CNOT-Efficient Circuits for Arbitrary Rank Many-Body Fermionic and Qubit Excitations.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Efficient quantum circuits are crucial for quantum algorithms on noisy intermediate-scale quantum devices.
• Unitary coupled-cluster (UCC) ansätze generate quantum circuits with exponentially scaling CNOT gates.
• Prior work introduced CNOT-efficient circuits for singles and doubles excitations in UCC ansätze.

Purpose of the Study:

• To extend CNOT-efficient quantum circuits to arbitrary excitation ranks.
• To demonstrate the benefits of compact Fermionic Excitation-based (FEB) and Qubit Excitation-based (QEB) circuits.
• To compare FEB- and QEB-SPQE performance against traditional SPQE and ADAPT-VQE.

Main Methods:

• Developed CNOT-efficient quantum circuits for arbitrary excitation ranks.
• Performed numerical simulations using the selected projective quantum eigensolver (SPQE) approach.
• Employed adaptive UCC ansätze built from arbitrary-order particle-hole excitation operators.

Main Results:

• FEB- and QEB-SPQE reduced CNOT gate counts by up to 15 times compared to traditional SPQE.
• QEB-SPQE generally requires more ansatz parameters than FEB-SPQE, increasing CNOT counts for higher excitations.
• SPQE requires significantly fewer residual element evaluations than ADAPT-VQE's gradient evaluations.

Conclusions:

• Extended CNOT-efficient circuits to arbitrary excitation ranks, enhancing UCC ansätze.
• FEB- and QEB-SPQE offer significant CNOT reductions, with FEB-SPQE being more parameter-efficient for higher excitations.
• SPQE presents a viable alternative to ADAPT-VQE, particularly in terms of computational cost for residual evaluations.