP = Gate([
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[1, 0, 0, 0],
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[0, 0, 1, 0],
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[0, 1, 0, 0],
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[0, 0, 0, 1],
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], name="SWAP", partials=[C_partial, C_partial])
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], name="SWAP",
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decomposition=lambda state, x, y:
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CNOT.on(CNOT.on(CNOT.on(state, [x, y]), [y, x]), [x, y])
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)
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TOFF = Gate([
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@ -1012,6 +1020,10 @@ def test_eigenstuff():
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def test_partials():
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# test single qbit state
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assert X.on(s("|000>"), which_qbit=1) == s("|010>")
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assert X.on(s("|000>"), which_qbit=[1]) == s("|010>")
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# normal 2 qbit state
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assert CNOT.on(s("|00>")) == s("|00>")
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assert CNOT.on(s("|10>")) == s("|11>")
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@ -1024,9 +1036,12 @@ def test_partials():
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assert CNOT.on(s("|01>"), which_qbit=[1, 0]) == s("|11>")
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assert CNOT.on(s("|001>"), which_qbit=[2, 0]) == s("|101>")
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# Test SWAP via 3 successive CNOTs, the second is flipped
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# Test SWAP via 3 successive CNOTs, the second CNOT is flipped
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assert CNOT.on(CNOT.on(CNOT.on(s("|10>")), which_qbit=[1, 0])) == s("|01>")
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# Test SWAP via 3 successive CNOTs, the 0<->2 are swapped
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assert CNOT.on(CNOT.on(CNOT.on(s("|100>"), [0, 2]), [2, 0]), [0, 2]) == s("|001>")
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# apply on 0, 1 of 3qbit state
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assert CNOT.on(s("|000>"), which_qbit=[0, 1]) == s("|000>")
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assert CNOT.on(s("|100>"), which_qbit=[0, 1]) == s("|110>")
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@ -1048,8 +1063,8 @@ def test_partials():
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# test SWAP gate
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assert SWAP.on(s("|10>")) == s("|01>")
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assert SWAP.on(s("|01>")) == s("|10>")
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# TODO:
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# assert SWAP.on(s("|001>"), which_qbit=[0, 2]) == s("|100>")
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# Tests SWAP on far-away gates
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assert SWAP.on(s("|001>"), which_qbit=[0, 2]) == s("|100>")
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# test Toffoli gate
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assert TOFF.on(s("|000>")) == s("|000>")
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