| @@ -50,7 +50,7 @@ Let's make a new ``GraphState`` object with a register of three qubits: | |||
| >>> from abp import GraphState | |||
| >>> 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() | |||
| |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 | |||
| |111❭: √1/8 + i √0 | |||
| We can also check the stabilizer tableau: | |||
| We can also check the stabilizer tableau:: | |||
| >>> print g.to_stabilizer() | |||
| 0 1 2 | |||
| @@ -71,7 +71,7 @@ We can also check the stabilizer tableau: | |||
| X | |||
| X | |||
| Or look directly at the vertex operators and neighbour lists: | |||
| Or look directly at the vertex operators and neighbour lists:: | |||
| >>> print g | |||
| 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. | |||
| 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) | |||
| >>> 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 - | |||
| 2: IA - | |||
| And now run some CZ gates: | |||
| And now run some CZ gates:: | |||
| >>> g.act_cz(0,1) | |||
| >>> g.act_cz(1,2) | |||
| @@ -107,7 +107,7 @@ And now run some CZ gates: | |||
| |001❭: √1/4 + i √0 | |||
| |011❭: -√1/4 + i √0 | |||
| Tidy up a bit: | |||
| Tidy up a bit:: | |||
| >>> g.del_node(0) | |||
| >>> g.act_hadamard(0) | |||
| @@ -115,7 +115,7 @@ Tidy up a bit: | |||
| |00❭: √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.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 | |||
| |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_hadamard(0) | |||
| >>> print psi | |||
| |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() | |||
| >>> print tab | |||