quairkit.database.random¶
The library of random data generation functions
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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 byrandom_pauli_str_generator(3, terms=2).Examples
observable = random_pauli_str_generator(num_qubits=2, terms=2) print(f'The Hamiltonian of randomly generated observable is:\n{observable}')The Hamiltonian of randomly generated observable is: [[-0.6019637631250563, 'y0'], [0.12777564473712655, 'x0,z1']]
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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(full rank).- is_real : bool | None¶
If the quantum state only contains real numbers. Defaults to
False.- size : int | List[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 the qubit case.
- Raises:¶
NotImplementedError – If the backend is wrong or not implemented.
- Returns:¶
The generated quantum state.
- Return type:¶
State
Examples
state = random_state(num_systems=1, size=1) print(f'The generated quantum state is:\n{state}') state = random_state(num_systems=1, rank=1) print(f'The generated quantum state is:\n{state}') state = random_state(num_systems=2, system_dim=[1, 2]) print(f'The generated quantum state is:\n{state}') state = random_state(num_systems=3, size=[2, 1], system_dim=[1, 2, 1]) print(f'The generated quantum state is:\n{state}')The generated quantum state is: --------------------------------------------------- Backend: state_vector System dimension: [2] System sequence: [0] [-0.33+0.72j -0.28+0.55j] --------------------------------------------------- The generated quantum state is: --------------------------------------------------- Backend: state_vector System dimension: [2] System sequence: [0] [ 0.83-0.31j -0.45+0.16j] --------------------------------------------------- The generated quantum state is: --------------------------------------------------- Backend: density_matrix System dimension: [1, 2] System sequence: [0, 1] [[ 0.63+0.j -0.12-0.13j] [-0.12+0.13j 0.37-0.j ]] --------------------------------------------------- The generated quantum state is: --------------------------------------------------- Backend: density_matrix System dimension: [1, 2, 1] System sequence: [0, 1, 2] Batch size: [2, 1] # 0: [[0.43+0.j 0.24-0.37j], [0.24+0.37j 0.57-0.j ]] # 1: [[ 0.88+0.j -0.29-0.11j], [-0.29+0.11j 0.12-0.j ]] ---------------------------------------------------
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quairkit.database.random.random_hamiltonian_generator(num_qubits, terms=
3)¶ Generate a random Hamiltonian.
Examples
Hamiltonian = random_hamiltonian_generator(3, 2) print(f'The randomly generated Hamiltonian is:\n{Hamiltonian}')The randomly generated Hamiltonian is: 0.11801365595625102 Z0, X2 0.9059897222160238 X0, Z1, Z2
- quairkit.database.random.random_hermitian(num_qubits)¶
Randomly generate a normalized \(2^n \times 2^n\) Hermitian matrix.
- Parameters:¶
- num_qubits : int¶
Number of qubits \(n\).
- Returns:¶
A \(2^n \times 2^n\) Hermitian matrix.
- Return type:¶
Tensor
Examples
Hermitian = random_hermitian(1) print(f'The randomly generated Hermitian matrix is:\n{Hermitian}')The randomly generated Hermitian matrix is: tensor([[0.1038+0.0000j, 0.4251+0.2414j], [0.4251-0.2414j, 0.7333+0.0000j]])
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quairkit.database.random.random_projector(num_systems, size=
1, system_dim=2)¶ Randomly generate a \(d \times d\) orthogonal projector.
Examples
Orthogonal_projector = random_orthogonal_projection(1) print(f'The randomly generated Orthogonal_projector is:\n{Orthogonal_projector}')The randomly generated Orthogonal_projector is: tensor([[0.9704+1.1123e-10j, 0.1692+7.7007e-03j], [0.1692-7.7008e-03j, 0.0296-1.1123e-10j]])
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quairkit.database.random.random_orthogonal_projection(num_systems, size=
1, system_dim=2)¶ Randomly generate a \(d \times d\) orthogonal projector.
Examples
Orthogonal_projector = random_orthogonal_projection(1) print(f'The randomly generated Orthogonal_projector is:\n{Orthogonal_projector}')The randomly generated Orthogonal_projector is: tensor([[0.9704+1.1123e-10j, 0.1692+7.7007e-03j], [0.1692-7.7008e-03j, 0.0296-1.1123e-10j]])
- 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
Examples
Density_matrix = random_density_matrix(1) print(f'The randomly generated density matrix is:\n{Density_matrix}')The randomly generated density matrix is: tensor([[0.3380+0.0000j, 0.4579+0.1185j], [0.4579-0.1185j, 0.6620+0.0000j]])
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quairkit.database.random.random_unitary(num_systems, size=
1, system_dim=2)¶ Randomly generate a \(d \times d\) unitary.
