Shadow process tomography of quantum channels

Journal Article · 03 April 2023 · Physical Review A

DOI: https://doi.org/10.1103/physreva.107.042403 · OSTI ID:2228608

Kunjummen, Jonathan  ^[1]; Tran, Minh C. ^[2]; Carney, Daniel ^[3]; Taylor, Jacob M. ^[1]

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1. National Institute of Standards and Technology (NIST)/University of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Institute of Standards and Technology (NIST)/University of Maryland, College Park, MD (United States). Joint Quantum Institute
2. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States); Harvard University, Cambridge, MA (United States)National Institute of Standards and Technology (NIST)/University of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Institute of Standards and Technology (NIST)/University of Maryland, College Park, MD (United States). Joint Quantum Institute
3. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scales exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. Furthermore, we make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography, enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: Quantum Information Science Enabled Discovery (QuantISED) for High Energy Physics; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 2228608
• Journal Information: Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 107; ISSN 2469-9926
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English