BCS Mean-Field Ground State Preparation

BCS Mean-Field Ground State Preparation

This Cirq example prepares the Bardeen-Cooper-Schrieffer (BCS) mean-field ground state, the variational state that describes superconductors and fermionic superfluids, on a quantum computer. Working with a one-dimensional four-site Hubbard model, it shows how a correlated many-body fermionic state can be built efficiently from a product of simple basis states using a structured sequence of quantum gates. The construction proceeds in two stages: pairwise Bogoliubov transformations, which mix basis states with opposite spin and momentum to introduce the characteristic Cooper pairing, followed by a fermionic Fourier transformation that moves between momentum and position representations. To run on qubit hardware, the fermionic system is mapped onto a ladder of qubits (two coupled chains) via the Jordan-Wigner transformation, with the upper and lower chains representing spin-up and spin-down states. The example demonstrates a complete state-preparation pipeline for condensed-matter physics, connecting the abstract BCS theory of superconductivity to an explicit, simulable quantum circuit, and serves as a worked introduction to preparing nontrivial many-body fermionic states for quantum simulation.

Run it

pip install -r requirements.txt
python bcs_mean_field.py

Source and license

Imported from examples/bcs_mean_field.py in quantumlib/Cirq at v1.6.1, under the Apache License 2.0. Original authors: The Cirq Developers. The upstream LICENSE is included alongside this example.