tensorcircuit.quantum#

Quantum state and operator class backend by tensornetwork

IMPORT

import tensorcircuit.quantum as qu

tensorcircuit.quantum.PauliString2COO(l: Sequence[int], weight: Optional[float] = None) → Any[源代码]#

Generate tensorflow sparse matrix from Pauli string sum

参数

l (Sequence[int]) -- 1D Tensor representing for a Pauli string, e.g. [1, 0, 0, 3, 2] is for \(X_0Z_3Y_4\)
weight (Optional[float], optional) -- the weight for the Pauli string defaults to None (all Pauli strings weight 1.0)

返回

the tensorflow sparse matrix

返回类型

Tensor

tensorcircuit.quantum.PauliStringSum2COO(ls: Sequence[Sequence[int]], weight: Optional[Sequence[float]] = None, numpy: bool = False) → Any[源代码]#

Generate sparse tensor from Pauli string sum. Currently requires tensorflow installed

参数

ls (Sequence[Sequence[int]]) -- 2D Tensor, each row is for a Pauli string, e.g. [1, 0, 0, 3, 2] is for \(X_0Z_3Y_4\)
weight (Optional[Sequence[float]], optional) -- 1D Tensor, each element corresponds the weight for each Pauli string defaults to None (all Pauli strings weight 1.0)
numpy (bool) -- default False. If True, return numpy coo else return backend compatible sparse tensor

返回

the scipy coo sparse matrix

返回类型

Tensor

tensorcircuit.quantum.PauliStringSum2COO_numpy(ls: Sequence[Sequence[int]], weight: Optional[Sequence[float]] = None, *, numpy: bool = True) → Any#

Generate sparse tensor from Pauli string sum. Currently requires tensorflow installed

参数

ls (Sequence[Sequence[int]]) -- 2D Tensor, each row is for a Pauli string, e.g. [1, 0, 0, 3, 2] is for \(X_0Z_3Y_4\)
weight (Optional[Sequence[float]], optional) -- 1D Tensor, each element corresponds the weight for each Pauli string defaults to None (all Pauli strings weight 1.0)
numpy (bool) -- default False. If True, return numpy coo else return backend compatible sparse tensor

返回

the scipy coo sparse matrix

返回类型

Tensor

tensorcircuit.quantum.PauliStringSum2COO_tf(ls: Sequence[Sequence[int]], weight: Optional[Sequence[float]] = None) → Any[源代码]#

Generate tensorflow sparse matrix from Pauli string sum

参数

ls (Sequence[Sequence[int]]) -- 2D Tensor, each row is for a Pauli string, e.g. [1, 0, 0, 3, 2] is for \(X_0Z_3Y_4\)
weight (Optional[Sequence[float]], optional) -- 1D Tensor, each element corresponds the weight for each Pauli string defaults to None (all Pauli strings weight 1.0)

返回

the tensorflow coo sparse matrix

返回类型

Tensor

tensorcircuit.quantum.PauliStringSum2Dense(ls: Sequence[Sequence[int]], weight: Optional[Sequence[float]] = None, numpy: bool = False) → Any[源代码]#

Generate dense matrix from Pauli string sum. Currently requires tensorflow installed.

参数

ls (Sequence[Sequence[int]]) -- 2D Tensor, each row is for a Pauli string, e.g. [1, 0, 0, 3, 2] is for \(X_0Z_3Y_4\)
weight (Optional[Sequence[float]], optional) -- 1D Tensor, each element corresponds the weight for each Pauli string defaults to None (all Pauli strings weight 1.0)
numpy (bool) -- default False. If True, return numpy coo else return backend compatible sparse tensor

返回

the tensorflow dense matrix

返回类型

Tensor

class tensorcircuit.quantum.QuAdjointVector(subsystem_edges: Sequence[tensornetwork.network_components.Edge], ref_nodes: Optional[Collection[tensornetwork.network_components.AbstractNode]] = None, ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None)[源代码]#

基类：tensorcircuit.quantum.QuOperator

Represents an adjoint (row) vector via a tensor network.

__init__(subsystem_edges: Sequence[tensornetwork.network_components.Edge], ref_nodes: Optional[Collection[tensornetwork.network_components.AbstractNode]] = None, ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None) → None[源代码]#

Constructs a new QuAdjointVector from a tensor network. This encapsulates an existing tensor network, interpreting it as an adjoint vector (row vector).

参数

subsystem_edges (Sequence[Edge]) -- The edges of the network to be used as the input edges.
ref_nodes (Optional[Collection[AbstractNode]], optional) -- Nodes used to refer to parts of the tensor network that are not connected to any input or output edges (for example: a scalar factor).
ignore_edges (Optional[Collection[Edge]], optional) -- Optional collection of edges to ignore when performing consistency checks.

adjoint() → tensorcircuit.quantum.QuOperator#

The adjoint of the operator. This creates a new QuOperator with complex-conjugate copies of all tensors in the network and with the input and output edges switched.

返回: The adjoint of the operator.
返回类型: QuOperator

check_network() → None#: Check that the network has the expected dimensionality. This checks that all input and output edges are dangling and that there are no other dangling edges (except any specified in ignore_edges). If not, an exception is raised.

contract(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → tensorcircuit.quantum.QuOperator#

Contract the tensor network in place. This modifies the tensor network representation of the operator (or vector, or scalar), reducing it to a single tensor, without changing the value.

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor.
返回: The present object.
返回类型: QuOperator

copy() → tensorcircuit.quantum.QuOperator#

The deep copy of the operator.

返回: The new copy of the operator.
返回类型: QuOperator

eval(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any#

Contracts the tensor network in place and returns the final tensor. Note that this modifies the tensor network representing the operator. The default ordering for the axes of the final tensor is: *out_edges, *in_edges. If there are any "ignored" edges, their axes come first: *ignored_edges, *out_edges, *in_edges.

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The final tensor representing the operator.
返回类型: Tensor

eval_matrix(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any#

Contracts the tensor network in place and returns the final tensor in two dimentional matrix. The default ordering for the axes of the final tensor is: (\(\prod\) dimension of out_edges, \(\prod\) dimension of in_edges)

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The two-dimentional tensor representing the operator.
返回类型: Tensor

classmethod from_local_tensor(tensor: Any, space: Sequence[int], loc: Sequence[int], out_axes: Optional[Sequence[int]] = None, in_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuOperator#

classmethod from_tensor(tensor: Any, subsystem_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuAdjointVector[源代码]#

Construct a QuAdjointVector directly from a single tensor. This first wraps the tensor in a Node, then constructs the QuAdjointVector from that Node.

Example

def show_attributes(op):
    print(f"op.is_scalar() \t\t-> {op.is_scalar()}")
    print(f"op.is_vector() \t\t-> {op.is_vector()}")
    print(f"op.is_adjoint_vector() \t-> {op.is_adjoint_vector()}")
    print(f"op.eval() \n{op.eval()}")

>>> psi_tensor = np.random.rand(2, 2)
>>> psi_tensor
array([[0.27260127, 0.91401091],
       [0.06490953, 0.38653646]])
>>> op = qu.QuAdjointVector.from_tensor(psi_tensor, [0, 1])
>>> show_attributes(op)
op.is_scalar()          -> False
op.is_vector()          -> False
op.is_adjoint_vector()  -> True
op.eval()
[[0.27260127 0.91401091]
 [0.06490953 0.38653646]]

参数

tensor (Tensor) -- The tensor for constructing an QuAdjointVector.
subsystem_axes (Optional[Sequence[int]], optional) -- Sequence of integer indices specifying the order in which to interpret the axes as subsystems (input edges). If not specified, the axes are taken in ascending order.