Examples
unitary_matrix_1 = random_unitary(num_systems=1, system_dim=2) print(f'The randomly generated unitary_matrix_1 is:\n{unitary_matrix_1}') unitary_matrix_2 = random_unitary(num_systems=2, system_dim=[1, 2]) print(f'The randomly generated unitary_matrix_2 is:\n{unitary_matrix_2}') unitary_matrix_3 = random_unitary(num_systems=1, size=[1,2]) print(f'The randomly generated unitary_matrix_3 is:\n{unitary_matrix_3}')The randomly generated unitary_matrix_1 is: tensor([[-0.5288+0.5296j, -0.5277-0.4019j], [-0.5321-0.3959j, -0.3627+0.6546j]]) The randomly generated unitary_matrix_2 is: tensor([[0.6996-0.1504j, 0.3414+0.6095j], [0.4954-0.4925j, -0.6315-0.3364j]]) The randomly generated unitary_matrix_3 is: tensor([[[[0.3240+0.1404j, 0.4166-0.8377j], [0.6068+0.7121j, -0.2804+0.2146j]], [[-0.2620-0.0886j, -0.3587+0.8916j], [0.5196-0.8084j, 0.2238+0.1624j]]]])
- 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
Examples
Unitary_hermitian = random_unitary_hermitian(1) print(f'The randomly generated hermitian unitary is:\n{Unitary_hermitian}')The randomly generated hermitian unitary is: tensor([[0.2298+2.2018e-09j, -0.8408+4.9013e-01j], [-0.8408-4.9013e-01j, -0.2298-2.2018e-09j]])
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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:¶
- Returns:¶
A \(2^n \times 2^n\) unitary matrix whose upper-left block is Hermitian.
- Return type:¶
Tensor
Examples
unitary_matrix_1 = random_unitary_with_hermitian_block(num_qubits=2, is_unitary=False) print(f'The randomly generated unitary matrix 1 with hermitian block is:\n{unitary_matrix_1}') unitary_matrix_2 = random_unitary_with_hermitian_block(num_qubits=2, is_unitary=True) print(f'The randomly generated unitary matrix 2 with hermitian block is:\n{unitary_matrix_2}')The randomly generated unitary matrix 1 with hermitian block is: tensor([[ 5.7873e-01+0.0000j, 2.2460e-01+0.2711j, -1.5514e-08+0.5646j, 3.6316e-01-0.3009j], [ 2.2460e-01-0.2711j, 7.0578e-01+0.0000j, -3.6316e-01-0.3009j, -2.2489e-08+0.3944j], [-1.5514e-08+0.5646j, 3.6316e-01-0.3009j, 5.7873e-01+0.0000j, 2.2460e-01+0.2711j], [-3.6316e-01-0.3009j, -2.2489e-08+0.3944j, 2.2460e-01-0.2711j, 7.0578e-01+0.0000j]]) The randomly generated unitary matrix 2 with hermitian block is: tensor([[-1.8185e-01-1.6847e-09j, 3.0894e-01+3.4855e-01j, 2.2516e-09+8.6603e-01j, -1.4451e-09-9.3500e-11j], [ 3.0894e-01-3.4855e-01j, 1.8185e-01+1.6847e-09j, 1.7456e-09-9.3500e-11j, 2.4038e-09+8.6603e-01j], [ 2.2516e-09+8.6603e-01j, -1.4451e-09-9.3500e-11j, -1.8185e-01-1.6847e-09j, 3.0894e-01+3.4855e-01j], [ 1.7456e-09-9.3500e-11j, 2.4038e-09+8.6603e-01j, 3.0894e-01-3.4855e-01j, 1.8185e-01+1.6847e-09j]])
- quairkit.database.random.haar_orthogonal(dim)¶
Randomly generate an orthogonal matrix following Haar measure, referenced by arXiv:math-ph/0609050v2.
- Parameters:¶
- dim : int¶
Dimension of the orthogonal matrix.
- Returns:¶
A \(d \times d\) orthogonal matrix.
- Return type:¶
Tensor
Examples
Haar_orthogonal = haar_orthogonal(2) print(f'The randomly generated orthogonal matrix is:\n{Haar_orthogonal}')The randomly generated orthogonal matrix is: tensor([[-0.6859+0.j, 0.7277+0.j], [ 0.7277+0.j, 0.6859+0.j]])
- quairkit.database.random.haar_unitary(dim)¶
Randomly generate a unitary following Haar measure, referenced by arXiv:math-ph/0609050v2.
- Parameters:¶
- dim : int¶
Dimension of the unitary.
