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Efficient classical shadow tomography with number conservation with Anushya Chandran
Qiskit Episode 154
Quantum state tomography aims to produce a complete classical description of the state of a quantum system: a prohibitive task requiring exponential resources. Recent works have taken a different approach. They build an efficient classical description of the state, the so-called classical shadow, that can accurately capture properties of interest such as few-body observables, but is a poor approximation to the entire density matrix. The protocol is simple to implement and predicts observables much more efficiently and accurately than other techniques. It has accordingly developed into an important experimental tool.
The original local shadow protocol does not apply to systems with fundamental number conservation laws, such as ultracold atomic systems. This is a serious shortcoming. I will describe a new local shadow tomographic protocol adapted to such systems. The ``All-Pairs'' protocol is simple to implement, tomographically complete, and efficiently invertible. I will present its analytic treatment using the representation theory of the permutation group, provide a reference implementation, and demonstrate the efficiency on simulated data.
Anushya Chandran is a many-body condensed matter physicist at Boston University with broad interests in driven quantum matter, localization, topological systems and many-body entanglement. She obtained her B.Tech degree from the Indian Institute of Technology in Madras in Electrical Engineering, and her PhD from Princeton University in physics. After a postdoctoral position at the Perimeter Institute, she moved to Boston University, where she is now an associate professor. Dr. Chandran is a recipient of the Sloan research Fellowship and the Faculty Early CAREER award from the NSF.
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