返回

The new constructed QuAdjointVector give from the given tensor.

返回类型

QuAdjointVector

property in_space: List[int]#

is_adjoint_vector() → bool#: Returns a bool indicating if QuOperator is an adjoint vector. Examples can be found in the QuOperator.from_tensor.

is_scalar() → bool#: Returns a bool indicating if QuOperator is a scalar. Examples can be found in the QuOperator.from_tensor.

is_vector() → bool#: Returns a bool indicating if QuOperator is a vector. Examples can be found in the QuOperator.from_tensor.

property nodes: Set[tensornetwork.network_components.AbstractNode]#: All tensor-network nodes involved in the operator.

norm() → tensorcircuit.quantum.QuOperator#: The norm of the operator. This is the 2-norm (also known as the Frobenius or Hilbert-Schmidt norm).

property out_space: List[int]#

partial_trace(subsystems_to_trace_out: Collection[int]) → tensorcircuit.quantum.QuOperator#

The partial trace of the operator. Subsystems to trace out are supplied as indices, so that dangling edges are connected to each other as: out_edges[i] ^ in_edges[i] for i in subsystems_to_trace_out This does not modify the original network. The original ordering of the remaining subsystems is maintained.

参数: subsystems_to_trace_out (Collection[int]) -- Indices of subsystems to trace out.
返回: A new QuOperator or QuScalar representing the result.
返回类型: QuOperator

projector() → tensorcircuit.quantum.QuOperator[源代码]#

The projector of the operator. The operator, as a linear operator, on the adjoint of the operator.

Set \(A\) is the operator in matrix form, then the projector of operator is defined as: \(A^\dagger A\)

返回: The projector of the operator.
返回类型: QuOperator

reduced_density(subsystems_to_trace_out: Collection[int]) → tensorcircuit.quantum.QuOperator[源代码]#

The reduced density of the operator.

Set \(A\) is the matrix of the operator, then the reduced density is defined as:

\[\mathrm{Tr}_{subsystems}(A^\dagger A)\]

Firstly, take the projector of the operator, then trace out the subsystems to trace out are supplied as indices, so that dangling edges are connected to each other as: out_edges[i] ^ in_edges[i] for i in subsystems_to_trace_out This does not modify the original network. The original ordering of the remaining subsystems is maintained.

参数: subsystems_to_trace_out (Collection[int]) -- Indices of subsystems to trace out.
返回: The QuOperator of the reduced density of the operator with given subsystems.
返回类型: QuOperator

property space: List[int]#

property subsystem_edges: List[tensornetwork.network_components.Edge]#

tensor_product(other: tensorcircuit.quantum.QuOperator) → tensorcircuit.quantum.QuOperator#

Tensor product with another operator. Given two operators A and B, produces a new operator AB representing \(A ⊗ B\). The out_edges (in_edges) of AB is simply the concatenation of the out_edges (in_edges) of A.copy() with that of B.copy(): new_out_edges = [*out_edges_A_copy, *out_edges_B_copy] new_in_edges = [*in_edges_A_copy, *in_edges_B_copy]

Example

>>> psi = qu.QuVector.from_tensor(np.random.rand(2, 2))
>>> psi_psi = psi.tensor_product(psi)
>>> len(psi_psi.subsystem_edges)
4
>>> float(psi_psi.norm().eval())
2.9887872748523585
>>> psi.norm().eval() ** 2
2.9887872748523585

参数: other (QuOperator) -- The other operator (B).
返回: The result (AB).
返回类型: QuOperator

trace() → tensorcircuit.quantum.QuOperator#: The trace of the operator.

class tensorcircuit.quantum.QuOperator(out_edges: Sequence[tensornetwork.network_components.Edge], in_edges: Sequence[tensornetwork.network_components.Edge], ref_nodes: Optional[Collection[tensornetwork.network_components.AbstractNode]] = None, ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None)[源代码]#

基类：object

Represents a linear operator via a tensor network. To interpret a tensor network as a linear operator, some of the dangling edges must be designated as out_edges (output edges) and the rest as in_edges (input edges). Considered as a matrix, the out_edges represent the row index and the in_edges represent the column index. The (right) action of the operator on another then consists of connecting the in_edges of the first operator to the out_edges of the second. Can be used to do simple linear algebra with tensor networks.

__init__(out_edges: Sequence[tensornetwork.network_components.Edge], in_edges: Sequence[tensornetwork.network_components.Edge], ref_nodes: Optional[Collection[tensornetwork.network_components.AbstractNode]] = None, ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None) → None[源代码]#

Creates a new QuOperator from a tensor network. This encapsulates an existing tensor network, interpreting it as a linear operator. The network is checked for consistency: All dangling edges must either be in out_edges, in_edges, or ignore_edges.

参数

out_edges (Sequence[Edge]) -- The edges of the network to be used as the output edges.
in_edges (Sequence[Edge]) -- The edges of the network to be used as the input edges.
ref_nodes (Optional[Collection[AbstractNode]], optional) -- Nodes used to refer to parts of the tensor network that are not connected to any input or output edges (for example: a scalar factor).
ignore_edges (Optional[Collection[Edge]], optional) -- Optional collection of dangling edges to ignore when performing consistency checks.

引发

ValueError -- At least one reference node is required to specify a scalar. None provided!

adjoint() → tensorcircuit.quantum.QuOperator[源代码]#

The adjoint of the operator. This creates a new QuOperator with complex-conjugate copies of all tensors in the network and with the input and output edges switched.

返回: The adjoint of the operator.
返回类型: QuOperator

check_network() → None[源代码]#: Check that the network has the expected dimensionality. This checks that all input and output edges are dangling and that there are no other dangling edges (except any specified in ignore_edges). If not, an exception is raised.

contract(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → tensorcircuit.quantum.QuOperator[源代码]#

Contract the tensor network in place. This modifies the tensor network representation of the operator (or vector, or scalar), reducing it to a single tensor, without changing the value.

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor.
返回: The present object.
返回类型: QuOperator

copy() → tensorcircuit.quantum.QuOperator[源代码]#

The deep copy of the operator.

返回: The new copy of the operator.
返回类型: QuOperator

eval(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any[源代码]#

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The final tensor representing the operator.
返回类型: Tensor

eval_matrix(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any[源代码]#

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The two-dimentional tensor representing the operator.
返回类型: Tensor

classmethod from_local_tensor(tensor: Any, space: Sequence[int], loc: Sequence[int], out_axes: Optional[Sequence[int]] = None, in_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuOperator[源代码]#

classmethod from_tensor(tensor: Any, out_axes: Optional[Sequence[int]] = None, in_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuOperator[源代码]#

Construct a QuOperator directly from a single tensor. This first wraps the tensor in a Node, then constructs the QuOperator from that Node.

