Fast Emulation of Fermionic Circuits with Matrix Product States

Area of Science:

• Quantum Computing
• Computational Physics
• Quantum Information Science

Background:

• Accurate simulation of fermionic systems is crucial for quantum computing.
• Full statevector emulation is limited to small system sizes.
• Approximation methods are needed to scale simulations.

Purpose of the Study:

• To introduce an open-source Matrix Product State (MPS) extension for the Fermionic Quantum Emulator (FQE) software.
• To enable approximate emulation of larger fermionic quantum circuits.
• To facilitate the study of quantum algorithms on systems beyond the reach of exact methods.

Main Methods:

• Developed MPS-FQE, integrating symmetry-adapted MPS theory with the FQE interface.
• Utilized pyblock3 and block2 libraries for tensor operations.
• Implemented a drop-in replacement for FQE for efficient, approximate emulation.

Main Results:

• MPS-FQE allows approximate emulation of larger fermionic circuits than full statevector methods.
• Demonstrated applications in quantum phase estimation, variational quantum eigensolvers, Trotter error analysis, and quantum dynamics.
• Enabled treatment of significantly larger systems for quantum algorithm testing.

Conclusions:

• MPS-FQE provides a powerful tool for approximate simulation of fermionic quantum systems.
• The software extends the capabilities of existing quantum emulators.
• Facilitates research in both near-term and fault-tolerant quantum algorithm development.