Diagonalization Quantum Circuits for a Scalable Three-state Interference on a Digital Quantum Computer

by Brian Chung Hang Cheung (ENS Paris)

Tuesday 4 Mar 2025, 11:00 → 12:00 Europe/Zurich

WHGA/121

Non-linear functionals of the form Tr[ρ₁ ... ρₖ], where ρ₁, ..., ρₖ are n-qubit density matrices, play a crucial role in quantum information science, with applications in Rényi entropies, entanglement detection, and quantum error mitigation. Existing methods, such as the Swap test and classical shadows, are either too resource-intensive in terms of CNOT gates or require a large sample complexity. A well-known alternative for estimating Tr[ρ₁ρ₂] uses a Bell measurement, which can be interpreted as a diagonalization circuit for the SWAP operator, requiring only a single CNOT gate. However, for k ≥ 3 registers, such diagonalization circuits remain unavailable. In this seminar, we present a diagonalization circuit for estimating Tr[ρ₁ρ₂ρ₃] that significantly reduces CNOT gate usage and features sample complexity independent of system size. This circuit enables an efficient implementation of three-state interference on a digital quantum computer. Finally, we demonstrate how our approach facilitates entanglement detection via the p₃-PPT criterion.