State utility functions for simulator

numqi.sim.state

`numqi.sim.state.measure_quantum_vector(q0, index, seed=None)`

measure the quantum vector

Parameters:

Name	Type	Description	Default
`q0`	`ndarray`	the quantum vector, `ndim=1`	required
`index`	`(int, tuple[int])`	the index to measure, must be sorted (ascending)	required
`seed`	`(int, None, Generator)`	the random seed	`None`

Returns:

Name	Type	Description
`bitstr`	`list[int]`	the measurement result
`prob`	`ndarray`	the probability of each result
`q1`	`ndarray`	the quantum vector after measurement

`numqi.sim.state.new_base(num_qubit, dtype=np.complex128)`

return the base state of the qubit quantum system

Parameters:

Name	Type	Description	Default
`num_qubit`	`int`	the number of qubits	required
`dtype`	`dtype`	the data type of the base state	`complex128`

Returns:

Name	Type	Description
`ret`	`ndarray`	the base state

`numqi.sim.state.reduce_shape_index(shape, index)`

reduce the shape and index

group index by None
group index by integer

Parameters:

Name	Type	Description	Default
`shape`	`tuple[int]`	the shape of the tensor	required
`index`	`tuple[int \| None]`	the index list	required

Returns:

Name	Type	Description
`reduced_shape`	`tuple[int]`	the reduced shape
`reduced_index`	`tuple[int \| None]`	the reduced index list

`numqi.sim.state.apply_gate(q0, op, index)`

apply the gate to the quantum vector

Parameters:

Name	Type	Description	Default
`q0`	`ndarray`	the quantum vector, `ndim=1`	required
`op`	`ndarray`	the gate, `ndim=2`	required
`index`	`(int, tuple[int])`	the index of the qubits to apply the gate, count from left to right \|0123>	required

Returns:

Name	Type	Description
`ret`	`ndarray`	the quantum vector after applying the gate

`numqi.sim.state.apply_gate_grad(q0_conj, q0_grad, op, index, tag_op_grad=True)`

gradient back propagation of apply_gate

Parameters:

Name	Type	Description	Default
`q0_conj`	`ndarray`	the conjugate of the quantum vector, `ndim=1`	required
`q0_grad`	`ndarray`	the gradient of the quantum vector, `ndim=1`	required
`op`	`ndarray`	the gate, `ndim=2`	required
`index`	`(int, tuple[int])`	the index of the qubits to apply the gate	required
`tag_op_grad`	`bool`	whether to calculate the gradient of the gate	`True`

Returns:

Name	Type	Description
`q0_conj`	`ndarray`	the conjugate of the quantum vector before applying the gate
`q0_grad`	`ndarray`	the gradient of the quantum vector before applying the gate
`op_grad`	`(ndarray, None)`	the gradient of the gate, None if `tag_op_grad=False`

`numqi.sim.state.apply_control_n_gate(q0, op, ind_control_set, ind_target)`

apply the n-controlled gate to the quantum vector

Parameters:

Name	Type	Description	Default
`q0`	`ndarray`	the quantum vector, `ndim=1`	required
`op`	`ndarray`	the gate, `ndim=2`	required
`ind_control_set`	`(int, set[int])`	the index of the control qubits	required
`ind_target`	`(int, tuple[int])`	the index of the target qubits	required

Returns:

Name	Type	Description
`ret`	`ndarray`	the quantum vector after applying the gate

`numqi.sim.state.apply_control_n_gate_grad(q0_conj, q0_grad, op, ind_control_set, ind_target, tag_op_grad=True)`

gradient back propagation of apply_control_n_gate

Parameters:

Name	Type	Description	Default
`q0_conj`	`ndarray`	the conjugate of the quantum vector, `ndim=1`	required
`q0_grad`	`ndarray`	the gradient of the quantum vector, `ndim=1`	required
`op`	`ndarray`	the gate, `ndim=2`	required
`ind_control_set`	`(int, set[int])`	the index of the control qubits	required
`ind_target`	`(int, tuple[int])`	the index of the target qubits	required
`tag_op_grad`	`bool`	whether to calculate the gradient of the gate	`True`

Returns:

Name	Type	Description
`q0_conj`	`ndarray`	the conjugate of the quantum vector before applying the gate
`q0_grad`	`ndarray`	the gradient of the quantum vector before applying the gate
`op_grad`	`(ndarray, None)`	the gradient of the gate, None if `tag_op_grad=False`

`numqi.sim.state.inner_product_psi0_O_psi1(psi0, psi1, op_list)`

calculate the inner product of

Parameters:

Name	Type	Description	Default
`psi0`	`ndarray`	the quantum vector, `ndim=1`	required
`psi1`	`ndarray`	the quantum vector, `ndim=1`	required
`op_list`	`list[list[tuple]]`	the operator list. The first level of list is the sum of the operator and the second level of list is matrix multiplication (from left to right). Each tuple is a gate and the index	required

Returns:

Name	Type	Description
`ret`	`ndarray`	the inner product, `ndim=1` of the length equal to the number of operators (first level of list)

`numqi.sim.state.reduce_to_probability(q0, keep_index_set)`

reduce the quantum vector to the probability

Parameters:

Name	Type	Description	Default
`q0`	`ndarray`	the quantum vector, `ndim=1`	required
`keep_index_set`	`set[int]`	the index to keep	required

Returns:

Name	Type	Description
`ret`	`ndarray`	the probability