Quantum Toolkit

Our Quantum Toolkit enables high-performance algorithms used in quantum many-body physics to be called natively in Aleph.

Global Constants

Name	Description
as_abstract	Constant object representing the StateInfo option AbstractT.
as_basisstate	Constant object representing the StateInfo option BasisStateT.
as_complete	Constant object representing the StateInfo option CompleteT.
as_dense	Constant object representing the StateInfo option DenseT.
as_fermion	Constant object representing the StateInfo option FermionT.
as_heterogenousqdit	Constant object representing the StateInfo option HeterogenousQditT.
as_homogenousqdit	Constant object representing the StateInfo option HomogenousQditT.
as_inversion	Constant object representing the StateInfo option InversionT.
as_magnetization	Constant object representing the StateInfo option MagnetizationT.
as_magnetizationspinfliptranslation	Constant object representing the StateInfo option MagnetizationSpinFlipTranslationT.
as_magnetizationtranslation	Constant object representing the StateInfo option MagnetizationTranslationT.
as_number	Constant object representing the StateInfo option NumberT.
as_singleparticle	Constant object representing the StateInfo option SingleParticleT.
as_sparse	Constant object representing the StateInfo option SparseT.
as_spinflip	Constant object representing the StateInfo option SpinFlipT.
as_spinhalf	Constant object representing the StateInfo option SpinhalfT.
as_statevector	Constant object representing the StateInfo option StateVectorT.
as_translation	Constant object representing the StateInfo option TranslationT.
as_unknown	Constant object representing the StateInfo option UnknownT.
as_unspecified	Constant object representing an unspecified StateInfo option.
eigsstatus	A global EigsStatus instance to select iterative eigensolver computation status.
spectrum	The spectrum selector has methods that return SpectrumItem objects that are used in the context of iterative eigensolvers. These SpectrumItem objects specify which part of the spectrum to target. For instance, one can create a SpectrumItem that targets the largest absolute eigenvalues by calling spectrum.largest_abs. Similarly, spectrum.smallest_real returns a SpectrumItem that targets the smallest real eigenvalues.

Factories

Name	Description
CNOT	Returns a spin-1/2 OperatorNamed for the CNOT (controlled-NOT) gate, taking a vector of site indices.
CoulombSum	Returns a Coulomb tensor operator $\sum_{i,j,k,l,\sigma,\sigma'} V_{ijkl} a_{i\sigma}^\dagger a_{j\sigma'}^\dagger a_{k\sigma'} a_{l\sigma}$.
Create	Returns the fermionic creation operator $f_{i}^\dagger$ with support on the specified site.
Destroy	Returns the fermionic annihilation operator $f_{i}$ with support on the specified site.
DoubleExcitation	Legacy alias for PairHop. Returns the pair hopping operator $f_{i}^\dagger f_{j}^\dagger f_{k} f_{l} + \mathrm{h.c.}$ with support on the specified sites.
DualUnitary	Returns a spin-1/2 dual unitary operator: $\exp(i(\frac{\pi}{4} X(i) X(j) + \frac{\pi}{4} Y(i) Y(j) + J_z Z(i) Z(j)))$ where $i, j$ are the site indices.
Fbit	Constructs a fermionic product state from a string of consecutive characters "$0$" and "$1$".
FermiId	Returns the fermionic identity operator $\mathcal{I}$.
Flip	Creates a spin-1/2 OperatorPermute that flips spins at specified sites.
FlipAll	Creates a spin-1/2 OperatorPermute that flips all spins.
Floquet	Returns a spin-1/2 Floquet$(J_x, J_y, J_z) = \exp(-i(J_x X(i) + J_y Y(i) + J_z Z(i)) Z(j))$ where $i, j$ are the site indices corresponding to the first and second elements of sites.
FourBody	Legacy alias for PairTransfer. Returns the directed pair transfer operator $f_{i}^\dagger f_{j}^\dagger f_{k} f_{l}$ with support on the specified sites.
Hgate	Returns a spin-1/2 OperatorNamed for the Hadamard gate.
Hop	Returns the fermionic hopping operator $f_{i}^\dagger f_{j} + f_{j}^\dagger f_{i}$ with support on the specified sites.
HopNumber	Returns the hop-number operator $(f_{i}^\dagger f_{j} + f_{j}^\dagger f_{i}) n_{k}$ with support on the specified sites.
