Reducing the Sampling Complexity of Energy Estimation in Quantum Many-Body Systems Using Empirical Variance...

Area of Science:

• Quantum computing
• Quantum chemistry
• Computational physics

Background:

• Accurate energy estimation is vital for quantum algorithms, especially in quantum chemistry.
• Current methods using Pauli decomposition and Hoeffding's inequality offer limited sampling complexity guarantees.
• Optimizing sampling complexity is crucial for efficient quantum state preparation.

Purpose of the Study:

• To develop a more efficient adaptive estimator for quantum state preparation energy.
• To improve upon existing single-shot estimators by leveraging the state's actual variance.
• To provide rigorous tail bounds for the new estimation method.

Main Methods:

• Constructed an adaptive estimator based on the empirical Bernstein stopping (EBS) algorithm.
• Utilized grouping schemes and the state's empirical variance for estimation.
• Provided rigorous tail bounds leveraging empirical variance for theoretical guarantees.

Main Results:

• The adaptive EBS estimator consistently improved upon elementary readout guarantees.
• Demonstrated up to a 1-order-of-magnitude improvement in numerical benchmarks.
• Successfully estimated ground-state energies of various Hamiltonians with enhanced accuracy.

Conclusions:

• The developed adaptive estimator offers significant improvements in sampling complexity for quantum energy estimation.
• Leveraging empirical variance with EBS provides a robust and more efficient approach.
• This method has strong implications for advancing quantum algorithms in fields like quantum chemistry.