Quantum algorithms for Kohn-Sham equations – QUAKE

Major recent technological advances have made quantum computers a reality. Now equipped with hundreds quantum bits (qubits), platforms with more than thousand qubits are expected in the years to come. Solving the electronic structure problem in quantum chemistry has been identified as the “killer application” of quantum computers, although a practical quantum advantage for applications with high industrial or societal impact has not been achieved yet. Two drastic limitations arise for a massive use of quantum computers for quantum chemistry: i) The quantum numerical error induced by the noise of the device is expected to remain larger than the desired chemical accuracy if no error mitigation or quantum error correction codes are used, and ii) The size of affordable systems is dictated by the number of (limited) available qubits. Because an increase of the number of qubits and circuit depth leads to an increase of the quantum noise, expected promises of quantum computing applications to quantum chemistry might be strongly reduced for some technological generations. As an alternative, the resolution of the Kohn-Sham equations of Density Functional Theory on quantum computers (Q-DFT) instead of the Schrödinger equation is here proposed to bypass the aforementioned limitations. By mapping the KS non-interacting system onto an exponentially smaller interacting one, it unlocks the treatment of large systems: only log(N) qubits are required to describe a system with N orbitals at the DFT level of approximation, each orbital being encoded on a bitstring of the log(N)-qubit register. The project aims at i) finding the optimal mapping to maximally reduce the quantum resources required to solve the Kohn-Sham problem, ii) developing Q-DFT to both the noisy and fault-tolerant era, and iii) implementing Q-DFT in the open-source BigDFT code to use the Daubechies wavelet basis functions, known to be advantageous for quantum computing applications.