Compressing Many-Body Fermion Operators under Unitary Constraints.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Efficient quantum circuits are crucial for simulating molecular systems.
• Current methods for preparing unitary coupled cluster states involve complex factorizations.
• Product formulas are used to simulate these operators, leading to interleaved Fermionic Gaussian and Ising circuits.

Purpose of the Study:

• To introduce a novel numerical algorithm for factorizing two-body operators in quantum chemistry.
• To improve the efficiency of preparing unitary coupled cluster states and initial states for variational algorithms.
• To reduce the number of squared one-body operators compared to analytical methods.

Main Methods:

• A numerical algorithm is presented for factorizing two-body operators into sums of squared one-body operators.
• The algorithm's iteration complexity is comparable to single-particle basis transformations.
• The method is applied to approximate unitary coupled cluster operators and prepare initial states.

Main Results:

• The numerical algorithm achieves efficient factorization of quantum operators.
• It often yields significantly fewer squared one-body operators than analytical decompositions.
• The protocol successfully approximates unitary coupled cluster operators.
• High-quality initial states for algorithms like ADAPT-VQE can be prepared.

Conclusions:

• The developed numerical algorithm offers a more efficient approach to quantum operator factorization.
• This advancement can enhance the performance of quantum algorithms in electronic structure calculations.
• The method provides a practical way to prepare essential initial states for quantum chemistry simulations.