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Pete Shadbolt 8 年之前
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@@ -50,7 +50,7 @@ Let's make a new ``GraphState`` object with a register of three qubits:
>>> from abp import GraphState >>> from abp import GraphState
>>> g = GraphState(3) >>> g = GraphState(3)


All the qubits are initialized by default in the :math:`|+\rangle` state:
All the qubits are initialized by default in the :math:`|+\rangle` state::


>>> print g.to_state_vector() >>> print g.to_state_vector()
|000❭: √1/8 + i √0 |000❭: √1/8 + i √0
@@ -62,7 +62,7 @@ All the qubits are initialized by default in the :math:`|+\rangle` state:
|011❭: √1/8 + i √0 |011❭: √1/8 + i √0
|111❭: √1/8 + i √0 |111❭: √1/8 + i √0


We can also check the stabilizer tableau:
We can also check the stabilizer tableau::


>>> print g.to_stabilizer() >>> print g.to_stabilizer()
0 1 2 0 1 2
@@ -71,7 +71,7 @@ We can also check the stabilizer tableau:
X X
X X


Or look directly at the vertex operators and neighbour lists:
Or look directly at the vertex operators and neighbour lists::


>>> print g >>> print g
0: IA - 0: IA -
@@ -80,7 +80,7 @@ Or look directly at the vertex operators and neighbour lists:


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. 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.


Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to the :math:`H|+\rangle = |1\rangle` state:
Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to the :math:`H|+\rangle = |1\rangle` state::


>>> g.act_hadamard(0) >>> g.act_hadamard(0)
>>> print g.to_state_vector() >>> print g.to_state_vector()
@@ -93,7 +93,7 @@ Let's act a Hadamard gate on the zeroth qubit -- this will evolve qubit ``0`` to
1: IA - 1: IA -
2: IA - 2: IA -


And now run some CZ gates:
And now run some CZ gates::


>>> g.act_cz(0,1) >>> g.act_cz(0,1)
>>> g.act_cz(1,2) >>> g.act_cz(1,2)
@@ -107,7 +107,7 @@ And now run some CZ gates:
|001❭: √1/4 + i √0 |001❭: √1/4 + i √0
|011❭: -√1/4 + i √0 |011❭: -√1/4 + i √0


Tidy up a bit:
Tidy up a bit::


>>> g.del_node(0) >>> g.del_node(0)
>>> g.act_hadamard(0) >>> g.act_hadamard(0)
@@ -115,7 +115,7 @@ Tidy up a bit:
|00❭: √1/2 + i √0 |00❭: √1/2 + i √0
|11❭: √1/2 + i √0 |11❭: √1/2 + i √0


Cool, we made a Bell state. Incidentally, those those state vectors and stabilizers are genuine Python objects, not just stringy representations of the state:
Cool, we made a Bell state. Incidentally, those those state vectors and stabilizers are genuine Python objects, not just stringy representations of the state::


>>> g = abp.GraphState(2) >>> g = abp.GraphState(2)
>>> g.act_cz(0, 1) >>> g.act_cz(0, 1)
@@ -125,14 +125,14 @@ Cool, we made a Bell state. Incidentally, those those state vectors and stabiliz
|00❭: √1/2 + i √0 |00❭: √1/2 + i √0
|11❭: √1/2 + i √0 |11❭: √1/2 + i √0


``psi`` is a state vector -- i.e. it is an exponentially large vector of complex numbers. We can still run gates on it:
``psi`` is a state vector -- i.e. it is an exponentially large vector of complex numbers. We can still run gates on it::


>>> psi.act_cnot(0, 1) >>> psi.act_cnot(0, 1)
>>> psi.act_hadamard(0) >>> psi.act_hadamard(0)
>>> print psi >>> print psi
|00❭: √1 + i √0 |00❭: √1 + i √0


But these operations will be very slow. Let's have a look at the stabilizer tableau:
But these operations will be very slow. Let's have a look at the stabilizer tableau::


>>> tab = g.to_stabilizer() >>> tab = g.to_stabilizer()
>>> print tab >>> print tab


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