ID	Returns a spin-1/2 OperatorNamed for the Identity operator. No site parameter is required as it acts globally.
ModeRotation	Returns the mode rotation operator $\exp(i \theta (f_{i}^\dagger f_{j} + f_{j}^\dagger f_{i}))$ with support on the specified sites.
NearestNumberSum	Returns the sum of nearest-neighbor number interactions $\sum_{i} n_{i} n_{i+1}$ with support on the specified sites.
NextNearestNumberSum	Returns the sum of next-nearest-neighbor number interactions $\sum_{i} n_{i} n_{i+2}$ with support on the specified sites.
Number	Returns the fermionic number operator $n_{i} = f_{i}^\dagger f_{i}$ with support on the specified site.
NumberN	Legacy alias for NumberSum. Returns the sum of fermionic number operators $\sum_{i \in \mathrm{sites}} n_{i}$ with support on the specified sites.
NumberNumber	Returns the two-site fermionic number-number interaction operator $n_{i} n_{j} = f_{i}^\dagger f_{i} f_{j}^\dagger f_{j}$ with support on the specified sites.
NumberNumberNN	Legacy alias for NearestNumberSum. Returns the sum of nearest-neighbor number interactions $\sum_{i} n_{i} n_{i+1}$ with support on the specified sites.
NumberNumberNNN	Legacy alias for NextNearestNumberSum. Returns the sum of next-nearest-neighbor number interactions $\sum_{i} n_{i} n_{i+2}$ with support on the specified sites.
NumberNumberPhase	Returns the two-site number-number phase operator $\exp(i \phi n_{i} n_{j})$ with support on the specified sites.
NumberPhase	Returns the site number phase operator $\exp(i \phi n_i)$ with support on the specified site.
NumberPotential	Returns an operator representing a weighted sum of number operators $\sum_{i=0}^{N-1} \alpha_i n_i$, where the site indices are implicitly $0, 1, \dots, N-1$. If a subset of sites or a different ordering is desired, use the factory overload that accepts an explicit list of site indices.
NumberSum	Returns the sum of fermionic number operators $\sum_{i \in \mathrm{sites}} n_{i}$ with support on the specified sites.
PairHop	Returns the pair hopping operator $f_{i}^\dagger f_{j}^\dagger f_{k} f_{l} + \mathrm{h.c.}$ with support on the specified sites.
PairRotation	Returns the pair rotation operator $\exp(i \theta (f_{i}^\dagger f_{j}^\dagger + f_{j} f_{i}))$ with support on the specified sites.
PairTransfer	Returns the directed pair transfer operator $f_{i}^\dagger f_{j}^\dagger f_{k} f_{l}$ with support on the specified sites.
Permute	Creates a spin-1/2 OperatorPermute that permutes spins according to a specified permutation.
Phase	Returns a global phase spin-1/2 operator $P(\phi) = e^{-i\phi}$.
PhaseHop	Returns the complex phase-hop operator $e^{i \phi} f_{i}^\dagger f_{j} + e^{-i \phi} f_{j}^\dagger f_{i}$ with support on the specified sites.
Proj0	Returns a spin-1/2 OperatorNamed for the projector $\|0\rangle\langle 0\|$.
Proj1	Returns a spin-1/2 OperatorNamed for the projector $\|1\rangle\langle 1\|$.
Qbit	Constructs a qubit product state of size num_sites with every qubit set to $0$.
Reflect	Creates a spin-1/2 OperatorPermute that reflects all spins about the center.
RotEuler	Returns a general spin-1/2 rotation operator RotEuler$(\phi,\theta,\omega) = RZ(\omega)RX(\theta)RZ(\phi) = e^{(-i \omega Z/2)} e^{(-i \theta X/2)} e^{(-i \phi Z/2)}$.
RotX	Returns a spin-1/2 RotX$(\phi) = e^{-i\phi X/2}$ rotation operator around the X-axis.
RotY	Returns a spin-1/2 RotY$(\phi) = e^{-i\phi Y/2}$ rotation operator around the Y-axis.
RotZ	Returns a spin-1/2 RotZ$(\phi) = e^{-i\phi Z/2}$ rotation operator around the Z-axis.
SWAP	Returns a spin-1/2 OperatorNamed for the SWAP gate, taking a vector of site indices.