Example

def show_attributes(op):
    print(f"op.is_scalar() \t\t-> {op.is_scalar()}")
    print(f"op.is_vector() \t\t-> {op.is_vector()}")
    print(f"op.is_adjoint_vector() \t-> {op.is_adjoint_vector()}")
    print(f"op.eval() \n{op.eval()}")

>>> psi_tensor = np.random.rand(2, 2)
>>> psi_tensor
array([[0.27260127, 0.91401091],
       [0.06490953, 0.38653646]])
>>> op = qu.QuOperator.from_tensor(psi_tensor, out_axes=[0], in_axes=[1])
>>> show_attributes(op)
op.is_scalar()          -> False
op.is_vector()          -> False
op.is_adjoint_vector()  -> False
op.eval()
[[0.27260127 0.91401091]
 [0.06490953 0.38653646]]

参数

tensor (Tensor) -- The tensor.
out_axes (Optional[Sequence[int]], optional) -- The axis indices of tensor to use as out_edges.
in_axes (Optional[Sequence[int]], optional) -- The axis indices of tensor to use as in_edges.

返回

The new operator.

返回类型

QuOperator

property in_space: List[int]#

is_adjoint_vector() → bool[源代码]#: Returns a bool indicating if QuOperator is an adjoint vector. Examples can be found in the QuOperator.from_tensor.

is_scalar() → bool[源代码]#: Returns a bool indicating if QuOperator is a scalar. Examples can be found in the QuOperator.from_tensor.

is_vector() → bool[源代码]#: Returns a bool indicating if QuOperator is a vector. Examples can be found in the QuOperator.from_tensor.

property nodes: Set[tensornetwork.network_components.AbstractNode]#: All tensor-network nodes involved in the operator.

norm() → tensorcircuit.quantum.QuOperator[源代码]#: The norm of the operator. This is the 2-norm (also known as the Frobenius or Hilbert-Schmidt norm).

property out_space: List[int]#

partial_trace(subsystems_to_trace_out: Collection[int]) → tensorcircuit.quantum.QuOperator[源代码]#

参数: subsystems_to_trace_out (Collection[int]) -- Indices of subsystems to trace out.
返回: A new QuOperator or QuScalar representing the result.
返回类型: QuOperator

tensor_product(other: tensorcircuit.quantum.QuOperator) → tensorcircuit.quantum.QuOperator[源代码]#

Example

>>> psi = qu.QuVector.from_tensor(np.random.rand(2, 2))
>>> psi_psi = psi.tensor_product(psi)
>>> len(psi_psi.subsystem_edges)
4
>>> float(psi_psi.norm().eval())
2.9887872748523585
>>> psi.norm().eval() ** 2
2.9887872748523585

参数: other (QuOperator) -- The other operator (B).
返回: The result (AB).
返回类型: QuOperator

trace() → tensorcircuit.quantum.QuOperator[源代码]#: The trace of the operator.

class tensorcircuit.quantum.QuScalar(ref_nodes: Collection[tensornetwork.network_components.AbstractNode], ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None)[源代码]#

基类：tensorcircuit.quantum.QuOperator

Represents a scalar via a tensor network.

__init__(ref_nodes: Collection[tensornetwork.network_components.AbstractNode], ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None) → None[源代码]#

Constructs a new QuScalar from a tensor network. This encapsulates an existing tensor network, interpreting it as a scalar.

参数

ref_nodes (Collection[AbstractNode]) -- Nodes used to refer to the tensor network (need not be exhaustive - one node from each disconnected subnetwork is sufficient).
ignore_edges (Optional[Collection[Edge]], optional) -- Optional collection of edges to ignore when performing consistency checks.

adjoint() → tensorcircuit.quantum.QuOperator#

The adjoint of the operator. This creates a new QuOperator with complex-conjugate copies of all tensors in the network and with the input and output edges switched.

返回: The adjoint of the operator.
返回类型: QuOperator

check_network() → None#: Check that the network has the expected dimensionality. This checks that all input and output edges are dangling and that there are no other dangling edges (except any specified in ignore_edges). If not, an exception is raised.

contract(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → tensorcircuit.quantum.QuOperator#

Contract the tensor network in place. This modifies the tensor network representation of the operator (or vector, or scalar), reducing it to a single tensor, without changing the value.

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor.
返回: The present object.
返回类型: QuOperator

copy() → tensorcircuit.quantum.QuOperator#

The deep copy of the operator.

返回: The new copy of the operator.
返回类型: QuOperator

eval(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any#

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The final tensor representing the operator.
返回类型: Tensor

eval_matrix(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any#

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The two-dimentional tensor representing the operator.
返回类型: Tensor

classmethod from_local_tensor(tensor: Any, space: Sequence[int], loc: Sequence[int], out_axes: Optional[Sequence[int]] = None, in_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuOperator#

classmethod from_tensor(tensor: Any) → tensorcircuit.quantum.QuScalar[源代码]#

Construct a QuScalar directly from a single tensor. This first wraps the tensor in a Node, then constructs the QuScalar from that Node.

Example

def show_attributes(op):
    print(f"op.is_scalar() \t\t-> {op.is_scalar()}")
    print(f"op.is_vector() \t\t-> {op.is_vector()}")
    print(f"op.is_adjoint_vector() \t-> {op.is_adjoint_vector()}")
    print(f"op.eval() \n{op.eval()}")

>>> op = qu.QuScalar.from_tensor(1.0)
>>> show_attributes(op)
op.is_scalar()          -> True
op.is_vector()          -> False
op.is_adjoint_vector()  -> False
op.eval()
1.0

参数: tensor (Tensor) -- The tensor for constructing a new QuScalar.
返回: The new constructed QuScalar from the given tensor.
返回类型: QuScalar

property in_space: List[int]#

is_adjoint_vector() → bool#: Returns a bool indicating if QuOperator is an adjoint vector. Examples can be found in the QuOperator.from_tensor.

is_scalar() → bool#: Returns a bool indicating if QuOperator is a scalar. Examples can be found in the QuOperator.from_tensor.

is_vector() → bool#: Returns a bool indicating if QuOperator is a vector. Examples can be found in the QuOperator.from_tensor.

property nodes: Set[tensornetwork.network_components.AbstractNode]#: All tensor-network nodes involved in the operator.

norm() → tensorcircuit.quantum.QuOperator#: The norm of the operator. This is the 2-norm (also known as the Frobenius or Hilbert-Schmidt norm).

property out_space: List[int]#

partial_trace(subsystems_to_trace_out: Collection[int]) → tensorcircuit.quantum.QuOperator#

参数: subsystems_to_trace_out (Collection[int]) -- Indices of subsystems to trace out.
返回: A new QuOperator or QuScalar representing the result.
返回类型: QuOperator

tensor_product(other: tensorcircuit.quantum.QuOperator) → tensorcircuit.quantum.QuOperator#

Example

>>> psi = qu.QuVector.from_tensor(np.random.rand(2, 2))
>>> psi_psi = psi.tensor_product(psi)
>>> len(psi_psi.subsystem_edges)
4
>>> float(psi_psi.norm().eval())
2.9887872748523585
>>> psi.norm().eval() ** 2
2.9887872748523585

参数: other (QuOperator) -- The other operator (B).
返回: The result (AB).
返回类型: QuOperator

trace() → tensorcircuit.quantum.QuOperator#: The trace of the operator.

class tensorcircuit.quantum.QuVector(subsystem_edges: Sequence[tensornetwork.network_components.Edge], ref_nodes: Optional[Collection[tensornetwork.network_components.AbstractNode]] = None, ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None)[源代码]#

基类：tensorcircuit.quantum.QuOperator

Represents a (column) vector via a tensor network.

