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@@ -50,7 +50,7 @@ Let's make a new ``GraphState`` object with a register of three qubits: |
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>>> from abp import GraphState |
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>>> g = GraphState(3) |
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All the qubits are initialized by default in the :math:`|+\rangle` state: |
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All the qubits are initialized by default in the :math:`|+\rangle` state:: |
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>>> print g.to_state_vector() |
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|000❭: √1/8 + i √0 |
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@@ -62,7 +62,7 @@ All the qubits are initialized by default in the :math:`|+\rangle` state: |
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|011❭: √1/8 + i √0 |
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|111❭: √1/8 + i √0 |
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We can also check the stabilizer tableau: |
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We can also check the stabilizer tableau:: |
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>>> print g.to_stabilizer() |
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0 1 2 |
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@@ -71,7 +71,7 @@ We can also check the stabilizer tableau: |
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X |
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X |
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Or look directly at the vertex operators and neighbour lists: |
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Or look directly at the vertex operators and neighbour lists:: |
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>>> print g |
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0: IA - |
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@@ -80,7 +80,7 @@ Or look directly at the vertex operators and neighbour lists: |
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This representation might be unfamiliar. Each row shows the index of the qubit, then the **vertex operator**, then a list of neighbouring qubits. To understand vertex operators, read the original paper by Anders and Briegel. |
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Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to the :math:`H|+\rangle = |1\rangle` state: |
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Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to the :math:`H|+\rangle = |1\rangle` state:: |
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>>> g.act_hadamard(0) |
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>>> print g.to_state_vector() |
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@@ -93,7 +93,7 @@ Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to |
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1: IA - |
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2: IA - |
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And now run some CZ gates: |
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And now run some CZ gates:: |
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>>> g.act_cz(0,1) |
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>>> g.act_cz(1,2) |
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@@ -107,7 +107,7 @@ And now run some CZ gates: |
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|001❭: √1/4 + i √0 |
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|011❭: -√1/4 + i √0 |
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Tidy up a bit: |
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Tidy up a bit:: |
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>>> g.del_node(0) |
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>>> g.act_hadamard(0) |
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@@ -115,7 +115,7 @@ Tidy up a bit: |
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|00❭: √1/2 + i √0 |
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|11❭: √1/2 + i √0 |
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Cool, we made a Bell state. Incidentally, those those state vectors and stabilizers are genuine Python objects, not just stringy representations of the state: |
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Cool, we made a Bell state. Incidentally, those those state vectors and stabilizers are genuine Python objects, not just stringy representations of the state:: |
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>>> g = abp.GraphState(2) |
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>>> g.act_cz(0, 1) |
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@@ -125,14 +125,14 @@ Cool, we made a Bell state. Incidentally, those those state vectors and stabiliz |
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|00❭: √1/2 + i √0 |
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|11❭: √1/2 + i √0 |
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``psi`` is a state vector -- i.e. it is an exponentially large vector of complex numbers. We can still run gates on it: |
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``psi`` is a state vector -- i.e. it is an exponentially large vector of complex numbers. We can still run gates on it:: |
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>>> psi.act_cnot(0, 1) |
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>>> psi.act_hadamard(0) |
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>>> print psi |
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|00❭: √1 + i √0 |
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But these operations will be very slow. Let's have a look at the stabilizer tableau: |
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But these operations will be very slow. Let's have a look at the stabilizer tableau:: |
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>>> tab = g.to_stabilizer() |
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>>> print tab |
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