SX	Returns a spin-1/2 OperatorNamed for Spin-X operator.
SY	Returns a spin-1/2 OperatorNamed for Spin-Y operator.
SZ	Returns a spin-1/2 OperatorNamed for Spin-Z operator.
Sgate	Returns a spin-1/2 OperatorNamed for the S gate.
Sminus	Returns a spin-1/2 OperatorNamed for Spin-minus operator.
Splus	Returns a spin-1/2 OperatorNamed for Spin-plus operator.
Tgate	Returns a spin-1/2 OperatorNamed for the T gate.
Transfer	Returns the directed fermionic transfer operator $f_{i}^\dagger f_{j}$ with support on the specified sites.
TransferNumber	Returns the transfer-number operator $f_{i}^\dagger f_{j} n_{k}$ with support on the specified sites.
Translate	Creates a spin-1/2 OperatorPermute that translates spins by a specified shift.
UnitaryXYZ	Returns a spin-1/2 UnitaryXYZ$(J_x, J_y, J_z)$ operator: $\exp(-i(J_x X(i) X(j) + J_y Y(i) Y(j) + J_z Z(i) Z(j)))$ where $i, j$ are the site indices.
X	Returns a spin-1/2 OperatorNamed for Pauli-X operator.
XX	Returns a spin-1/2 OperatorNamed for $X_i \cdot X_j$ operator, taking a vector of site indices.
XXPYY	Returns a spin-1/2 OperatorNamed for $X_i \cdot X_j + Y_i \cdot Y_j$ operator, taking a vector of site indices.
Y	Returns a spin-1/2 OperatorNamed for Pauli-Y operator.
YY	Returns a spin-1/2 OperatorNamed for $Y_i \cdot Y_j$ operator, taking a vector of site indices.
Z	Returns a spin-1/2 OperatorNamed for Pauli-Z operator.
ZN	Returns a spin-1/2 OperatorNamed for $\sum_{i \in \text{sites}} Z_i$ operator.
ZZ	Returns a spin-1/2 OperatorNamed for $Z_i \cdot Z_j$ operator, taking a vector of site indices.
ZZNN	Returns a spin-1/2 OperatorNamed for $\sum_{i \in \text{sites}} Z_i \otimes Z_{i+1}$ operator.
ZZNNN	Returns a spin-1/2 OperatorNamed for $\sum_{i \in \text{sites}} Z_i \otimes Z_{i+2}$ operator.
accumulator	Factory for constructing accumulators.
coefficient	Creates a Coefficient that can be added to a Model.
lattice	Constructor for lattice class.
lattice_coordinate	Constructor for lattice coordinate.
make_random_mpo	Generate a random Matrix Product Operator (MPO) with Complex values.
make_random_mps	Generate a random Matrix Product State (MPS) with Complex values.
matrix	Converts the operator to its matrix representation.
model	Constructs a model containing a lattice.
neighbourhood_rule	Constructor for a neighbourhood rule.
operator_dense	Returns a spin-1/2 OperatorDense parametrized by the given matrix.
operator_diagonal	Returns a spin-1/2 diagonal operator with specified diagonal elements.
operator_free	Generates an operator that represents the hopping terms of the input matrix.
operator_function	Approximates a matrix function using the Krylov subspace method.
operator_generic	Creates a spin-1/2 OperatorGeneric from a string representation.
operator_prod	Creates an empty OperatorProduct.
operator_sparse	Returns a spin-1/2 OperatorSparse parametrized by the given matrix.
operator_stencil	Generates a stencil operator.
operator_sum	Creates an empty ComplexOperatorSum with complex coefficients (default behavior).
pauli_string	Creates a spin-1/2 OperatorPauliString from a string representation.
qbit_range	Creates a range of Qbit objects with the specified number of sites.
sse_order_estimator	Constructs the estimator for the order in an SSE simulation.
sse_simulation	Constructs an SSE simulation instance.
state_range	Creates an iterator for a range of state objects matching the provided option.
state_vector	State vector factory.
support_table	Constructs a SupportTable from a vector of NeighbourhoodRule and a Lattice.
term	Constructs a term that can be added to a model.

Types

Name	Description
Accumulator	Base class for all accumulators.
AlephSingleSiteOperatorFactory	A function taking an index corresponding to a site on a lattice and returning an Operator.
BasisState	Represents a quantum product state \vert s_1s_2...s_n\rangle.