Constructs a new QuVector from a tensor network. This encapsulates an existing tensor network, interpreting it as a (column) vector.

参数

subsystem_edges (Sequence[Edge]) -- The edges of the network to be used as the output edges.
ref_nodes (Optional[Collection[AbstractNode]], optional) -- Nodes used to refer to parts of the tensor network that are not connected to any input or output edges (for example: a scalar factor).
ignore_edges (Optional[Collection[Edge]], optional) -- Optional collection of edges to ignore when performing consistency checks.

adjoint() → tensorcircuit.quantum.QuOperator#

The adjoint of the operator. This creates a new QuOperator with complex-conjugate copies of all tensors in the network and with the input and output edges switched.

返回: The adjoint of the operator.
返回类型: QuOperator

check_network() → None#: Check that the network has the expected dimensionality. This checks that all input and output edges are dangling and that there are no other dangling edges (except any specified in ignore_edges). If not, an exception is raised.

contract(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → tensorcircuit.quantum.QuOperator#

Contract the tensor network in place. This modifies the tensor network representation of the operator (or vector, or scalar), reducing it to a single tensor, without changing the value.

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor.
返回: The present object.
返回类型: QuOperator

copy() → tensorcircuit.quantum.QuOperator#

The deep copy of the operator.

返回: The new copy of the operator.
返回类型: QuOperator

eval(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any#

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The final tensor representing the operator.
返回类型: Tensor

eval_matrix(final_edge_order: Optional[Sequence[tensornetwork.network_components.Edge]] = None) → Any#

参数: final_edge_order (Optional[Sequence[Edge]], optional) -- Manually specify the axis ordering of the final tensor. The default ordering is determined by out_edges and in_edges (see above).
引发: ValueError -- Node count '{}' > 1 after contraction!
返回: The two-dimentional tensor representing the operator.
返回类型: Tensor

classmethod from_local_tensor(tensor: Any, space: Sequence[int], loc: Sequence[int], out_axes: Optional[Sequence[int]] = None, in_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuOperator#

classmethod from_tensor(tensor: Any, subsystem_axes: Optional[Sequence[int]] = None) → tensorcircuit.quantum.QuVector[源代码]#

Construct a QuVector directly from a single tensor. This first wraps the tensor in a Node, then constructs the QuVector from that Node.

Example

def show_attributes(op):
    print(f"op.is_scalar() \t\t-> {op.is_scalar()}")
    print(f"op.is_vector() \t\t-> {op.is_vector()}")
    print(f"op.is_adjoint_vector() \t-> {op.is_adjoint_vector()}")
    print(f"op.eval() \n{op.eval()}")

>>> psi_tensor = np.random.rand(2, 2)
>>> psi_tensor
array([[0.27260127, 0.91401091],
       [0.06490953, 0.38653646]])
>>> op = qu.QuVector.from_tensor(psi_tensor, [0, 1])
>>> show_attributes(op)
op.is_scalar()          -> False
op.is_vector()          -> True
op.is_adjoint_vector()  -> False
op.eval()
[[0.27260127 0.91401091]
 [0.06490953 0.38653646]]

参数

tensor (Tensor) -- The tensor for constructing a "QuVector".
subsystem_axes (Optional[Sequence[int]], optional) -- Sequence of integer indices specifying the order in which to interpret the axes as subsystems (output edges). If not specified, the axes are taken in ascending order.

返回

The new constructed QuVector from the given tensor.

返回类型

QuVector

property in_space: List[int]#

is_adjoint_vector() → bool#: Returns a bool indicating if QuOperator is an adjoint vector. Examples can be found in the QuOperator.from_tensor.

is_scalar() → bool#: Returns a bool indicating if QuOperator is a scalar. Examples can be found in the QuOperator.from_tensor.

is_vector() → bool#: Returns a bool indicating if QuOperator is a vector. Examples can be found in the QuOperator.from_tensor.

property nodes: Set[tensornetwork.network_components.AbstractNode]#: All tensor-network nodes involved in the operator.

norm() → tensorcircuit.quantum.QuOperator#: The norm of the operator. This is the 2-norm (also known as the Frobenius or Hilbert-Schmidt norm).

property out_space: List[int]#

partial_trace(subsystems_to_trace_out: Collection[int]) → tensorcircuit.quantum.QuOperator#

参数: subsystems_to_trace_out (Collection[int]) -- Indices of subsystems to trace out.
返回: A new QuOperator or QuScalar representing the result.
返回类型: QuOperator

projector() → tensorcircuit.quantum.QuOperator[源代码]#

The projector of the operator. The operator, as a linear operator, on the adjoint of the operator.

Set \(A\) is the operator in matrix form, then the projector of operator is defined as: \(A A^\dagger\)

返回: The projector of the operator.
返回类型: QuOperator

reduced_density(subsystems_to_trace_out: Collection[int]) → tensorcircuit.quantum.QuOperator[源代码]#

The reduced density of the operator.

Set \(A\) is the matrix of the operator, then the reduced density is defined as:

\[\mathrm{Tr}_{subsystems}(A A^\dagger)\]

参数: subsystems_to_trace_out (Collection[int]) -- Indices of subsystems to trace out.
返回: The QuOperator of the reduced density of the operator with given subsystems.
返回类型: QuOperator

property space: List[int]#

property subsystem_edges: List[tensornetwork.network_components.Edge]#

tensor_product(other: tensorcircuit.quantum.QuOperator) → tensorcircuit.quantum.QuOperator#

Example

>>> psi = qu.QuVector.from_tensor(np.random.rand(2, 2))
>>> psi_psi = psi.tensor_product(psi)
>>> len(psi_psi.subsystem_edges)
4
>>> float(psi_psi.norm().eval())
2.9887872748523585
>>> psi.norm().eval() ** 2
2.9887872748523585

参数: other (QuOperator) -- The other operator (B).
返回: The result (AB).
返回类型: QuOperator

trace() → tensorcircuit.quantum.QuOperator#: The trace of the operator.

tensorcircuit.quantum.check_spaces(edges_1: Sequence[tensornetwork.network_components.Edge], edges_2: Sequence[tensornetwork.network_components.Edge]) → None[源代码]#

Check the vector spaces represented by two lists of edges are compatible. The number of edges must be the same and the dimensions of each pair of edges must match. Otherwise, an exception is raised.

参数

edges_1 (Sequence[Edge]) -- List of edges representing a many-body Hilbert space.
edges_2 (Sequence[Edge]) -- List of edges representing a many-body Hilbert space.

