Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session M08: NISQ: Noise Resilience, Mitigation, and Characterization
11:15 AM–2:03 PM,
Wednesday, March 4, 2020
Room: 104
Sponsoring
Unit:
DQI
Chair: Charles Tahan, Laboratory for Physical Sciences
Abstract: M08.00012 : Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States*
Presenter:
Xavier Bonet-Monroig
(Insitute Lorentz, Leiden University)
Authors:
Xavier Bonet-Monroig
(Insitute Lorentz, Leiden University)
Ryan Babbush
(Google Inc.)
Thomas O'Brien
(Insitute Lorentz, Leiden University)
In this work we design schemes for such parallelization with near-optimal complexity in the system size N. We describe a scheme to sample all elements of a qubit k-RDM using only O(3k logk-1(N)) unique measurements. We detail a scheme to sample all elements of the fermionic 2-RDM using only O(N2) unique measurements, with O(N)-depth measurement circuit. We prove a lower bound of O(Nk) on the number of unique measurements required to directly sample all elements of a fermionic k-RDM, making our fermionic 2-RDM scheme asymptotically optimal. We finally construct circuits to sample the expectation value of a linear combination of ω anti-commuting 2-body fermionic operators with O(ω) gates on a linear array.
*Research funded by the Netherlands Organization for Scientific Research (NWO/OCW) NanoFront and StartImpuls programs, and by Shell Global Solutions BV.
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