Efficient Quantum Imaginary Time Evolution by Drifting Real-Time Evolution: An Approach with Low Gate and Measurement...

Area of Science:

• Quantum computing
• Quantum chemistry
• Computational physics

Background:

• Quantum imaginary time evolution (QITE) is a key quantum algorithm for determining eigenvalues and eigenstates of Hamiltonians.
• The original QITE method faces challenges with deep quantum circuits and extensive measurements due to large Pauli operator pools and Trotterization.

Purpose of the Study:

• To develop a more efficient QITE algorithm by reducing circuit depth and measurement overhead.
• To improve the practical applicability of QITE for quantum chemistry and materials science.

Main Methods:

• Introduced a time-dependent drifting scheme inspired by the qDRIFT algorithm to mitigate circuit depth requirements.
• Developed a deterministic algorithm for selecting dominant Pauli terms to minimize fluctuations during ground state preparation.
• Implemented an efficient measurement reduction scheme across Trotter steps to decrease computational cost.

Main Results:

• The proposed drifting scheme eliminates depth dependency on the operator pool size and shows inverse convergence with the number of steps.
• The deterministic algorithm and measurement reduction scheme significantly reduce fluctuations and measurement costs, respectively.
• Numerical simulations on benchmark molecules, including LiH, demonstrate comparable circuit depths to advanced adaptive VQE methods with substantially fewer measurements.

Conclusions:

• The enhanced QITE algorithm offers a practical and efficient approach for quantum eigenvalue problems.
• This method significantly reduces the resource requirements for quantum simulations, making it more accessible on current quantum hardware.
• The improvements pave the way for more accurate and feasible quantum computational chemistry studies.