引发

ValueError -- Hilbert-space mismatch: "Cannot connect {} subsystems with {} subsystems", or "Input dimension {} != output dimension {}."

tensorcircuit.quantum.correlation_from_counts(index: Sequence[int], results: Any) → Any[源代码]#

Compute \(\prod_{i\in \\text{index}} s_i\), where the probability for each bitstring is given as a vector results. Results is in the format of "count_vector"

Example

>>> prob = tc.array_to_tensor(np.array([0.6, 0.4, 0, 0]))
>>> qu.correlation_from_counts([0, 1], prob)
(0.20000002+0j)
>>> qu.correlation_from_counts([1], prob)
(0.20000002+0j)

参数

index (Sequence[int]) -- list of int, indicating the position in the bitstring
results (Tensor) -- probability vector of shape 2^n

返回

Correlation expectation from measurement shots.

返回类型

Tensor

tensorcircuit.quantum.correlation_from_samples(index: Sequence[int], results: Any, n: int) → Any[源代码]#

Compute \(\prod_{i\in \\text{index}} s_i (s=\pm 1)\), Results is in the format of "sample_int" or "sample_bin"

参数

index (Sequence[int]) -- list of int, indicating the position in the bitstring
results (Tensor) -- sample tensor
n (int) -- number of qubits

返回

Correlation expectation from measurement shots

返回类型

Tensor

tensorcircuit.quantum.count_d2s(drepr: Any, eps: float = 1e-07) → Tuple[Any, Any][源代码]#

measurement shots results, dense representation to sparse tuple representation non-jittable due to the non fixed return shape count_tuple to count_vector

Example

>>> tc.quantum.counts_d2s(np.array([0.1, 0, -0.3, 0.2]))
(array([0, 2, 3]), array([ 0.1, -0.3,  0.2]))

参数

drepr (Tensor) -- [description]
eps (float, optional) -- cutoff to determine nonzero elements, defaults to 1e-7

返回

[description]

返回类型

Tuple[Tensor, Tensor]

tensorcircuit.quantum.count_s2d(srepr: Tuple[Any, Any], n: int) → Any[源代码]#

measurement shots results, sparse tuple representation to dense representation count_vector to count_tuple

参数

srepr (Tuple[Tensor, Tensor]) -- [description]
n (int) -- number of qubits

返回

[description]

返回类型

Tensor

tensorcircuit.quantum.count_t2v(drepr: Any, eps: float = 1e-07) → Tuple[Any, Any]#

measurement shots results, dense representation to sparse tuple representation non-jittable due to the non fixed return shape count_tuple to count_vector

Example

>>> tc.quantum.counts_d2s(np.array([0.1, 0, -0.3, 0.2]))
(array([0, 2, 3]), array([ 0.1, -0.3,  0.2]))

参数

drepr (Tensor) -- [description]
eps (float, optional) -- cutoff to determine nonzero elements, defaults to 1e-7

返回

[description]

返回类型

Tuple[Tensor, Tensor]

tensorcircuit.quantum.count_tuple2dict(count: Tuple[Any, Any], n: int, key: str = 'bin') → Dict[Any, int][源代码]#

count_tuple to count_dict_bin or count_dict_int

参数

count (Tuple[Tensor, Tensor]) -- count_tuple format
n (int) -- number of qubits
key (str, optional) -- can be "int" or "bin", defaults to "bin"

返回

count_dict

返回类型

_type_

tensorcircuit.quantum.count_vector2dict(count: Any, n: int, key: str = 'bin') → Dict[Any, int][源代码]#

convert_vector to count_dict_bin or count_dict_int

参数

count (Tensor) -- tensor in shape [2**n]
n (int) -- number of qubits
key (str, optional) -- can be "int" or "bin", defaults to "bin"

返回

_description_

返回类型

_type_

tensorcircuit.quantum.counts_v2t(srepr: Tuple[Any, Any], n: int) → Any#

measurement shots results, sparse tuple representation to dense representation count_vector to count_tuple

参数

srepr (Tuple[Tensor, Tensor]) -- [description]
n (int) -- number of qubits

返回

[description]

返回类型

Tensor

tensorcircuit.quantum.double_state(h: Any, beta: float = 1) → Any[源代码]#

Compute the double state of the given Hamiltonian operator h.

参数

h (Tensor) -- Hamiltonian operator in form of Tensor.
beta (float, optional) -- Constant for the optimization, default is 1.

返回

The double state of h with the given beta.

返回类型

Tensor

tensorcircuit.quantum.eliminate_identities(nodes: Collection[tensornetwork.network_components.AbstractNode]) → Tuple[dict, dict][源代码]#

Eliminates any connected CopyNodes that are identity matrices. This will modify the network represented by nodes. Only identities that are connected to other nodes are eliminated.

参数: nodes (Collection[AbstractNode]) -- Collection of nodes to search.
返回: The Dictionary mapping remaining Nodes to any replacements, Dictionary specifying all dangling-edge replacements.
返回类型: Dict[Union[CopyNode, AbstractNode], Union[Node, AbstractNode]], Dict[Edge, Edge]

tensorcircuit.quantum.entanglement_entropy(state: Any, cut: Union[int, List[int]]) → Any[源代码]#

tensorcircuit.quantum.entanglement_negativity(rho: Any, transposed_sites: List[int]) → Any[源代码]#

_summary_

参数

rho (Tensor) -- _description_
transposed_sites (List[int]) -- _description_

返回

_description_

返回类型

Tensor

tensorcircuit.quantum.entropy(rho: Union[Any, tensorcircuit.quantum.QuOperator], eps: Optional[float] = None) → Any[源代码]#

Compute the entropy from the given density matrix rho.

Example

@partial(tc.backend.jit, jit_compile=False, static_argnums=(1, 2))
def entanglement1(param, n, nlayers):
    c = tc.Circuit(n)
    c = tc.templates.blocks.example_block(c, param, nlayers)
    w = c.wavefunction()
    rm = qu.reduced_density_matrix(w, int(n / 2))
    return qu.entropy(rm)

@partial(tc.backend.jit, jit_compile=False, static_argnums=(1, 2))
def entanglement2(param, n, nlayers):
    c = tc.Circuit(n)
    c = tc.templates.blocks.example_block(c, param, nlayers)
    w = c.get_quvector()
    rm = w.reduced_density([i for i in range(int(n / 2))])
    return qu.entropy(rm)

>>> param = tc.backend.ones([6, 6])
>>> tc.backend.trace(param)
>>> entanglement1(param, 6, 3)
1.3132654
>>> entanglement2(param, 6, 3)
1.3132653

参数

rho (Union[Tensor, QuOperator]) -- The density matrix in form of Tensor or QuOperator.
eps (float) -- Epsilon, default is 1e-12.

返回

Entropy on the given density matrix.

返回类型

Tensor

tensorcircuit.quantum.fidelity(rho: Any, rho0: Any) → Any[源代码]#

Return fidelity scalar between two states rho and rho0.

\[\operatorname{Tr}(\sqrt{\sqrt{rho} rho_0 \sqrt{rho}})\]

参数

rho (Tensor) -- The density matrix in form of Tensor.
rho0 (Tensor) -- The density matrix in form of Tensor.

返回

The sqrtm of a Hermitian matrix a.

返回类型

Tensor

tensorcircuit.quantum.free_energy(rho: Union[Any, tensorcircuit.quantum.QuOperator], h: Union[Any, tensorcircuit.quantum.QuOperator], beta: float = 1, eps: float = 1e-12) → Any[源代码]#

Compute the free energy of the given density matrix.

