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Beyond T₁: Measuring Coherence with State and Process Tomography

John Martinis, University of California, Santa Barbara

(Session 101 : Thursday from 13:30-15:30)

Abstract. The tutorial would review the physics and mathematics behind the metrology of qubit coherence, using specific examples from recent experiments on superconducting qubits.

Outline of Tutorial

I. Qubit basics
• Two-state quantum system
• Time evolution of state with external control
• Simple physical picture of decoherence
• Example: Josephson phase qubit
II. T₁- and T₂-ology
• T₁, T₂, polarization describes memory of practically all qubits
• T2 is approximate concept, depends on details
• Why are simple T₁, T₂ measurements not sufficient?
III. Single-qubit: state and process tomography
• Density matrix description
• How measured - two methods
• Dynamic errors (to other states) measured to 10^-4 via "Ramsey filtering"
• Errors in memory storage described by process tomography
• Research issue: going from matrix to "what needs fixing"
IV. Two-qubit: state and process tomography
• Density matrix description
• How measured from single qubit rotatins
• Experiment to demonstrate entanglement, measure matrix
• Process tomography
• Bell-violation experiment
V. Multi-qubit state and process tomography - the problem

John Martinis,

(Session 7 : Saturday from )

Abstract.