Getting started

PauliStrings.jl is a Julia package for many-body quantum mechanics with Pauli string represented as binary integers (as in https://journals.aps.org/pra/abstract/10.1103/PhysRevA.68.042318).

Initializing an operator

Import the library and initialize a operator of 4 qubits

using PauliStrings
import PauliStrings as ps
H = ps.Operator(4)

Add a Pauli strings to the operator

H += "XYZ1"
H += "1YZY"

julia> H
(1.0 - 0.0im) XYZ1
(1.0 - 0.0im) 1YZY

Add a Pauli string with a coeficient

H += -1.2,"XXXZ" #coeficient can be complex

Add a 2-qubit string coupling qubits i and j with X and Y:

H += 2, "X", i, "Y", j # with a coeficient=2
H += "X", i, "Y", j # with a coeficient=1

Add a 1-qubit string on site 1

H += 2, "Z", i # with a coeficient=2
H += "Z", i # with a coeficient=1
H += "S+", i

Supported sites operators are X, Y, Z, Sx$=X/2$, Sy$=Y/2$, Sz$=Z/2$, S+$=(X+iY)/2$, S-$=(X-iY)/2$.

Basic Algebra

The Operator type supports the +,-,* operators with other Operators and Numbers:

H3 = H1*H2
H3 = H1+H2
H3 = H1-H2
H3 = H1+2 # adding a scalar is equivalent to adding the unit times the scalar
H = 5*H # multiply operator by a scalar

Trace : ps.trace(H)

Frobenius norm : ps.opnorm(H)

Conjugate transpose : ps.dagger(H)

Number of terms: length(H)

Commutator: ps.com(H1, H2). This is much faster than H1*H2-H2*H1