Example

>>> rho = np.array([[1.0, 0], [0, 0]])
>>> h = np.array([[-1.0, 0], [0, 1]])
>>> qu.free_energy(rho, h, 0.5)
-0.9999999999979998
>>> hq = qu.QuOperator.from_tensor(h)
>>> qu.free_energy(rho, hq, 0.5)
array([[-1.]])

参数

rho (Union[Tensor, QuOperator]) -- The density matrix in form of Tensor or QuOperator.
h (Union[Tensor, QuOperator]) -- Hamiltonian operator in form of Tensor or QuOperator.
beta (float, optional) -- Constant for the optimization, default is 1.
eps (float, optional) -- Epsilon, default is 1e-12.

返回

The free energy of the given density matrix with the Hamiltonian operator.

返回类型

Tensor

tensorcircuit.quantum.generate_local_hamiltonian(*hlist: Sequence[Any], matrix_form: bool = True) → Union[tensorcircuit.quantum.QuOperator, Any][源代码]#

Generate a local Hamiltonian operator based on the given sequence of Tensor. Note: further jit is recommended. For large Hilbert space, sparse Hamiltonian is recommended

参数

hlist (Sequence[Tensor]) -- A sequence of Tensor.
matrix_form (bool, optional) -- Return Hamiltonian operator in form of matrix, defaults to True.

返回

The Hamiltonian operator in form of QuOperator or matrix.

返回类型

Union[QuOperator, Tensor]

tensorcircuit.quantum.gibbs_state(h: Any, beta: float = 1) → Any[源代码]#

Compute the Gibbs state of the given Hamiltonian operator h.

参数

h (Tensor) -- Hamiltonian operator in form of Tensor.
beta (float, optional) -- Constant for the optimization, default is 1.

返回

The Gibbs state of h with the given beta.

返回类型

Tensor

tensorcircuit.quantum.heisenberg_hamiltonian(g: Any, hzz: float = 1.0, hxx: float = 1.0, hyy: float = 1.0, hz: float = 0.0, hx: float = 0.0, hy: float = 0.0, sparse: bool = True, numpy: bool = False) → Any[源代码]#

Generate Heisenberg Hamiltonian with possible external fields. Currently requires tensorflow installed

Example

>>> g = tc.templates.graphs.Line1D(6)
>>> h = qu.heisenberg_hamiltonian(g, sparse=False)
>>> tc.backend.eigh(h)[0][:10]
array([-11.2111025,  -8.4721365,  -8.472136 ,  -8.472136 ,  -6.       ,
        -5.123106 ,  -5.123106 ,  -5.1231055,  -5.1231055,  -5.1231055],
    dtype=float32)

参数

g (Graph) -- input circuit graph
hzz (float) -- zz coupling, default is 1.0
hxx (float) -- xx coupling, default is 1.0
hyy (float) -- yy coupling, default is 1.0
hz (float) -- External field on z direction, default is 0.0
hx (float) -- External field on y direction, default is 0.0
hy (float) -- External field on x direction, default is 0.0
sparse (bool, defalts True) -- Whether to return sparse Hamiltonian operator, default is True.
numpy (bool, defaults False,) -- whether return the matrix in numpy or tensorflow form

返回

Hamiltonian measurements

返回类型

Tensor

tensorcircuit.quantum.identity(space: Sequence[int], dtype: Optional[Any] = None) → tensorcircuit.quantum.QuOperator[源代码]#

Construct a 'QuOperator' representing the identity on a given space. Internally, this is done by constructing 'CopyNode's for each edge, with dimension according to 'space'.

Example

>>> E = qu.identity((2, 3, 4))
>>> float(E.trace().eval())
24.0

>>> tensor = np.random.rand(2, 2)
>>> psi = qu.QuVector.from_tensor(tensor)
>>> E = qu.identity((2, 2))
>>> psi.eval()
array([[0.03964233, 0.99298281],
       [0.38564989, 0.00950596]])
>>> (E @ psi).eval()
array([[0.03964233, 0.99298281],
       [0.38564989, 0.00950596]])
>>>
>>> (psi.adjoint() @ E @ psi).eval()
array(1.13640257)
>>> psi.norm().eval()
array(1.13640257)

参数

space (Sequence[int]) -- A sequence of integers for the dimensions of the tensor product factors of the space (the edges in the tensor network).
dtype (Any type) -- The data type by np.* (for conversion to dense). defaults None to tc dtype.

返回

The desired identity operator.

返回类型

QuOperator

tensorcircuit.quantum.log_negativity(rho: Any, transposed_sites: List[int], base: str = 'e') → Any[源代码]#

_summary_

参数

rho (Tensor) -- _description_
transposed_sites (List[int]) -- _description_
base (str, optional) -- whether use 2 based log or e based log, defaults to "e"

返回

_description_

返回类型

Tensor

tensorcircuit.quantum.measurement_counts(state: Any, counts: Optional[int] = 8192, format: str = 'count_vector', is_prob: bool = False, random_generator: Optional[Any] = None, status: Optional[Any] = None, jittable: bool = False) → Any[源代码]#

Simulate the measuring of each qubit of p in the computational basis, thus producing output like that of qiskit.

Six formats of measurement counts results:

"sample_int": # np.array([0, 0])

"sample_bin": # [np.array([1, 0]), np.array([1, 0])]

"count_vector": # np.array([2, 0, 0, 0])

"count_tuple": # (np.array([0]), np.array([2]))

"count_dict_bin": # {"00": 2, "01": 0, "10": 0, "11": 0}

"count_dict_int": # {0: 2, 1: 0, 2: 0, 3: 0}

Example

>>> n = 4
>>> w = tc.backend.ones([2**n])
>>> tc.quantum.measurement_results(w, counts=3, format="sample_bin", jittable=True)
array([[0, 0, 1, 0],
    [0, 1, 1, 0],
    [0, 1, 1, 1]])
>>> tc.quantum.measurement_results(w, counts=3, format="sample_int", jittable=True)
array([ 7, 15, 11])
>>> tc.quantum.measurement_results(w, counts=3, format="count_vector", jittable=True)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1])
>>> tc.quantum.measurement_results(w, counts=3, format="count_tuple")
(array([1, 2, 8]), array([1, 1, 1]))
>>> tc.quantum.measurement_results(w, counts=3, format="count_dict_bin")
{'0001': 1, '0011': 1, '1101': 1}
>>> tc.quantum.measurement_results(w, counts=3, format="count_dict_int")
{3: 1, 6: 2}

参数

state (Tensor) -- The quantum state, assumed to be normalized, as either a ket or density operator.
counts (int) -- The number of counts to perform.
shots (int) -- alias for the argument counts
format (str) -- defaults to be "direct", see supported format above
format -- alias for the argument format
is_prob (bool) -- if True, the state is directly regarded as a probability list, defaults to be False
random_generator (Optional[Any]) -- random_generator, defaults to None
status (Optional[Tensor]) -- external randomness given by tensor uniformly from [0, 1], if set, can overwrite random_generator
jittable (bool) -- if True, jax backend try using a jittable count, defaults to False

返回

The counts for each bit string measured.

