Quantum process tomography of the quantum Fourier transform.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Experimental Quantum Physics

Background:

• Quantum process tomography (QPT) is essential for characterizing quantum operations.
• Nuclear Magnetic Resonance (NMR) quantum information processors offer a platform for implementing quantum algorithms.
• The quantum Fourier transform (QFT) is a key component in several quantum algorithms.

Purpose of the Study:

• To perform QPT on a three-qubit NMR quantum information processor.
• To analyze implementation errors of the quantum Fourier transform (QFT).
• To model and decompose errors into coherent, incoherent, and decoherent components.

Main Methods:

• Utilized quantum process tomography on a three-qubit NMR quantum information processor.
• Applied strongly modulating control fields for precise quantum operations.
• Analyzed experimental results using a detailed system-plus-apparatus model.
• Decomposed errors into coherent, incoherent, and decoherent components.

Main Results:

• Experimental QPT results were consistent with the detailed system model.
• The implemented QFT superoperator showed strong correlation with the theoretical expectation.
• Identified non-complete positivity, largely due to incoherent errors during the QPT procedure.
• Gate fidelity was 0.64, with a superoperator correlation of 0.79.

Conclusions:

• The study successfully modeled and analyzed errors in a three-qubit NMR QFT implementation.
• Incoherent errors significantly impacted the complete positivity of the quantum operation.
• Distinct error components can be identified by their spectral effects on the superoperator.
• Cumulative small errors in single-qubit gates explained most discrepancies with simulations.