Double-Bracket Quantum Algorithms for Quantum Imaginary-Time Evolution

Area of Science:

• Quantum computing
• Quantum algorithms
• Condensed matter physics

Background:

• Preparing ground states of strongly correlated systems is crucial but challenging on quantum hardware.
• Existing methods for imaginary-time evolution often use heuristic or deep quantum circuits.

Purpose of the Study:

• To develop an efficient quantum algorithm for preparing approximate ground states.
• To synthesize quantum circuits that coherently implement imaginary-time evolution.

Main Methods:

• Utilizing the insight that quantum imaginary-time evolution is a solution to Brockett's double-bracket flow.
• Synthesizing quantum circuits to implement double-bracket flows coherently.
• Proving the cooling guarantees of the developed algorithm.

Main Results:

• The double-bracket quantum imaginary-time evolution (DB-QITE) algorithm guarantees energy decrease and fidelity increase with the ground state at each step.
• Numerical simulations show DB-QITE outperforms quantum phase estimation in certain scenarios.
• DB-QITE utilizes shallow quantum circuits for systematic ground state approximation.

Conclusions:

• DB-QITE offers a novel and efficient approach to approximate ground state preparation on quantum computers.
• The algorithm provides a systematic way to improve ground state approximations with guaranteed convergence properties.
• This method advances the application of quantum computing to strongly correlated systems.