返回类型

Tuple[]

tensorcircuit.quantum.measurement_results(state: Any, counts: Optional[int] = 8192, format: str = 'count_vector', is_prob: bool = False, random_generator: Optional[Any] = None, status: Optional[Any] = None, jittable: bool = False) → Any#

Simulate the measuring of each qubit of p in the computational basis, thus producing output like that of qiskit.

Six formats of measurement counts results:

"sample_int": # np.array([0, 0])

"sample_bin": # [np.array([1, 0]), np.array([1, 0])]

"count_vector": # np.array([2, 0, 0, 0])

"count_tuple": # (np.array([0]), np.array([2]))

"count_dict_bin": # {"00": 2, "01": 0, "10": 0, "11": 0}

"count_dict_int": # {0: 2, 1: 0, 2: 0, 3: 0}

Example

>>> n = 4
>>> w = tc.backend.ones([2**n])
>>> tc.quantum.measurement_results(w, counts=3, format="sample_bin", jittable=True)
array([[0, 0, 1, 0],
    [0, 1, 1, 0],
    [0, 1, 1, 1]])
>>> tc.quantum.measurement_results(w, counts=3, format="sample_int", jittable=True)
array([ 7, 15, 11])
>>> tc.quantum.measurement_results(w, counts=3, format="count_vector", jittable=True)
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1])
>>> tc.quantum.measurement_results(w, counts=3, format="count_tuple")
(array([1, 2, 8]), array([1, 1, 1]))
>>> tc.quantum.measurement_results(w, counts=3, format="count_dict_bin")
{'0001': 1, '0011': 1, '1101': 1}
>>> tc.quantum.measurement_results(w, counts=3, format="count_dict_int")
{3: 1, 6: 2}

参数

state (Tensor) -- The quantum state, assumed to be normalized, as either a ket or density operator.
counts (int) -- The number of counts to perform.
shots (int) -- alias for the argument counts
format (str) -- defaults to be "direct", see supported format above
format -- alias for the argument format
is_prob (bool) -- if True, the state is directly regarded as a probability list, defaults to be False
random_generator (Optional[Any]) -- random_generator, defaults to None
status (Optional[Tensor]) -- external randomness given by tensor uniformly from [0, 1], if set, can overwrite random_generator
jittable (bool) -- if True, jax backend try using a jittable count, defaults to False

返回

The counts for each bit string measured.

返回类型

Tuple[]

tensorcircuit.quantum.mutual_information(s: Any, cut: Union[int, List[int]]) → Any[源代码]#

Mutual information between AB subsystem described by cut.

参数

s (Tensor) -- The density matrix in form of Tensor.
cut (Union[int, List[int]]) -- The AB subsystem.

返回

The mutual information between AB subsystem described by cut.

返回类型

Tensor

tensorcircuit.quantum.op2tensor(fn: Callable[[...], Any], op_argnums: Union[int, Sequence[int]] = 0) → Callable[[...], Any][源代码]#

tensorcircuit.quantum.partial_transpose(rho: Any, transposed_sites: List[int]) → Any[源代码]#

_summary_

参数

rho (Tensor) -- density matrix
transposed_sites (List[int]) -- sites int list to be transposed

返回

_description_

返回类型

Tensor

tensorcircuit.quantum.ps2coo_core(idx_x: Any, idx_y: Any, idx_z: Any, weight: Any, nqubits: int) → Tuple[Any, Any][源代码]#

tensorcircuit.quantum.ps2xyz(ps: List[int]) → Dict[str, List[int]][源代码]#

pauli string list to xyz dict

# ps2xyz([1, 2, 2, 0]) = {"x": [0], "y": [1, 2], "z": []}

参数: ps (List[int]) -- _description_
返回: _description_
返回类型: Dict[str, List[int]]

tensorcircuit.quantum.quantum_constructor(out_edges: Sequence[tensornetwork.network_components.Edge], in_edges: Sequence[tensornetwork.network_components.Edge], ref_nodes: Optional[Collection[tensornetwork.network_components.AbstractNode]] = None, ignore_edges: Optional[Collection[tensornetwork.network_components.Edge]] = None) → tensorcircuit.quantum.QuOperator[源代码]#

Constructs an appropriately specialized QuOperator. If there are no edges, creates a QuScalar. If the are only output (input) edges, creates a QuVector (QuAdjointVector). Otherwise creates a QuOperator.

Example

def show_attributes(op):
    print(f"op.is_scalar()              -> {op.is_scalar()}")
    print(f"op.is_vector()              -> {op.is_vector()}")
    print(f"op.is_adjoint_vector()      -> {op.is_adjoint_vector()}")
    print(f"len(op.out_edges)   -> {len(op.out_edges)}")
    print(f"len(op.in_edges)    -> {len(op.in_edges)}")

>>> psi_node = tn.Node(np.random.rand(2, 2))
>>>
>>> op = qu.quantum_constructor([psi_node[0]], [psi_node[1]])
>>> show_attributes(op)
op.is_scalar()          -> False
op.is_vector()          -> False
op.is_adjoint_vector()  -> False
len(op.out_edges)       -> 1
len(op.in_edges)        -> 1
>>> # psi_node[0] -> op.out_edges[0]
>>> # psi_node[1] -> op.in_edges[0]

>>> op = qu.quantum_constructor([psi_node[0], psi_node[1]], [])
>>> show_attributes(op)
op.is_scalar()          -> False
op.is_vector()          -> True
op.is_adjoint_vector()  -> False
len(op.out_edges)       -> 2
len(op.in_edges)        -> 0
>>> # psi_node[0] -> op.out_edges[0]
>>> # psi_node[1] -> op.out_edges[1]

>>> op = qu.quantum_constructor([], [psi_node[0], psi_node[1]])
>>> show_attributes(op)
op.is_scalar()          -> False
op.is_vector()          -> False
op.is_adjoint_vector()  -> True
len(op.out_edges)       -> 0
len(op.in_edges)        -> 2
>>> # psi_node[0] -> op.in_edges[0]
>>> # psi_node[1] -> op.in_edges[1]

参数

out_edges (Sequence[Edge]) -- A list of output edges.
in_edges (Sequence[Edge]) -- A list of input edges.
ref_nodes (Optional[Collection[AbstractNode]], optional) -- Reference nodes for the tensor network (needed if there is a. scalar component).
ignore_edges (Optional[Collection[Edge]], optional) -- Edges to ignore when checking the dimensionality of the tensor network.

返回

The new created QuOperator object.

返回类型

QuOperator

tensorcircuit.quantum.quimb2qop(qb_mpo: Any) → tensorcircuit.quantum.QuOperator[源代码]#

Convert MPO in Quimb package to QuOperator.

参数: tn_mpo (quimb.tensor.tensor_gen.*) -- MPO in the form of Quimb package
返回: MPO in the form of QuOperator
返回类型: QuOperator

tensorcircuit.quantum.reduced_density_matrix(state: Union[Any, tensorcircuit.quantum.QuOperator], cut: Union[int, List[int]], p: Optional[Any] = None) → Union[Any, tensorcircuit.quantum.QuOperator][源代码]#

Compute the reduced density matrix from the quantum state state.

