quairkit.database.random¶

The library of random data generation functions

quairkit.database.random.random_pauli_str_generator(num_qubits, terms=3)¶

Generate a random observable in list form.

An observable \(O=0.3X\otimes I\otimes I+0.5Y\otimes I\otimes Z\)’s list form is [[0.3, 'x0'], [0.5, 'y0,z2']]. Such an observable is generated by random_pauli_str_generator(3, terms=2)

Parameters:¶

num_qubits : int¶: Number of qubits.
terms : int | None¶: Number of terms in the observable. Defaults to 3.

Returns:¶

The Hamiltonian of randomly generated observable.

Return type:¶

List

quairkit.database.random.random_state(num_systems, rank=None, is_real=False, size=1, system_dim=2)¶

Generate a random quantum state.

Parameters:¶

num_systems : int¶: The number of qubits contained in the quantum state.
rank : int | None¶: The rank of the density matrix. Defaults to None which means full rank.
is_real : bool | None¶: If the quantum state only contains the real number. Defaults to False.
size : List[int] | int | None¶: Batch size. Defaults to 1
system_dim : List[int] | int¶: dimension of systems. Can be a list of system dimensions or an int representing the dimension of all systems. Defaults to be qubit case.

Raises:¶

NotImplementedError – If the backend is wrong or not implemented.

Returns:¶

The generated quantum state.

Return type:¶

State

quairkit.database.random.random_hamiltonian_generator(num_qubits, terms=3)¶

Generate a random Hamiltonian.

Parameters:¶

num_qubits : int¶: Number of qubits.
terms : int | None¶: Number of terms in the Hamiltonian. Defaults to 3.

Returns:¶

The randomly generated Hamiltonian.

Return type:¶

Hamiltonian

quairkit.database.random.random_hermitian(num_qubits)¶

randomly generate a \(2^n \times 2^n\) hermitian matrix

Parameters:¶

num_qubits : int¶: number of qubits \(n\)

Returns:¶

a \(2^n \times 2^n\) hermitian matrix

Return type:¶

Tensor

quairkit.database.random.random_orthogonal_projection(num_qubits)¶

randomly generate a \(2^n \times 2^n\) rank-1 orthogonal projector

Parameters:¶

num_qubits : int¶: number of qubits \(n\)

Returns:¶

a \(2^n \times 2^n\) orthogonal projector

Return type:¶

Tensor

quairkit.database.random.random_density_matrix(num_qubits)¶

randomly generate an num_qubits-qubit state in density matrix form

Parameters:¶

num_qubits : int¶: number of qubits \(n\)

Returns:¶

a \(2^n \times 2^n\) density matrix

Return type:¶

Tensor

quairkit.database.random.random_unitary(num_systems, size=1, system_dim=2)¶

randomly generate a \(d \times d\) unitary

Parameters:¶

num_systems : int¶: number of systems in this unitary. Alias of num_qubits.
size : List[int] | int | None¶: batch size. Defaults to 1
system_dim : List[int] | int¶: dimension of systems. Can be a list of system dimensions or an int representing the dimension of all systems. Defaults to be qubit case.

Returns:¶

\(d \times d\) unitary matrix

Return type:¶

Tensor

quairkit.database.random.random_unitary_hermitian(num_qubits)¶

randomly generate a \(2^n \times 2^n\) hermitian unitary

Parameters:¶

num_qubits : int¶: number of qubits \(n\)

Returns:¶

a \(2^n \times 2^n\) hermitian unitary matrix

Return type:¶

Tensor

quairkit.database.random.random_unitary_with_hermitian_block(num_qubits, is_unitary=False)¶

randomly generate a unitary \(2^n \times 2^n\) matrix that is a block encoding of a \(2^{n/2} \times 2^{n/2}\) Hermitian matrix

Parameters:¶

num_qubits : int¶: number of qubits \(n\)
is_unitary : bool¶: whether the hermitian block is a unitary divided by 2 (for tutorial only)

Returns:¶

a \(2^n \times 2^n\) unitary matrix that its upper-left block is a Hermitian matrix

Return type:¶

Tensor

quairkit.database.random.haar_orthogonal(dim)¶

randomly generate an orthogonal matrix following Haar random, referenced by arXiv:math-ph/0609050v2

Parameters:¶

dim : int¶: dimension of orthogonal matrix

Returns:¶

a \(2^n \times 2^n\) orthogonal matrix

Return type:¶

Tensor

quairkit.database.random.haar_unitary(dim)¶

randomly generate a unitary following Haar random, referenced by arXiv:math-ph/0609050v2

Parameters:¶

dim : int¶: dimension of unitary

Returns:¶

a \(d \times d\) unitary

Return type:¶

Tensor

quairkit.database.random.haar_state_vector(dim, is_real=False)¶

randomly generate a state vector following Haar random

Parameters:¶

dim : int¶: dimension of density matrix
is_real : bool | None¶: whether the vector is real, default to be False

Returns:¶

a \(2^n \times 1\) state vector

Return type:¶

Tensor

quairkit.database.random.haar_density_operator(dim, rank, is_real=False)¶

randomly generate a density matrix following Haar random

Parameters:¶

dim : int¶: dimension of density matrix
rank : int¶: rank of density matrix, default to be None refering to full ranks
is_real : bool | None¶: whether the density matrix is real, default to be False

Returns:¶

a \(2^n \times 2^n\) density matrix

Return type:¶

Tensor

quairkit.database.random.random_channel(num_systems, rank=None, target='kraus', size=1, system_dim=2)¶

Generate a random channel from its Stinespring representation

Parameters:¶

num_systems : int¶: number of systems
rank : int¶: rank of this Channel. Defaults to be random sampled from \([1, d]\)
target : str¶: target representation, should to be 'choi', 'kraus' or 'stinespring'
size : int | None¶: batch size. Defaults to 1
system_dim : List[int] | int¶: dimension of systems. Can be a list of system dimensions or an int representing the dimension of all systems. Defaults to be qubit case.

Returns:¶

the target representation of a random channel.

Return type:¶

Tensor