Quantum Overlapping Tomography

Jordan Cotler and Frank Wilczek

Phys. Rev. Lett. 124, 100401 – Published 10 March 2020

Abstract

It is now experimentally possible to entangle thousands of qubits, and efficiently measure each qubit in parallel in a distinct basis. To fully characterize an unknown entangled state of $n$ qubits, one requires an exponential number of measurements in $n$ , which is experimentally unfeasible even for modest system sizes. By leveraging (i) that single-qubit measurements can be made in parallel, and (ii) the theory of perfect hash families, we show that all $k$ -qubit reduced density matrices of an $n$ qubit state can be determined with at most $e^{O (k)} \log^{2} (n)$ rounds of parallel measurements. We provide concrete measurement protocols which realize this bound. As an example, we argue that with near-term experiments, every two-point correlator in a system of 1024 qubits could be measured and completely characterized in a few days. This corresponds to determining nearly 4.5 million correlators.

Received 22 August 2019
Accepted 10 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.100401

Physics Subject Headings (PhySH)

Quantum entanglement Quantum tomography

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Jordan Cotler^1,* and Frank Wilczek ^{2,3,4,5,6,†}

¹Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
²Center for Theoretical Physics, MIT, Cambridge, Massachusetts 02139, USA
³T. D. Lee Institute, Shanghai, China
⁴Wilczek Quantum Center, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁵Department of Physics, Stockholm University, Stockholm, Sweden
⁶Department of Physics and Origins Project, Arizona State University, Tempe, Arizona 25287, USA