carcara 26.7.8

A framework for fermionic quantum simulation based on variational quantum algorithms.

Carcará

Carcará is a framework for fermionic quantum simulation based on variational quantum algorithms, engineered from the ground up for deployment on real quantum hardware.

Overview

Carcará connects theoretical condensed matter physics with NISQ-era quantum hardware. Engineered around variational workflows, the framework streamlines the pipeline from mapping complex fermionic Hamiltonians onto qubit operators to optimizing ansatz states and executing error-mitigated circuits on real quantum backends.

Key Features

• Fermion-to-Qubit Mapping: Built-in, optimized transformations including Jordan-Wigner, Bravyi-Kitaev, and parity mappings to translate fermionic creation/annihilation operators into Pauli strings.

• Hardware-Efficient & Physics-Inspired Ansatzes: Ready-to-use ansatz generation, including Unitary Coupled Cluster (UCCSD) and hardware-efficient templates designed to minimize circuit depth and gate errors on real QPUs.

• Hybrid Variational Solvers: Robust implementation of the Variational Quantum Eigensolver (VQE) and its time-dependent variants, coupled with state-of-the-art classical optimizers (e.g., SPSA, COBYLA, SLSQP).

• Real Hardware Deployment: Seamless integration with major quantum cloud providers (IBM Quantum Platform) with native support.

• Advanced Error Mitigation: Built-in noise-resilient pipelines featuring Zero-Noise Extrapolation (ZNE) and symmetry verification.

Installation

From pip

The easiest way to install Carcará is with pip:

pip install carcara

From github

To install Carcará directly from the GitHub repository, run the following commands:

git clone https://github.com/seixas-research/carcara.git
cd carcara
pip install -e .

Getting started

One- and two-body integrals for H2

The carcara.integrals module computes real-space one- and two-body integrals over any localized basis. The example below builds a minimal basis of one hydrogen 1s orbital on each proton and evaluates the core Hamiltonian and the electron-repulsion tensor. The full script lives in examples/H2_integrals.py.

import numpy as np

from carcara.basis import HydrogenicOrbital
from carcara.integrals import Grid, IntegralEngine, Potentials

# Geometry: the user-facing API uses Angstrom for lengths and eV for energies.
# H2 equilibrium bond length ~0.74 A; two protons about the origin.
Z, R = 1.0, 0.74
proton_a = np.array([0.0, 0.0, -R / 2])
proton_b = np.array([0.0, 0.0, +R / 2])

# External electron-nuclear potential V(r) = -sum_A Z / |r - R_A|.
potentials = Potentials([(Z, proton_a), (Z, proton_b)])

grid = Grid(center=[0.0, 0.0, 0.0], box_size=5.0, h=0.10)  # Angstrom
basis = [HydrogenicOrbital(1, 0, 0, Z=Z, center=proton_a),
         HydrogenicOrbital(1, 0, 0, Z=Z, center=proton_b)]

engine = IntegralEngine(basis, grid)

# One-body: kinetic T and nuclear attraction V -> core Hamiltonian (eV).
T, V = engine.one_body(potentials.nuclear_potential)
h_core = T + V

# Two-body electron-repulsion tensor (ab|cd) in chemists' notation (eV).
eri = engine.two_body(method="fft")

print("Core Hamiltonian h = T + V (eV):")
print(h_core.real)
print(f"(00|00) on-site repulsion = {eri[0, 0, 0, 0].real:.3f} eV")

Running it prints the 2 x 2 core Hamiltonian and the on-site repulsion (00|00) ~ 17.0 eV, in agreement with the exact hydrogen 1s value of 5/8 Ha = 17.007 eV.

A heteronuclear molecule: LiH

The same machinery scales to multi-orbital, heteronuclear systems. The example examples/LiH_integrals.py builds a small minimal basis for LiH -- the Li 1s, 2s and 2p_z orbitals plus the H 1s -- using the true nuclear charges (Z_Li = 3, Z_H = 1) in the potential and effective charges from Slater's rules for the hydrogenic basis orbitals via HydrogenicOrbital.from_slater:

labels = ["Li 1s", "Li 2s", "Li 2pz", "H 1s"]
basis = [HydrogenicOrbital.from_slater(1, 0, 0, atomic_number=3, center=li_pos),
         HydrogenicOrbital.from_slater(2, 0, 0, atomic_number=3, center=li_pos),
         HydrogenicOrbital.from_slater(2, 1, 0, atomic_number=3, center=li_pos),
         HydrogenicOrbital.from_slater(1, 0, 0, atomic_number=1, center=h_pos)]

potentials = Potentials([(3.0, li_pos), (1.0, h_pos)])  # true nuclear charges
engine = IntegralEngine(basis, grid)
T, V = engine.one_body(potentials.nuclear_potential)
eri = engine.two_body(method="fft")

This yields the 4 x 4 one-body matrices and the 4 x 4 x 4 x 4 electron-repulsion tensor. The H 1s on-site integral (33|33) ~ 17.0 eV again recovers the exact 5/8 Ha.

License

This is an open source code under MIT License.

Acknowledgements

We thank financial support from INCT Materials Informatics (Grant No. 406447/2022-5).