BinningAccumulator	Accumulator that stores bin means.
BoundaryConditionType	Boundary condition for Lattice geometries.
ChebyshevSeries	A Chebyshev series representation of a real-valued function.
Coefficient	Represents a coefficient in a model that multiplies a term. Can be either a real number of a function of a list of lattice coordinates returning a real number.
CoefficientFactory	A function of a List of LatticeCoordinate that returns a real number.
ComplexFreeMatrix	This operator efficiently represents a sum of fermionic hopping and number operators. It is designed to provide efficient kernels for solving single particle (free) fermionic problems.
ComplexFreeStencil	This operator is designed to provide efficient methods for calculations involving a structured free operator (single particle symmetry sector of a fermionic Hilbert space). A free operator which can be written as a stencil assumes the general form $\sum_{s}\sum_{n=0}^N \alpha_{n}c_{s}^{\dagger}c_{s+\delta_n}$ where $\delta_n$are displacement vectors, $s$ are lattice position vectors, the $\alpha_n$ are position independent coefficients and $N$ is the number of such coefficients. To construct a stencil, the above parameters must be passed explicitly, together with information about the lattice dimensions and the boundary conditions. For more details, please see the operator_free factory.
ComplexMPO	Matrix Product Operator (MPO) of Complex values. Compressed representation of large-dimensional tensors, well suited to the representation of quantum operators for 1D many-body physics problems.
ComplexMPS	Matrix Product State (MPS) of Complex values. Compressed representation of a large-dimensional tensor, well suited for state vectors of some 1D many-body quantum mechanics problems.
ComplexOperatorCoulombSum	Represents a Coulomb tensor operator, with interactions defined as a 4-rank tensor.
ComplexOperatorSum	Represents a sum of operators with complex scalar coefficients. Each term consists of a complex coefficient and an operator. Create instances using the operator_sum() factory function.
Constraint	A function taking in a lattice coordinate and returning a Boolean that specifies when a given lattice coordinate is a valid reference for a neighbourhood.
EigsArnoldi<LinearOperator<complex>>	EigsArnoldi iterative eigensolver.
EigsArnoldi<LinearOperator<real>>	EigsArnoldi iterative eigensolver.
EigsBase<LinearOperator<complex>>	Base class for iterative eigensolvers.
EigsBase<LinearOperator<real>>	Base class for iterative eigensolvers.
EigsLanczos<LinearOperator<complex>>	EigsLanczos iterative eigensolver.
EigsLanczos<LinearOperator<real>>	EigsLanczos iterative eigensolver.
EigsStatus	Helper class to access CompInfo enum values.
EigsStatusItem	Computation info for iterative eigensolvers. The computation info indicates the status of the computation after running an iterative eigensolver. The allowed values are:...
Estimate	Statistical estimate from binned values containing value of estimate and variance on the value.
Estimator	Base class for estimators.
Fbit	An object representing a product state of fermionic modes.
FbitRange	A range of Fbit objects.
HeterogenousQdit	Qdit type.
HomogenousQdit	Qdit type.
Interval	Represents a closed interval [a, b] of real numbers.
Lattice	Class that represents a crystal lattice (Bravais lattice and atomic basis)
LatticeCoordinate	Represents a lattice coordinate in terms of primitive indices and a basis index.
LatticeRange	A range of lattice coordinates used to iterate over lattice coordinates.
LinearOperator<complex>	Spectra operator wrapper for complex-valued operators.
LinearOperator<real>	Spectra operator wrapper for real-valued operators.
List<AlephSingleSiteOperatorFactory>	A list of single site operator factories.
List<Fbit>	A list of Fbit objects.
List<HeterogenousQdit>	A list of HeterogenousQdit objects.
List<HomogenousQdit>	A list of HomogenousQdit objects.
List<Qbit>	A list of Qbit objects.
List<SSECell>	A list of SSECells produced by the Monte Carlo.
List<SSEConfig>	A list of SSEConfigEntry.
List<SSEConfigEntry>	A list of SSEConfigEntry.
Model	Stores the terms of a lattice Hamiltonian and associated observables in terms of lattice coordinates and neighbourhoods.
NeighbourhoodRule	A representation of a neighbourhood of a given LatticeCoordinate on a Lattice
NoBinningAccumulator	Accumulator that doesn't bin values.
Operator	Base class for all quantum operators.
