Transition-Aware Decomposition of Single-Qudit Gates

Area of Science:

• Quantum Information Science
• Quantum Computing Hardware

Background:

• Quantum computation utilizes qudits (d-level quantum systems) for a richer computational space than qubits.
• Implementing arbitrary qudit operations requires decomposition into sequences of native pulses, constrained by selection rules between energy levels.
• Pulse count is critical, as each pulse introduces execution time and potential errors.

Purpose of the Study:

• To propose a resource-efficient algorithm for decomposing single-qudit operations into allowed pulse sequences.
• To establish an upper bound on the number of pulses required for any single-qudit operation.

Main Methods:

• Developed a novel algorithm for decomposing single-qudit operations.
• Analyzed the algorithm's pulse count, establishing a maximum of d(d-1)/2 pulses.
• Compared decomposition strategies across various trapped-ion systems (Yb+171, Ba+137, Ca+40) and superconducting qudits.

Main Results:

• The proposed algorithm decomposes arbitrary single-qudit operations using at most d(d-1)/2 pulses.
• Specific operations may require fewer pulses than the established upper bound.
• Demonstrated and compared qudit decomposition strategies for different hardware platforms.

Conclusions:

• The developed algorithm offers an efficient method for single-qudit operation decomposition, crucial for advancing qudit-based quantum computing.
• This approach is vital for implementing two-qudit operations by leveraging efficient single-qudit gates.