Release notes

v1.5.0 (2024-07-19)

This is a minor release with some bug fixes and new features:

  • Add heisenberg_eom_system function to generate a system of Heisenberg equations of motion for either the expectation values or the cumulants / correlators of operator products, starting from a Hamiltonian and Lindblad operators describing decoherence. Typically, these equation systems are not closed without approximations as equations for products of n operators involve products of m>n operators, so the system has to be truncated. This is achieved with a filter function that removes higher-order terms or rewrites them (approximately) in terms of lower-order expressions. Simple example:
    julia> using QuantumAlgebra
julia> @boson_ops a;
julia> H = Pr"ω"*a'()*a() + Pr"χ"*a'()*(a'()+a())*a();
julia> Ls = ((Pr"γ",a()),);
julia> EQ = heisenberg_eom_system(H,2,Ls,a())
dₜ⟨a()⟩ = -1//2 γ ⟨a()⟩  - 1i ω ⟨a()⟩  - 2i χ ⟨a†() a()⟩  - 1i χ ⟨a()²⟩ 
dₜ⟨a†() a()⟩ = -γ ⟨a†() a()⟩ 
dₜ⟨a()²⟩ = -2i χ ⟨a()⟩  - γ ⟨a()²⟩  - 2i ω ⟨a()²⟩
  • Add additional argument modes_in_vacuum to vacA, Avac, and vacExpVal, to restrict the modes that are considered to be in the vacuum state, with all other operators unaffected.
  • Fix a LaTeX output error where Latexify misinterpreted a superscript "^+" as a sum and replaced "x^+ - y" with "x^- y".

v1.4.0 (2024-06-29)

This is a minor release with some bug fixes and new features:

  • Allow Number type inputs for most exported functions so that they do not require QuExpr wrapping, such that expval(3) or Avac(1) no longer raise errors (closes #14).

  • Support interoperability with symbolic computer algebra systems (CAS) such as Symbolics.jl or SymPy.jl / SymPyPythonCall.jl. Expressions provided by these systems can be used as the "scalar" factors of each term in a QuExpr, and thus provide an alternative to the QuantumAlgebra Param objects. In contrast to Params, they do not support symbolic indices, but provide much more flexibility in terms of the mathematical operations and powerful manipulation functions. For example, one can use

    julia> using QuantumAlgebra, Symbolics
julia> @boson_ops a;
julia> @variables x y;
julia> H = cos(x)^2 * a() * a'() + sin(x)^2 * a'() * a();
julia> Symbolics.simplify(normal_form(H))
cos(x)^2 + a†() a()

julia> Symbolics.substitute(H, x => y)
sin(y)^2 a†() a() + cos(y)^2 a() a†()

julia> Symbolics.substitute(H, x => 2)
0.826821810431806 a†() a() + 0.17317818956819406 a() a†()

julia> Symbolics.substitute(H, x => 2; fold=false)
sin(2)^2 a†() a() + cos(2)^2 a() a†()

    While overloads for some functions (like simplify and substitute from Symbolics) are available, all other functions/manipulations from the CAS packages can be applied with the new function map_scalar_function which applies a function to each scalar factor in a QuExpr. This can be used as, e.g.,

    julia> map_scalar_function(Symbolics.simplify, normal_form(H))
cos(x)^2 + a†() a()

    In order not to add dependencies on several CAS packages to QuantumAlgebra, the interoperability helpers are defined in extension modules, using PackageExtensionCompat.jl to maintain compatibility with Julia versions before v1.9.

v1.3.1 (2023-12-22)

This is a patch release with some bug fixes and performance improvements.

v1.3.0 (2023-09-19)

This is a minor release with some bug fixes in LaTeX output, added unit tests for many functions, and some new features and deprecations:

  • The functions that generate operators now can be conjugated directly, e.g., a'() is equivalent to adag() (and to a()', which was already the case beforehand). The old _dag functions for bosons and fermions are deprecated and will be removed in a future version.
  • Preferences.jl is now used to set and store preferences. The following preferences are available:
    • "define_default_ops": if this is set to false (default is true), the "default" operators a, adag, f, fdag, σx, σy, σz, σp, σm are not defined upon import. Note that changing this value requires restarting the Julia session to take effect. The setting can be changed with QuantumAlgebra.set_define_default_ops(true/false) (which will inform you whether a restart is required) or with Preferences.set_preferences!(QuantumAlgebra,"define_default_ops"=>true/false).
    • "auto_normal_form": Choose whether all expressions are automatically converted to normal form upon creation. The default is false. It can be changed for a single session with QuantumAlgebra.auto_normal_form(true/false), and can be made permanent with QuantumAlgebra.auto_normal_form(true/false; set_preference=true) or with Preferences.set_preferences!(QuantumAlgebra,"auto_normal_form"=>true/false). Note that this could previously be set by defining an environment variable "QUANTUMALGEBRA_AUTO_NORMAL_FORM", but this usage has been deprecated and will be removed in a future version.
    • "use_σpm": Choose whether for two-level systems, the "basic" operators are excitation/deexcitation operators $σ^{±}$ or the Pauli matrices $σ^{xyz}$. This can be changed in a single session by calling QuantumAlgebra.use_σpm(true/false), and can be made permanent with QuantumAlgebra.use_σpm(true/false; set_preference=true) or with Preferences.set_preferences!(QuantumAlgebra,"use_σpm"=>true/false).
  • Use PrecompileTools.jl instead of SnoopPrecompile.jl for precompilation.

v1.2.0 (2023-04-22)

This is a minor revision with some bug fixes, and some new features:

  • Add the heisenberg_eom function to calculate the Heisenberg equations of motions of operators.
  • Switch the LaTeX output to use Latexify.jl, which also enables support for display of vectors, tuples, etc of QuExpr.
  • Require at least Julia v1.6.

v1.1.0 (2021-09-02)

This is a minor revision with some and bug fixes, and one new feature: It is now possible to use @anticommuting_fermion_group to define several fermionic operators that mutually anticommute, allowing to refer to different kinds of states for the same "species" (e.g., localized and itinerant electrons):

julia> @anticommuting_fermion_group c d

julia> normal_form(c()*d() + d()*c())
0

v1.0.0 (2021-07-23)

This is a major revision with some breaking changes. The backend has been almost completely rewritten to make the code more efficient when dealing with large expressions, and the interface has been cleaned up in several places.

Important changes:

  • Canonical normal form is not automatically enforced by default. In order to transform expressions to normal form, use normal_form(x). Since automatic conversion to normal form can be convenient for interactive work, it can be enabled with QuantumAlgebra.auto_normal_form(true), or alternatively by setting the environment variable QUANTUMALGEBRA_AUTO_NORMAL_FORM to "true" (or any value that parse(Bool,value) parses as true) before using QuantumAlgebra.
  • The function to obtain expectation values is now expval(A) (instead of ExpVal), and expval_as_corrs(A) to express an expectation value through a correlator / cumulant expansion, e.g., $⟨AB⟩ = ⟨AB⟩_{c}$ - $⟨A⟩_{c} ⟨B⟩_{c}$, with corresponding extensions for products of more operators. Note that for a single operator, $⟨A⟩_{c} = ⟨A⟩$, but we distinguish the two formally for clarity.
  • There is a new function julia_expression(A) that converts a QuantumAlgebra object to a julia expression, which helps in using QuantumAlgebra to programatically derive codes for numerical implementation. The object A cannot contain any "bare" operators, but only expectation values or correlators. See the documentation for more details.
  • QuantumAlgebra expressions are now printed in pretty format in the terminal etc.