OperatorChebyshevSeries	A Chebyshev series operator is defined in terms of a Chebyshev series and an operator. It applies the Chebyshev series to the operator when acting on vectors. For example, a Chebyshev series $p(x) = \sum_{n=0}^{N} a_n T_n(x)$ becomes $p(A) = \sum_{n=0}^{N} a_n T_n(A)$ when applied to an operator $A$, where $T_n$ are the Chebyshev polynomials.
OperatorDense<complex>	Class representing a spin-1/2 dense operator. The operator is parametrized with a dense matrix and the site indices. The matrix dimension must be equal to $2^{n} \times 2^{n}$, where $n$ is the number of sites the operator acts on.
OperatorDense<real>	Class representing a spin-1/2 dense operator. The operator is parametrized with a dense matrix and the site indices. The matrix dimension must be equal to $2^{n} \times 2^{n}$, where $n$ is the number of sites the operator acts on.
OperatorDiagonal<complex>	Class representing a spin-1/2 diagonal operator. The operator is parametrized with the diagonal elements and the site indices. The number of diagonal elements must be equal to $2^{n}$, where $n$ is the number of sites the operator acts on.
OperatorDiagonal<real>	Class representing a spin-1/2 diagonal operator. The operator is parametrized with the diagonal elements and the site indices. The number of diagonal elements must be equal to $2^{n}$, where $n$ is the number of sites the operator acts on.
OperatorFermiNamed	Represents a named fermionic operator acting on specified sites. Create instances using factory functions like Create(), Destroy(), Number(), or Hop().
OperatorGeneric<complex>	Class representing a generic operator. The operator is parametrized with a function accepting a matrix of state vector coefficients and an array of integers labelling the basis states corresponding to the coefficients. The function modifies the matrix in-place to apply the operator effect. The operator also includes the site indices where it acts.
OperatorGeneric<real>	Class representing a generic operator. The operator is parametrized with a function accepting a matrix of state vector coefficients and an array of integers labelling the basis states corresponding to the coefficients. The function modifies the matrix in-place to apply the operator effect. The operator also includes the site indices where it acts.
OperatorNamed	Represents a named spin-1/2 operator acting on specified sites. Create instances using factory functions like X(), Y(), Z(), CNOT(), SWAP(), etc.
OperatorParam<real>	Represents a parametrized spin-1/2 operator with rotation angles or phase parameters. Create instances using factory functions like Phase(), RotX(), RotY(), RotZ(), RotEuler(), etc.
OperatorPauliString	Represents a Pauli string operator constructed from a sequence of Pauli operators. Create instances using the pauli_string() factory function.
OperatorPermute	Represents a permutation operator that rearranges or transforms qubit states. Create instances using factory functions like Flip(), FlipAll(), Reflect(), or Translate().
OperatorPolynomial	A polynomial operator is defined in terms of a polynomial and an operator. It applies the polynomial to the operator when acting on vectors. For example, a polynomial $p(x) = \sum_{n=0}^{N} a_n x^n$ becomes $p(A) = \sum_{n=0}^{N} a_n A^n$ when applied to an operator $A$.
OperatorProduct	Represents a product of operators without scalar coefficients. For products with coefficients (e.g., 2.0*X(0)*Y(1)), use OperatorSum instead. Create instances using the operator_prod() factory function.
OperatorSparse<complex>	Class representing a spin-1/2 sparse operator. The operator is parametrized with a sparse matrix and the site indices. The matrix dimension must be equal to $2^{n} \times 2^{n}$, where $n$ is the number of sites the operator acts on.
OperatorSparse<real>	Class representing a spin-1/2 sparse operator. The operator is parametrized with a sparse matrix and the site indices. The matrix dimension must be equal to $2^{n} \times 2^{n}$, where $n$ is the number of sites the operator acts on.
Polynomial<complex>	A Polynomial<complex>-valued polynomial.
Polynomial<real>	A Polynomial<real>-valued polynomial.
Qbit	An object representing a product state of qubits.
QbitRange	A range of Qbit objects.
RealFreeMatrix	This operator efficiently represents a sum of fermionic hopping and number operators. It is designed to provide efficient kernels for solving single particle (free) fermionic problems.
