# The 23rd series of seminars organized by QRST

Online Event Link: https://www.eventbrite.ca/e/qrst-october-2022-tickets-427968434107

Quantum Research Seminars Toronto consist of two 30 min talks about some Quantum Computation topic. Seminars are given by high-level quantum computing researchers with the focus on disseminating their research among other researchers from this field. We encourage to attend researchers regardless of their experience as well as graduate and undergraduate students with particular interest in this field. Basic notions on quantum computing are assumed, but no expertise in any particular subject of this field.

In this 22nd series of seminars, the speakers will be Weiyuan Gong from Tsinghua University and Guoming Qang from Zapata Computing. Their talks are titled "Learning Distributions over Quantum Measurement Outcomes" and "Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision", respectively.

The event recording, slides and chat history will be published in our Youtube channel and sent to the registered participants.

Looking forward to seeing you all!

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Talk 1: Learning Distributions over Quantum Measurement Outcomes

Speaker: Weiyuan Gong, Institute for Interdisciplinary Information Sciences

Abstract: Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state ρ and M unknown quantum measurements M1,...,M_M with K≥2 outcomes, estimating the probability distribution for applying M_i on ρ to within total variation distance ϵ. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring Õ (K log^2(M)log(d/ϵ^4)) copies of ρ. We further prove an information-theoretic lower bound that at least Ω(min{d2,K+logM}/ϵ2) copies of ρ are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

Bio: Weiyuan Gong is a senior student at Institute for Interdisciplinary Information Sciences, Tsinghua University supervised by Dong-Ling Deng. He was a remote research intern in spring 2022 at UT Austin under the supervision of Scott Aaronson, where he improved the shadow tomography procedure and extended it to general measurement cases.

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Talk 2: Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

Speaker: Guoming Wang, Zapata Computing

Abstract: A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state of the art classical methods. The current understanding is that achieving quantum advantage in this area will require some degree of error correction. While hardware is improving towards this milestone, optimizing quantum algorithms also brings it closer to the present. Existing methods for ground state energy estimation require circuit depths that scale as O(1/? · polylog(1/?)) to reach accuracy ?. In this work, we develop and analyze ground state energy estimation algorithms that use just one auxilliary qubit and for which the circuit depths scale as O(1/∆ · polylog(∆/?)), where ∆ ≥ ? is a lower bound on the energy gap of the Hamiltonian. With this Oe(∆/?) reduction in circuit depth, relative to recent resource estimates of ground state energy estimation for the industrially-relevant molecules of ethelyne-carbonate and PF−6, the estimated gate count and circuit depth is reduced by a factor of 43 and 78, respectively. Furthermore, the algorithm can take advantage of larger available circuit depths to reduce the total runtime. By setting α ∈ [0, 1] and using depth proportional to ?−α∆−1+α true , the resulting total runtime is O(e^(−2+α)∆^(1−α)), where ∆ is the true energy gap of the Hamiltonian. These features make our algorithm a promising candidate for realizing quantum advantage in the era of early fault-tolerant quantum computing.

Bio: Guoming Wang is currently a Quantum Research Scientist at Zapata Computing Canada Inc. He received his B.S and M.S. in Computer Science from Tsinghua University, and his Ph.D. in Computer Science from University of California, Berkeley. Before joining Zapata, he worked as a postdoc at the Institute for Quantum Computing (IQC) at University of Waterloo and at the Joint Center for Quantum Information and Computer Science (QuICS) at University of Maryland. His research interests include quantum algorithms, quantum complexity theory and quantum information theory. In particular, in the past, he has designed fast quantum algorithms for solving various linear systems of equations on fault-tolerant quantum computers. Recently, he is developing more near-term or intermediate-term quantum techniques for studying the properties of quantum systems.