- Returns:¶
A \(d \times d\) unitary.
- Return type:¶
Tensor
Examples
Haar_unitary = haar_unitary(2) print(f'The randomly generated unitary is:\n{Haar_unitary}')The randomly generated unitary is: tensor([[ 0.2800+0.6235j, 0.7298+0.0160j], [-0.7289-0.0396j, 0.3267-0.6003j]])
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quairkit.database.random.haar_state_vector(dim, is_real=
False)¶ Randomly generate a state vector following Haar measure.
Examples
Haar_state_vector = haar_state_vector(3, is_real=True) print(f'The randomly generated state vector is:\n{Haar_state_vector}')The randomly generated state vector is: tensor([[0.9908+0.j], [-0.1356+0.j]])
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quairkit.database.random.haar_density_operator(dim, rank, is_real=
False)¶ Randomly generate a density matrix following Haar measure.
Examples
rho1 = haar_density_operator(dim=2, rank=2) print(f'The randomly generated density matrix 1 is:\n{rho1}') rho2 = haar_density_operator(dim=2, rank=1, is_real=True) print(f'The randomly generated density matrix 2 is:\n{rho2}')The randomly generated density matrix 1 is: tensor([[0.8296+1.1215e-18j, -0.0430+3.5193e-01j], [-0.0430-3.5193e-01j, 0.1704-1.1215e-18j]]) The randomly generated density matrix 2 is: tensor([[0.6113+0.j, -0.4875+0.j], [-0.4875+0.j, 0.3887+0.j]])
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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. If None, it is randomly sampled from \([1, d]\).
- target : str¶
Target representation; should 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 the qubit case.
- Returns:¶
The target representation of a random channel.
- Return type:¶
Tensor
Examples
channel_kraus = random_channel(num_systems=1, target="kraus", system_dim=2) print(f'The randomly generated kraus channel is:\n{channel_kraus}') channel_choi = random_channel(num_systems=1, target="choi", system_dim=2) print(f'The randomly generated choi channel is:\n{channel_choi}') channel_stinespring = random_channel(num_systems=1, target="stinespring", size=1, rank=1) print(f'The randomly generated stinespring channel is:\n{channel_stinespring}') batch_channels = random_channel(num_systems=2, size=2, target="kraus", system_dim=[1,2], rank=2) print(f'The randomly generated kraus channel is:\n{batch_channels}')The randomly generated kraus channel is: tensor([[[ 0.2361+0.7497j, 0.0224+0.6178j], [ 0.5942-0.1706j, -0.7860+0.0085j]]]) The randomly generated choi channel is: tensor([[ 0.5136+0.0000j, -0.4784-0.1446j, -0.2850-0.4106j, -0.1583-0.4886j], [-0.4784+0.1446j, 0.4864+0.0000j, 0.3811+0.3023j, 0.2850+0.4106j], [-0.2850+0.4106j, 0.3811-0.3023j, 0.4864+0.0000j, 0.4784+0.1446j], [-0.1583+0.4886j, 0.2850-0.4106j, 0.4784-0.1446j, 0.5136+0.0000j]]) The randomly generated stinespring channel is: tensor([[ 0.1652+0.5347j, 0.6310+0.5372j], [ 0.4751+0.6790j, -0.5167-0.2150j]]) The randomly generated kraus channel is: tensor([[[[-0.3189-0.6385j, -0.1873+0.1634j], [ 0.2218+0.0440j, -0.6294+0.0947j]], [[-0.0072+0.0749j, -0.0790+0.6740j], [-0.5121-0.4142j, -0.0357-0.2671j]]], [[[-0.1163-0.1931j, 0.2001-0.5852j], [-0.5174+0.5253j, 0.1128-0.2459j]], [[-0.1362+0.3280j, -0.2677+0.5444j], [ 0.4328-0.3033j, -0.3862-0.1646j]]]])
- quairkit.database.random.random_clifford(num_qubits)¶
Generate a random Clifford unitary.
- Parameters:¶
- num_qubits : int¶
The number of qubits (n).
- Returns:¶
The matrix form of a random Clifford unitary.
- Return type:¶
Tensor
- Reference:
Sergey Bravyi and Dmitri Maslov, Hadamard-free circuits expose the structure of the Clifford group. IEEE Transactions on Information Theory 67(7), 4546-4563 (2021).
Examples
num_qubits = 1 clifford_matrix = random_clifford(num_qubits) print(f'The randomly generated Clifford unitary is:\n{clifford_matrix}')The randomly generated Clifford unitary is: tensor([[ 0.7071+0.0000j, -0.7071+0.0000j], [ 0.0000+0.7071j, 0.0000+0.7071j]])