RealFreeStencil	This operator is designed to provide efficient methods for calculations involving a structured free operator (single particle symmetry sector of a fermionic Hilbert space). A free operator which can be written as a stencil assumes the general form $\sum_{s}\sum_{n=0}^N \alpha_{n}c_{s}^{\dagger}c_{s+\delta_n}$ where $\delta_n$are displacement vectors, $s$ are lattice position vectors, the $\alpha_n$ are position independent coefficients and $N$ is the number of such coefficients. To construct a stencil, the above parameters must be passed explicitly, together with information about the lattice dimensions and the boundary conditions. For more details, please see the operator_free factory.
RealMPO	Matrix Product Operator (MPO) of Real values. Compressed representation of large-dimensional tensors, well suited to the representation of quantum operators for 1D many-body physics problems.
RealMPS	Matrix Product State (MPS) of Real values. Compressed representation of a large-dimensional tensor, well suited for state vectors of some 1D many-body quantum mechanics problems.
RealOperatorCoulombSum	Represents a Coulomb tensor operator, with interactions defined as a 4-rank tensor.
RealOperatorFermiParam	Represents a named fermionic operator acting on specified sites. Create instances using factory functions like Create(), Destroy(), Number(), or Hop().
RealOperatorSum	Represents a sum of operators with real scalar coefficients. Each term consists of a real coefficient and an operator. Create instances using the operator_sum() factory function.
SSECell	Simulation Cell generated by the stochastic series expansion Monte Carlo.
SSECellParameters	Parameters for the simulation cell.
SSEConfigEntry	Configuration entry with vertex index, support index, and the sites acted on.
SSEOrderEstimator	Estimator for the order of the stochastic series expansion
SSESimulation	Simulation manager for the stochastic series expansion.
SSEVertex	Vertex used in the stochastic series expansion Monte Carlo.
SingleAccumulator	Base class for all accumulators.
SpectrumItem	Target spectrum enumerator for iterative eigensolvers. Iterative eigensolvers target specific parts of the spectrum. The allowed values are:...
State	Base class for all quantum state representations.
StateInfo	An object representing the combination of a set of mutually compatible options. It is used in conjunction with the state_vector factory to specify the desired state.
StateVector	Base class for all state vector representations.
StateVector<Complex,Fermion,Dense,Complete>	A class representing a fermionic state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that appears in the state vector. It provides various optimized quantum routines and is compatible with any fermionic operator.
StateVector<Complex,Fermion,Dense,SingleParticle>	A class representing a fermionic state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that appears in the state vector. It provides various optimized quantum routines and is compatible with any fermionic operator.
StateVector<Complex,Spinhalf,Dense,Complete>	A class representing a spin-1/2 state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each spin-1/2 product state that form the basis of the state vector. It provides various optimized quantum routines and is compatible with any spin-1/2 operator.
StateVector<Complex,Unknown,Dense,Complete>	A class representing a spin half state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that for the basis of the state vector. It provides various optimized quantum routines and is compatible with any spin half operator.
StateVector<Real,Fermion,Dense,Complete>	A class representing a fermionic state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that appears in the state vector. It provides various optimized quantum routines and is compatible with any fermionic operator.
StateVector<Real,Fermion,Dense,SingleParticle>	A class representing a fermionic state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that appears in the state vector. It provides various optimized quantum routines and is compatible with any fermionic operator.
StateVector<Real,Fermion,Sparse,Number>	A class representing a fermionic state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that appears in the state vector. It provides various optimized quantum routines and is compatible with any fermionic operator.
StateVector<Real,Spinhalf,Dense,Complete>	A class representing a spin-1/2 state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each spin-1/2 product state that form the basis of the state vector. It provides various optimized quantum routines and is compatible with any spin-1/2 operator.
StateVector<Real,Unknown,Dense,Complete>	A class representing a spin half state vector. The object stores a set of coefficients corresponding to the multiplicative coefficients in front of each computational basis state that for the basis of the state vector. It provides various optimized quantum routines and is compatible with any spin half operator.
SupportTable	Stores the linear indices associated with some number of name neighbourhoods.
Term	Represents a term in a model storing a coefficient name, a list of functions to produce an operator product, and the name of a neighbourhood rule.

Module Functions

Name	Description
Heisenberg	Returns a Heisenberg model Hamiltonian: $H = h\sum_i F(i) + \sum_i [J_x \sigma^x_i \sigma^x_{i+1} + J_y \sigma^y_i \sigma^y_{i+1} + J_z \sigma^z_i \sigma^z_{i+1}]$.
