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@@ -78,7 +78,7 @@ Or look directly at the vertex operators and neighbour lists: |
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1: IA - |
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2: IA - |
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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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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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@@ -88,7 +88,6 @@ Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to |
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|010❭: √1/4 + i √0 |
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|001❭: √1/4 + i √0 |
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|011❭: √1/4 + i √0 |
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>>> print g |
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0: YC - |
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1: IA - |
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@@ -102,7 +101,6 @@ And now run some CZ gates: |
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0: YC - |
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1: IA (2,) |
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2: IA (1,) |
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>>> print g.to_state_vector() |
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|000❭: √1/4 + i √0 |
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|010❭: √1/4 + i √0 |
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@@ -117,9 +115,35 @@ 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 real objects with methods, not just string-like 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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>>> g.act_hadamard(0) |
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>>> psi = g.to_state_vector() |
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>>> print psi |
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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.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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>>> tab = g.to_stabilizer() |
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>>> print tab |
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0 1 |
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------ |
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Z Z |
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X X |
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>>> print tab.tableau |
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{0: {0: 3, 1: 3}, 1: {0: 1, 1: 1}} |
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>>> print tab[0, 0] |
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3 |
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GraphState API |
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