Speaker
Description
In quantum computations and simulations, it is important to have methods for measuring properties of interest of the quantum system. For small systems containing only a few qubits, the gold standard is to reconstruct these properties via quantum state tomography (QST). However, the number of distinct measurement settings required to obtain a tomographically complete dataset scales exponentially with the number of qubits. For intermediate-scale quantum simulators beyond only a few qubits, QST already becomes unfeasible. We therefore forsake the goal of reconstructing the entire quantum state and turn to methods that allow arbitrary properties of a quantum state's density matrix to be estimated directly.
One such method is the implementation of a symmetric informationally complete positive operator-valued measure (SIC-POVM), in which a single experimental setting provides access to an informationally complete measurement record.
I will present our latest experimental advances in implementing such a SIC-POVM-based measurement on our trapped-ion quantum simulator with 91 highly connected ion qubits arranged in a 2D crystal. Following Ref. [1], we implement the SIC-POVM by locally mapping the prepared qubit state onto multiple energy eigenstates of the $^{40}\mathrm{Ca}^{+}$ ion and detecting the POVM outcomes in a sequence of repeated exposures recorded in a single camera image, differentiating between four different brightness levels.
In contrast to more commonly used measurement schemes based on projection-valued measures, which require an additional layer of single-qubit addressing to apply random unitaries or rotate each qubit into the desired measurement basis, thereby adding experimental complexity and potentially errors, the method we use can be implemented entirely within a single experimental setting. It is independent of system size due to the use of global laser pulses acting on all ions in parallel. Because each shot of the SIC-POVM samples from an informationally complete distribution of the full quantum state, the method naturally combines with recent advances in randomized measurements and enables realtime estimation of arbitrary polynomial functions of the density matrix, with precision improving as more repetitions are accumulated.
[1] Stricker et al., PRX Quantum 3, 040310 (2022)
| Academic level | PhD student |
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