QuantumMAMBO.jl: Efficient many-body routines in Julia

QuantumMAMBO provides structures for many-body objects in quantum computing. They can all be seen in src/UTILS/structures.jl. In particular, it provides the fermionic operators F_OP specially geared towards two-electron number-conserving operators, Q_OP for qubit operators, and M_OPfor Majorana operators coming from fermionic operators. All operators and unitaries have structured classes, which in the future will be used for efficient compilation of quantum circuits and resource estimates.

QuantumMAMBO.jl includes efficient implementations for fermionic and qubit operators. To obtain results shown in Ref.(1), run on a terminal (e.g. for LiH):

julia L1.jl lih

All options and tolerances can be seen in src/config.jl. By default, QuantumMAMBO.jl will use the package PythonCall for calling Python, installing all necessary Python packages on a fresh conda environment using MicroMamba. Change the PY_ENV variable in src/config.jl to "Null" for using local Python enviornment instead. There are three ways in which QuantumMAMBO can be used, which are now decribed.

Using Julia's package manager, add the QuantumMAMBO package. Can either be done by typing ] on the Julia REPL, followed by add QuantumMAMBO, or by running the following lines:

import Pkg
Pkg.add("QuantumMAMBO")

For development, this repository can be cloned and called from a Julia session in the directory with the commands:

import Pkg
Pkg.activate("./")
Pkg.instantiate()
using QuantumMAMBO

This allows for changes to be done in the package and tried out before creating a pull request for uploading a new version of the package.

For using QuantumMAMBO from a Python session, the juliacall Python package is required, which can be installed with pip install juliacall. Once installed, QuantumMAMBO can be installed on Python as:

import juliacall
from juliacall import Main as jl

jl.seval('import Pkg')
jl.seval('Pkg.add("QuantumMAMBO")')

Once installed, it can be imported as a Python module by running:

import juliacall
from juliacall import Main as jl

jl.seval("using QuantumMAMBO")

QM = jl.QuantumMAMBO

See pyMAMBO.py for an example script of interfacing Python with QuantumMAMBO. QuantumMAMBO can also be called from a local installation for Python by instead using the following script:

import juliacall
from juliacall import Main as jl

jl.seval('import Pkg; Pkg.activate("./")')
jl.seval('Pkg.instantiate()')
jl.seval("using .QuantumMAMBO")

QM = jl.QuantumMAMBO

• L1.jl : full workflow for obtaining LCU 1-norms for all decompositions/methods
• LCU.jl : workflow for obtaining circuits of LCUs using cirq-ft
• Project.toml : package metadata and dependencies
• CondaPkg.toml : python installation dependencies for micromamba environment
• pyMAMBO.py : example of python script using QuantumMAMBO

• config.jl : general parameters and settings for all functions
• QuantumMAMBO.jl : wrapper for the module, includes all necessary files
• UTILS folder : contains all functions

• bliss.jl : functions for BLISS routine (see Ref. 2)
• circuits.jl : julia wrappers for interfacing QuantumMAMBO LCU decompositions with cirq circuit building
• circuits.py : python wrapper which includes all cirq building tools in cirq folder
• cirq : folder containing all python functions for building cirq LCU oracles
• cost.jl : functions for calculating different norms of operators. Mainly 1- and 2-norms of fermionic operators.
• decompose.jl : CSA, DF, and related decompositions of fermionic operators
• ferm_utils.py : utilities for fermionic operators in python, interfaces with openfermion
• fermionic.jl : utilities for QuantumMAMBO fermionic operators class (F_OP, defined in structures.jl)
• gradient.jl : gradients for CSA and CSA_SD optimizations
• guesses.jl : initial guesses for decomposition routines
• ham_utils.py : python utilities for the electronic structure Hamiltonian, interfaces with openfermion
• lcu.jl : calculation of lcu 1-norms for different decompositions
• linprog.jl : linear programming routines for symmetry-shift optimization (see Refs. 1 and 2, corresponds to "partial" routine in Ref. 2)
• majorana.jl : utilities for QuantumMAMBO Majorana operators class (M_OP, defined in structures.jl)
• orbitals.jl : orbital optimization routine for 1-norm minimization (see Koridon et al., Phys. Rev. Res. 3 (3), 2021. Material is also covered in Refs. 1 and 2)
• parallel.jl : code with parallel capabilities, mainly for trotter bounds (under construction)
• planted.jl : routines for obtaining planted solutions for a given Hamiltonian
• projectors.jl : builds projectors of Fock space into constant number of electrons subspace, useful for Trotter bounds (under progress)
• py_qubits.jl : python utilities for qubit operators, interfaces with openfermion
• py_utils.jl : julia interface to all python modules and openfermion
• qubit.jl : utilities for QuantumMAMBO qubit operators class (Q_OP, defined in structures.jl)
• saving.jl : save-load utilities for decompositions and optimization results, uses HDF5
• structures.jl : definition of classes for many-body operators
• symmetries.jl : building of symmetry operators, e.g. Sz, Ne
• symplectic.jl : utilities for representing and manipulating qubit space as symplectic vectors
• trotter.jl : Trotterization implementation, errors and bounds (under construction)
• unitaries.jl : unitary transformations related to fermionic QuantumMAMBO operators (i.e. F_OP)
• wrappers.jl : runner functions which run workflows for obtaining all necessary quantities for e.g. tables in Refs. 1 and 2

This code was developped and used for all results in the publications:

[1] I. Loaiza, A. Marefat Khah, N. Wiebe, and A. F. Izmaylov, Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches. Quantum Sci. Technol. 8 (3) 035019, 2023.

[2] I. Loaiza, A. F. Izmaylov, Block-Invariant Symmetry Shift: Preprocessing technique for second-quantized Hamiltonians to improve their decompositions to Linear Combination of Unitaries. arXiv:2304.13772, 2023.

• Ignacio Loaiza (@iloaiza)
• Aritra Brahmachari (@AritraBrahmachari)
• Joshua T. Cantin (@jtcantin)
• Linjun Wang (@Zephrous5747): author of module_sdstate