## Program

#### SESSION 13: Quantum characterization and tomography

Chair: (Robin Blume-Kohout)
3:15pm - 3:45pmScott Aaronson, University of Texas, Austin
Gentle measurement of quantum states and differential privacy
Abstract.

In differential privacy (DP), we want to query a database about n users, in a way that "leaks at most $${\epsilon}$$ about any individual user," conditioned on any outcome of the query. Meanwhile, in gentle measurement, we want to measure n quantum states, in a way that "damages the states by at most $${\alpha}$$," conditioned on any outcome of the measurement. In both cases, we can achieve the goal by techniques like deliberately adding noise to the outcome before returning it. We prove a new and general connection between the two subjects. Specifically, on products of n quantum states, any measurement that is $${\alpha}$$-gentle for small $${\alpha}$$ is also O($${\alpha}$$)-DP, and any product measurement that is $${\epsilon}$$-DP is also O($${\epsilon}$$$${ \sqrt{n}}$$) -gentle.

Illustrating the power of this connection, we apply it to the recently studied problem of shadow tomography. Given an unknown d-dimensional quantum state $${\rho}$$, as well as known two-outcome measurements $$E_1$$,...,$$E_m$$, shadow tomography asks us to estimate Pr[$$E_1$$ accepts $${\rho}$$], for every i $${\in}$$[m], by measuring few copies of $${\rho}$$. Using our connection theorem, together with a quantum analog of the so-called private multiplicative weights algorithm of Hardt and Rothblum, we give a protocol to solve this problem using $$O\Bigl(\left(log m\right)^2 (log d)^2\Bigr)$$ copies of $${\rho}$$, compared to Aaronson's previous bound of $$Õ\Bigl(\left(log m\right)^4 (log d)\Bigr)$$. Our protocol has the advantages of being online (that is, the $$E_1$$'s are processed one at a time), gentle, and conceptually simple.

3:45pm - 4:15pmKristine Boone, University of Waterloo
Randomized benchmarking under different gatesets
Abstract. We provide a comprehensive analysis of the differences between two important standards for randomized benchmarking (RB): the Clifford-group RB protocol proposed originally in Emerson et al (2005) and Dankert et al (2006), and a variant of that RB protocol proposed later by the NIST group in Knill et al, PRA (2008). While these two protocols are frequently conflated or presumed equivalent, we prove that they produce distinct exponential fidelity decays leading to differences of up to a factor of 3 in the estimated error rates under experimentally realistic conditions. These differences arise because the NIST RB protocol does not satisfy the unitary two-design condition for the twirl in the Clifford-group protocol and thus the decay rate depends on non-invariant features of the error model. Our analysis provides an important first step towards developing definitive standards for benchmarking quantum gates and a more rigorous theoretical underpinning for the NIST protocol and other RB protocols lacking a group-structure. We conclude by discussing the potential impact of these differences for estimating fault-tolerant overheads.
4:15pm - 4:45pmJohn Gamble, Microsoft Research
Operational, gauge-free quantum tomography
Abstract. As quantum processors become increasingly refined, benchmarking them in useful ways becomes a critical topic. Traditional approaches to quantum tomography, such as state tomography, suffer from self-consistency problems, requiring either perfectly pre-calibrated operations or measurements. This problem has recently been tackled by explicitly self-consistent protocols such as randomized benchmarking, robust phase estimation, and gate set tomography (GST). An undesired side-effect of self-consistency is the presence of gauge degrees of freedom, arising from the lack fiducial reference frames, and leading to large families of gauge-equivalent descriptions of a quantum gate set which are difficult to interpret. We solve this problem through introducing a gauge-free representation of a quantum gate set inspired by linear inversion GST. This allows for the efficient computation of any experimental frequency without a gauge fixing procedure. We use this approach to implement a Bayesian version of GST using the particle filter approach, which was previously not possible due to the gauge. Within Bayesian GST, the prior information allows for inference on tomographically incomplete data sets, such as Ramsey experiments, without giving up self-consistency. We demonstrate simulated examples of this approach for a variety of experimentally-relevant situations, showing the stability and generality of both our gauge-free representation and Bayesian GST.
4:45pm - 5:15pmTimothy Proctor, Sandia National Laboratories
Randomized benchmarking of many-qubit devices
Abstract. Quantum information processors incorporating 5 - 10s of qubits are now commonplace, but the standard method for benchmarking quantum gates - Clifford randomized benchmarking - is infeasible to implement on more than a few qubits in any near-term devices. In this talk, we present a series of modifications to Clifford randomized benchmarking that enable truly holistic benchmarking of entire devices. Importantly, these new techniques are adaptable based on experimental goals. They can be made highly robust or more scalable as needed, and they can be used to estimate, e.g., two-qubit gate error rates or the magnitude of crosstalk errors. Moreover, our methods allow for the benchmarking of universal gates, and continuously parameterized gates. We demonstrate our techniques on current systems, with experimental results on up to 16 qubits. Sandia National Labs is managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This research was funded by IARPA. The views expressed in the article do not necessarily represent the views of the DOE, IARPA, the ODNI, or the U.S. Government.

SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu

SQuInT Local Organizers
Rafael Alexander, Postdoctoral Fellow
Chris Jackson, Postdoctoral Fellow