Quantum States

qubits(n::Int)

Generate a $n$-qubit Hilbert space spanned by a basis $\{\sigma_j\}_{j=1}^n$. Each local degree of freedom is represented by an ITensors.Index object, which encode the local Hilbert space dimension and a unique identifier for automated tensor contractions.

q = qubits(3)
# 3-element Vector{ITensors.Index{Int64}}:
#  (dim=2|id=114|"Qubit,Site,n=1")
#  (dim=2|id=142|"Qubit,Site,n=2")
#  (dim=2|id=830|"Qubit,Site,n=3")

qudits(n::Int; dim::Int = 3)
qudits(d⃗::Vector)

Generate a $n$-qudit Hilbert space spanned by a basis $\{\sigma_j\}_{j=1}^n$. Each local degree of freedom is represented by an ITensors.Index object with dimension $d_j$. Accepted inputs are either the number of qudits (with the same local dimension $d$), or a vector of local dimensions $\mathrm{d}=(d_1,\dots,d_n)$.

q = qudits([3,5,3])
# 3-element Vector{ITensors.Index{Int64}}:
#  (dim=3|id=639|"Qudit,Site,n=1")
#  (dim=5|id=212|"Qudit,Site,n=2")
#  (dim=3|id=372|"Qudit,Site,n=3")

productstate(hilbert::Vector{<:Index})
productstate(n::Int; dim = 2)

Generate an MPS wavefunction correponsponding to the product state

$|\psi\rangle = |0\rangle_1\otimes|0\rangle_2\otimes\dots|0\rangle_n$

It accepts both a Hilbert space or the number of modes and local dimension.

productstate(N::Int, states::Vector{T})
productstate(hilbert::Vector{<:Index}, states::Vector{T})

Generate an MPS wavefunction for a given input product state states. The state T can be specified either with bit values $|\psi\rangle = |1\rangle\otimes|0\rangle\otimes|1\rangle$

ψ = productstate(q, [1,0,1])
# MPS
# [1] ((dim=2|id=717|"Qubit,Site,n=1"),)
# [2] ((dim=2|id=89|"Qubit,Site,n=2"),)
# [3] ((dim=2|id=895|"Qubit,Site,n=3"),)

or with String $|\psi\rangle = |+\rangle\otimes|0\rangle\otimes|-i\rangle$

ψ = productstate(q, ["X+","Z+","Y-"]);