Heisenberg_1d	Generate the Hamiltonian MPO for the 1D Heisenberg model with Complex values.
Ising_1d	Generate the Hamiltonian MPO for the 1D transverse-field Ising model with Complex values.
LinearOperator	Constructs an LinearOperator from an Operator.
SupportTable	Constructs a SupportTable from a vector of NeighbourhoodRule and a Lattice.
both_ends	Returns the both_ends enum value.
chebyshev_series_delta	Generates a Chebyshev series that approximates a delta function over the specified interval.
coefficient_matrix	Creates a bipartite coefficient matrix from a single state vector using arbitrary subsystem cuts.
commutator	Computes the commutator of two quantum operators [A,B] = AB - BA. Returns zero operator for identical operators or operators acting on disjoint sites.
converted_to_create_destroy	Converts a sum or product of named fermion operators to their equivalent representation in terms of creation and annihilation operators.
dmrg	Compute the ground state of a quantum many-body system using the Density Matrix Renormalization Group (DMRG) algorithm.
fbit_range	Creates a range of Fbit objects with the specified number of sites.
fermionic_site_reorder	Reorders sum or products of creation and annihilation operators in place by site while preserving order on each site.
flatten	Flattens any operator by expanding all expressions into a sum of products (in-place).
flattened	Flattens any operator by expanding all expressions into a sum of products (out-of-place).
fused_into_number	Fuses the appropriate creation and annihilation operators into number operators.
haar_matrix	Generate a square Haar random unitary matrix of a specified size.
haar_vector	Generates a Haar random vector of a specified size.
integer	Returns the integer representation of the qubit state.
interval	Constructs an interval [lower, upper].
is_disjoint_support	Returns true if operators act on non-overlapping sites (commute).
iterative_eigensolver	Iterative eigensolver for matrices.
kron	Returns the tensor product of two fermionic product states.
largest_abs	Returns the largest_abs enum value.
largest_imag	Returns the largest_imag enum value.
largest_real	Returns the largest_real enum value.
lattice_range	Constructs a LatticeRange.
merge	Simplifies an OperatorSum by combining like terms (in-place).
merged	Simplifies an OperatorSum by combining like terms (out-of-place).
neighbourhood_rule	Constructor for a neighbourhood rule.
open	Returns the open enum value.
operator_chebyshev_series	Constructs an OperatorChebyshevSeries from an Operator and a Chebyshev series.
operator_function	Approximates a matrix (or operator) function.
periodic	Returns the periodic enum value.
prune	Prunes operators from an OperatorSum based on their effective norm (in-place).
pruned	Prunes operators from an OperatorSum based on their effective norm (out-of-place).
reduced_density_matrix	Calculates the reduced density matrix for a subsystem using a linear cut. Returns the reduced density matrix for the sites to the left of the linear cut.
reduced_number_power	Reduces powers of the number operator on the same site to at most 1.
renyi_entropy	Calculates the Rényi entropy of order q for a density matrix.
reorder_by_site	Reorders operators within a product by their site indices while preserving quantum commutation rules.
simplified_create_destroy	Simplifies and reorders a product of creation and annihilation operators by site while preserving site order. Terms are killed if there are too many creation or annihilation operators.
simplify_paulis	Simplifies any Operator containing Pauli operators according to Pauli algebra rules. Handles single Pauli operators, products, and sums by converting to OperatorSum format.
smallest_abs	Returns the smallest_abs enum value.
smallest_imag	Returns the smallest_imag enum value.
smallest_real	Returns the smallest_real enum value.
sse_order_estimator	Constructs the estimator for the order in an SSE simulation.
sse_simulation	Reads an SSE Simulation from the group at the given path.
sse_vertex	Constructs a diagonal SSE vertex.
string	Format a vector of boundary conditions as a string.
von_neumann_entropy	Calculates the von Neumann entropy of a density matrix.
write	Writes an SSE simulation and returns the file for chaining.

Module Symbols

Name	Description
!=	Returns true if the lattice coordinates are not equal.
*	Multiplies complex scalar by an operator.
+	Adds the primitive vectors and basis indices of the given lattice coordinates.
==	Returns true if the two StateInfo options are equivalent.
[]	Array access operator with Fbit states.
|	Combines two compatible StateInfo options.