Electron-Phonon Systems on a Universal Quantum Computer.

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Quantum Computing

Background:

• Simulating fermion systems is crucial in quantum chemistry and condensed matter physics.
• Existing quantum algorithms primarily focus on fermions, limiting the simulation of systems with bosonic excitations like phonons.
• Electron-phonon interactions are fundamental to many physical phenomena.

Purpose of the Study:

• To develop a quantum algorithm that extends fermion simulation capabilities to include bosons, specifically phonons.
• To enable efficient and accurate simulation of electron-phonon systems using quantum computers.
• To investigate the impact of electron-phonon coupling on quantum states.

Main Methods:

• Introduced a novel qubit representation for the low-energy phonon subspace.
• Utilized the Nyquist-Shannon sampling theorem for exponential accuracy in phonon representation.
• Implemented the algorithm on a quantum simulator using the quantum phase estimation method.
• Investigated a Holstein polaron problem.

Main Results:

• The algorithm efficiently simulates the electron-phonon system's evolution operator.
• Phonons are represented with exponential accuracy in a discretized Hilbert space.
• The number of qubits scales linearly with system size, and circuit depth is manageable.
• Simulated polaron energy and phonon distribution match exact diagonalization results across various coupling strengths.

Conclusions:

• The developed quantum algorithm effectively simulates electron-phonon interactions, including phonons.
• The qubit representation offers an efficient approach for quantum simulations of these systems.
• The method provides accurate results, validated against exact diagonalization, for diverse electron-phonon coupling regimes.