参数

state (Union[Tensor, QuOperator]) -- The quantum state in form of Tensor or QuOperator.
cut (Union[int, List[int]]) -- the index list that is traced out, if cut is a int, it indicates [0, cut] as the traced out region
p (Optional[Tensor]) -- probability decoration, default is None.

返回

The reduced density matrix.

返回类型

Union[Tensor, QuOperator]

tensorcircuit.quantum.reduced_wavefunction(state: Any, cut: List[int], measure: Optional[List[int]] = None) → Any[源代码]#

Compute the reduced wavefunction from the quantum state state. The fixed measure result is guaranteed by users, otherwise final normalization may required in the return

参数

state (Tensor) -- _description_
cut (List[int]) -- the list of position for qubit to be reduced
measure (List[int]) -- the fixed results of given qubits in the same shape list as cut

返回

_description_

返回类型

Tensor

tensorcircuit.quantum.renyi_entropy(rho: Union[Any, tensorcircuit.quantum.QuOperator], k: int = 2) → Any[源代码]#

Compute the Rényi entropy of order \(k\) by given density matrix.

参数

rho (Union[Tensor, QuOperator]) -- The density matrix in form of Tensor or QuOperator.
k (int, optional) -- The order of Rényi entropy, default is 2.

返回

The \(k\) th order of Rényi entropy.

返回类型

Tensor

tensorcircuit.quantum.renyi_free_energy(rho: Union[Any, tensorcircuit.quantum.QuOperator], h: Union[Any, tensorcircuit.quantum.QuOperator], beta: float = 1, k: int = 2) → Any[源代码]#

Compute the Rényi free energy of the corresponding density matrix and Hamiltonian.

Example

>>> rho = np.array([[1.0, 0], [0, 0]])
>>> h = np.array([[-1.0, 0], [0, 1]])
>>> qu.renyi_free_energy(rho, h, 0.5)
-1.0
>>> qu.free_energy(rho, h, 0.5)
-0.9999999999979998

参数

rho (Union[Tensor, QuOperator]) -- The density matrix in form of Tensor or QuOperator.
h (Union[Tensor, QuOperator]) -- Hamiltonian operator in form of Tensor or QuOperator.
beta (float, optional) -- Constant for the optimization, default is 1.
k (int, optional) -- The order of Rényi entropy, default is 2.

返回

The \(k\) th order of Rényi entropy.

返回类型

Tensor

tensorcircuit.quantum.sample2all(sample: Any, n: int, format: str = 'count_vector', jittable: bool = False) → Any[源代码]#

transform sample_int or sample_bin form results to other forms specified by format

参数

sample (Tensor) -- measurement shots results in sample_int or sample_bin format
n (int) -- number of qubits
format (str, optional) -- see the doc in the doc in tensorcircuit.quantum.measurement_results(), defaults to "count_vector"
format -- alias for the argument format
jittable (bool, optional) -- only applicable to count transformation in jax backend, defaults to False

返回

measurement results specified as format

返回类型

Any

tensorcircuit.quantum.sample2count(sample: Any, n: int, jittable: bool = True) → Tuple[Any, Any][源代码]#

sample_int to count_tuple

参数

sample (Tensor) -- _description_
n (int) -- _description_
jittable (bool, optional) -- _description_, defaults to True

返回

_description_

返回类型

Tuple[Tensor, Tensor]

tensorcircuit.quantum.sample_bin2int(sample: Any, n: int) → Any[源代码]#

bin sample to int sample

参数

sample (Tensor) -- in shape [trials, n] of elements (0, 1)
n (int) -- number of qubits

返回

in shape [trials]

返回类型

Tensor

tensorcircuit.quantum.sample_int2bin(sample: Any, n: int) → Any[源代码]#

int sample to bin sample

参数

sample (Tensor) -- in shape [trials] of int elements in the range [0, 2**n)
n (int) -- number of qubits

返回

in shape [trials, n] of element (0, 1)

返回类型

Tensor

tensorcircuit.quantum.spin_by_basis(n: int, m: int, elements: Tuple[int, int] = (1, - 1)) → Any[源代码]#

Generate all n-bitstrings as an array, each row is a bitstring basis. Return m-th col.

Example

>>> qu.spin_by_basis(2, 1)
array([ 1, -1,  1, -1])

参数

n (int) -- length of a bitstring
m (int) -- m<n,
elements (Tuple[int, int], optional) -- the binary elements to generate, default is (1, -1).

返回

The value for the m-th position in bitstring when going through all bitstring basis.

返回类型

Tensor

tensorcircuit.quantum.taylorlnm(x: Any, k: int) → Any[源代码]#

Taylor expansion of \(ln(x+1)\).

参数

x (Tensor) -- The density matrix in form of Tensor.
k (int, optional) -- The \(k\) th order, default is 2.

返回

The \(k\) th order of Taylor expansion of \(ln(x+1)\).

返回类型

Tensor

tensorcircuit.quantum.tn2qop(tn_mpo: Any) → tensorcircuit.quantum.QuOperator[源代码]#

Convert MPO in TensorNetwork package to QuOperator.

参数: tn_mpo (tn.matrixproductstates.mpo.*) -- MPO in the form of TensorNetwork package
返回: MPO in the form of QuOperator
返回类型: QuOperator

tensorcircuit.quantum.trace_distance(rho: Any, rho0: Any, eps: float = 1e-12) → Any[源代码]#

Compute the trace distance between two density matrix rho and rho2.

参数

rho (Tensor) -- The density matrix in form of Tensor.
rho0 (Tensor) -- The density matrix in form of Tensor.
eps (float, optional) -- Epsilon, defaults to 1e-12

返回

The trace distance between two density matrix rho and rho2.

返回类型

Tensor

tensorcircuit.quantum.trace_product(*o: Union[Any, tensorcircuit.quantum.QuOperator]) → Any[源代码]#

Compute the trace of several inputs o as tensor or QuOperator.

\[\operatorname{Tr}(\prod_i O_i)\]

Example

>>> o = np.ones([2, 2])
>>> h = np.eye(2)
>>> qu.trace_product(o, h)
2.0
>>> oq = qu.QuOperator.from_tensor(o)
>>> hq = qu.QuOperator.from_tensor(h)
>>> qu.trace_product(oq, hq)
array([[2.]])
>>> qu.trace_product(oq, h)
array([[2.]])
>>> qu.trace_product(o, hq)
array([[2.]])

返回: The trace of several inputs.
返回类型: Tensor

tensorcircuit.quantum.truncated_free_energy(rho: Any, h: Any, beta: float = 1, k: int = 2) → Any[源代码]#

Compute the truncated free energy from the given density matrix rho.

参数

rho (Tensor) -- The density matrix in form of Tensor.
h (Tensor) -- Hamiltonian operator in form of Tensor.
beta (float, optional) -- Constant for the optimization, default is 1.
k (int, optional) -- The \(k\) th order, defaults to 2

返回

The \(k\) th order of the truncated free energy.

返回类型

Tensor

tensorcircuit.quantum.xyz2ps(xyz: Dict[str, List[int]], n: Optional[int] = None) → List[int][源代码]#

xyz dict to pauli string list

参数

xyz (Dict[str, List[int]]) -- _description_
n (Optional[int], optional) -- _description_, defaults to None

返回

_description_

返回类型

List[int]