quairkit.core.state.backend¶

The module that implements various backends of the state.

class quairkit.core.state.backend.State(data, sys_dim, system_seq=None)¶

The abstract base class for quantum states in QuAIRKit.

Parameters:¶

data : Tensor¶: tensor array for quantum state(s).
sys_dim : List[int]¶: a list of dimensions for each system.
system_seq : List[int] | None¶: the system order of this state. Defaults to be from 0 to n - 1.

abstract prob_select(outcome_idx, prob_idx=-1)¶

Indexing probability outcome from the State batch along the given dimension.

Parameters:¶

outcome_idx : Tensor¶: the 1-D tensor containing the outcomes to index
prob_idx : int¶: the int that indexing which probability distribution. Defaults to be the last distribution.

Returns:¶

States that are selected by the specific probability outcomes.

Return type:¶

State

abstract expand(batch_dim)¶

Expand the batch dimension of the State.

Parameters:¶

batch_dim : List[int]¶: the new batch dimension

Note

See torch.expand() for more information about expand. This expand function, however, may change the format of _data to keep save memory.

expand_as(other)¶

Expand this tensor to the same size as other.

Parameters:¶

other : State | Tensor¶: the state/tensor to be expanded to. Note that if other is a torch.Tensor, the batch dimension of the state will be expanded to the same size as other.

Note

See torch.Tensor.expand_as() for more information about expand. This expand function, however, may change the format of _data to keep save memory.

abstract property backend : str¶: The backend of this state.

abstract static check(data, sys_dim, eps=0.0001)¶

Assert whether the input data is valid for the specific State class.

Parameters:¶

data : Tensor¶: tensor array for quantum state(s).
sys_dim : int | List[int]¶: (list of) dimension(s) of the systems, can be a list of integers or an integer.
eps : float | None¶: the tolerance for the numerical check. Can be None means the check is overridden.

Returns:¶

the number of systems.

Return type:¶

int

property data : Tensor¶: The data tensor of this state

property probability : Tensor¶: The probability distribution(s) of these states’ occurrences

property batch_dim : list[int]¶: The batch dimension of this state

property shape : Size¶: The shape of this state

property dtype : dtype¶: The data type of this state

property device : device¶: The device of this state

numel()¶

The number of elements in this data

property dim : int¶: The dimension of this state

property system_dim : list[int]¶: The list of dimensions for each system

are_qubits()¶

Whether all systems are qubits

are_qutrits()¶

Whether all systems are qutrits

property num_systems : int¶: The number of systems

property num_qubits : int¶: The number of qubits of this state, when all systems are qubits

abstract property ket : Tensor¶: The ket form of this state

Note

If the state is pure, the ket form is the statevector representation. If the state is mixed, the ket form is the vectorization of its density matrix representation.

property bra : Tensor¶: Dagger of the ket form.

abstract property density_matrix : Tensor¶: The density matrix representation of this state.

property vec : Tensor¶

\(\textrm{vec}(|i \rangle\langle j|)=|j, i \rangle\)

Type:¶: Vectorization of the state

property rank : list[int]¶: The rank of the state.

abstract normalize()¶

Normalize this state

numpy()¶

Get the data in numpy.

Returns:¶: The numpy array of the data for the quantum state.
Return type:¶: ndarray

abstract clone()¶

Return a copy of the quantum state.

abstract fit(state_backend)¶

Convert the data to the specified backend.

Parameters:¶

state_backend : str¶: the target backend of the state. Available options see quairkit.Backend.

Returns:¶

a copy of the fitted data.

Return type:¶

Tensor

to(dtype=None, device=None)¶

Change the property of the data tensor, and return a copy of this State

Parameters:¶

dtype : str | None¶: the new data type of the state.
device : str | None¶: the new device of the state.

abstract property system_seq : list[int]¶: The system order of this state

permute(target_seq)¶

Permute the systems order of the state.

Parameters:¶

target_seq : List[int]¶: the target systems order.

reset_sequence()¶

reset the system order to default sequence i.e. from 0 to n - 1.

evolve(unitary, sys_idx=None)¶

Evolve this state with unitary operators.

Parameters:¶

unitary : Tensor¶: the unitary operator.
sys_idx : List[int] | int | None¶: the system indices to be acted on. Defaults to all systems.

Returns:¶

the evolved state.

Return type:¶

State

Note

Evolve support the broadcast rule.

transform(op, sys_idx=None, repr_type='kraus')¶

Apply a general linear operator to the state.

Parameters:¶

op : Tensor¶: the input operator.
sys_idx : List[int] | int | None¶: the qubit indices to be applied. Defaults to all systems.
repr_type : str¶: the representation type of input operator. Defaults to ‘kraus’.

Returns:¶

the transformed state.

Return type:¶

State

expec_val(hamiltonian, shots=0, decompose=False)¶

The expectation value of the observable with respect to the quantum state.

Parameters:¶

hamiltonian : Hamiltonian¶: Input observable.
decompose : bool | None¶: If decompose is True, it will return the expectation value of each term.

Returns:¶

The expectation value (per term) of the input observable for the quantum state.

Return type:¶

Tensor | List[Tensor]

Note

currently only run in qubit case.

expec_state(prob_idx=None)¶

The expectation with respect to the specific probability distribution(s) of states

Parameters:¶

prob_idx : List[int] | int | None¶: indices of probability distributions. Defaults to all distributions.

Returns:¶

The expected State obtained from the taken probability distributions.

Return type:¶

State

measure(measured_op=None, sys_idx=None, is_povm=False, keep_state=False)¶

Measure the quantum state

Parameters:¶

measured_op : Tensor | None¶: measurement operator. Defaults to the computational basis.
sys_idx : List[int] | int | None¶: the system indices to be measured. Defaults to all systems.
is_povm : bool¶: whether the measurement is a POVM.
keep_state : bool¶: whether to keep the state after measurement.

Returns:¶

The probability of each measurement result. The corresponding collapsed state will also be returned if is_povm is False or keep_state is True.

Raises:¶

UserWarning – is_povm and keep_state cannot be both True,
since a general POVM does not distinguish states. –

Return type:¶

Tensor | Tuple[Tensor, State]

abstract sqrt()¶

Matrix square root of the state.

abstract log()¶

Matrix logarithm of the state.

trace(trace_idx=None)¶

(Partial) trace of the state

Parameters:¶

trace_idx : List[int] | int | None¶: the subsystem indices to be traced out. Defaults to all systems.

Returns:¶

the trace of the state as a Tensor, or a new state if sys_idx is not None.

Return type:¶

Tensor | State

transpose(transpose_idx=None)¶

(Partial) transpose of the state

Parameters:¶

transpose_idx : List[int] | int | None¶: the subsystem indices to be transposed. Defaults to all systems.

Returns:¶

the transpose of the state as a Tensor, or a new state if sys_idx is not None.

Return type:¶

State