# The 25th series of seminars organized by QRST

Online Event Link: https://www.eventbrite.ca/e/qrst-march-2023-tickets-596196789647

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 25th series of seminars, the speakers will be Noah Watch of Kirchhoff-Institut fur Physik and Kouhei Nakaji of University of Toronto. Their talks are titled "Data Re-uploading with a Single Qubit" and "qSWIFT: High-order randomized compiler for Hamiltonian simulation", 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: Data Re-uploading with a Single Qubit

Speaker: Noah Watch, University of Heidelberg

Abstract: Quantum two-level systems, i.e. qubits, form the basis for most quantum machine learning approaches that have been proposed throughout the years. However, in some cases, higher dimensional quantum systems may prove to be advantageous. Here, we explore the capabilities of multi-level quantum systems, so-called qudits, for their use in a quantum machine learning context. We formulate classification and regression problems with the data re-uploading approach and demonstrate that a quantum circuit operating on a single qudit is able to successfully learn highly non-linear decision boundaries of classification problems such as the MNIST digit recognition problem. We demonstrate that the performance strongly depends on the relation between the qudit states representing the labels and the structure of labels in the training data set. Such a bias can lead to substantial performance improvement over qubit-based circuits in cases where the labels and qudit states are well-aligned. Furthermore, we elucidate the influence of the choice of the elementary operators and show that the non-linear squeezing operator is necessary to achieve good performances. We also show that there exists a trade-off for qudit systems between the number of circuit-generating operators in each processing layer and the total number of layers needed to achieve a given accuracy. Finally, we compare classification results from numerically exact simulations and their equivalent implementation on actual IBM quantum hardware. The findings of our work support the notion that qudit-based algorithms exhibit attractive traits and constitute a promising route to increasing the computational capabilities of quantum machine learning approaches.

Bio: Noah L. Wach started studying physics in 2018 at the University of Heidelberg in Germany. In 2021 he finished his Bachelor degree in the group of Fred Jendrzejewski on the topic of „Data re-uploading on qudits“. After going to Amsterdam for a research semester, working on ultracold RbSr molecules in the group of Florian Schreck, and going to the Imperial College London for an exchange semester, he is currently continuing his studies in Heidelberg to finish his M.Sc. degree.

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Talk 2: qSWIFT: High-order randomized compiler for Hamiltonian simulation

Speaker: Kouhei Nakaji, University of Toronto

Abstract: Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this talk, we present qSWIFT, a high-order randomized algorithm for Hamiltonian simulation. In qSWIFT, the required number of gates for a given precision is independent of the number of terms in Hamiltonian, while the systematic error is exponentially reduced with regards to the order parameter. In this respect, our qSWIFT is a higher-order counterpart of the previously proposed quantum stochastic drift protocol (qDRIFT), whose number of gates scales linearly with the inverse of the precision required. We construct the qSWIFT channel and establish a rigorous bound for the systematic error by using the diamond norm. qSWIFT provides an algorithm to estimate given physical quantities by using a system with one ancilla qubit, which is as simple as other product-formula-based approaches such as regular Trotter-Suzuki decompositions and qDRIFT. Our numerical experiment reveals that the required number of gates in qSWIFT is significantly reduced compared to qDRIFT. Particularly, the advantage is significant for problems where high precision is required; for example, to achieve a systematic relative propagation error of $10^{-6}$, the required number of gates in third-order qSWIFT is 1000 times smaller than that of qDRIFT.

Bio: Kouhei Nakaji is a postdoctoral researcher in the Matter Lab of Professor Alan Aspuru-Guzik, affiliated with the Japan Society for the Promotion of Science (JSPS) as a cross-border postdoc. He received his B.S. and M.S. degrees in Elementary Particle Physics Theory from the University of Tokyo, and his Ph.D. in near-term quantum algorithms from Keio Quantum Computing Center. His research interests include quantum algorithms, quantum chemistry, and machine learning.