# Current students

## Tight bounds for Quantum Learning and Testing without Quantum Memory

### Jerry Li - Microsoft Research

In this talk, we consider two fundamental tasks in quantum state estimation, namely, quantum tomography and quantum state certification. In the former, we are given n copies of an unknown mixed state rho, and the goal is to learn it to good accuracy in trace norm. In the latter, the goal is to distinguish if rho is equal to some specified state, or far from it. When we are allowed to perform arbitrary (possibly entangled) measurements on our copies, then the exact sample complexity of these problems is well-understood. However, arbitrary measurements are expensive, especially in terms of quantum memory, and impossible to perform on near-term devices. In light of this, a recent line of work has focused on understanding the complexity of these problems when the learner is restricted to making incoherent (aka single-copy) measurements, which can be performed much more efficiently, and crucially, capture the set of measurements that can be be performed without quantum memory. However, characterizing the copy complexity of such algorithms has proven to be a challenging task, and closing this gap has been posed as an open question in various previous papers.

### Quantum Machine Learning Prediction Model for Retinal Conditions: Performance Analysis

Quantum machine learning predictive models are emerging and in this study we developed a classifier to infer the ophthalmic disease from OCT images. We used OCT images of the retina in vision threatening conditions such as choroidal neovascularization (CNV) and diabetic macular edema (DME). PennyLane an open-source software tool based on the concept of quantum differentiable programming was used mainly to train the quantum circuits. The training was tested on an IBM 5 qubits System “ibmq_belem” and 32 qubits simulator “ibmq_qasm_simulator”. The results are promising.

## IQC alum reaches impressive NIST milestone with standardized code

Researchers at IQC have made significant contributions to a Post-Quantum Cryptography standardization process run by the National Institute for Standards and Technology (NIST). As the process enters its fourth round, researchers are one step closer to identifying codes that will be widely accepted as reliable and safe against attacks enabled by emerging quantum computers.

Previously, higher-order Hamiltonians (HoH) had been shown to offer an advantage in both metrology and quantum energy storage. In this work, we axiomatize a model of computation that allows us to consider such Hamiltonians for the purposes of computation. From this axiomatic model, we formally prove that an HoH-based algorithm can gain up to a quadratic speed-up (in the size of the input) over classical sequential algorithms—for any possible classical computation. We show how our axiomatic model is grounded in the same physics as that used in HoH-based quantum advantage for metrology and battery charging. Thus we argue that any advance in implementing HoH-based quantum advantage in those scenarios can be co-opted for the purpose of speeding up computation.

QNC 1201

### Improved Synthesis of Restricted Clifford+T Circuits

In quantum information theory, the decomposition of unitary operators into gates from some fixed universal set is of great research interest. Since 2013, researchers have discovered a correspondence between certain quantum circuits and matrices over rings of algebraic integers. For example, there is a correspondence between a family of restricted Clifford+T circuits and the group On(Z[1/2]). Therefore, in order to study quantum circuits, we can study the corresponding matrix groups and try to solve the constructive membership problem (CMP): given a set of generators and an element of the group, how to factor this element as a product of generators? Since a good solution to CMP yields a smaller decomposition of an arbitrary group element, it helps us implement quantum circuits using fewer resources.

### Noncommuting charges: Bridging theory to experiment

Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities—energy, particles, electric charge, etc.—that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries—about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This work provides a methodology for building this bridge systematically: we present a prescription for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, and with trapped ions.

Quantum measurements are inherently probabilistic. Further defying our classical intuition, quantum theory often forbids us to precisely determine the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, this problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. In this talk, we will go over some basic notions of graph theory that will allow us to derive uncertainty relations valid for any set of dichotomic quantum observables. We will then specify the many cases for which these relations are tight, depending on properties of some graphs, and discuss a conjecture for the untight cases. Finally, we will show some direct applications to several problems in quantum information, namely, in constructing entropic uncertainty relations, separability criteria and entanglement witnesses.

The optimal rates for compression of mixed states was found by Koashi and Imoto in 2001 for the blind case and by Horodecki and independently by Hayashi for the visible case respectively in 2000 and 2006. However, it was not known so far whether the strong converse property holds for these compression problems. In this work, we show that the strong converse holds for the blind compression scheme. For the visible scheme, the strong converse holds up to the continuity of the regularized Renyi entanglement of purification.

## Photon Detector Module gearing up for International Space Station

A single-photon detector and counting module (SPODECT) recently built by Waterloo’s Quantum Photonics Lab for the International Space Station (ISS) will be used to verify quantum entanglement and test its survivability in space as part of the *Space Entanglement and Annealing QUantum Experiment (SEAQUE)* mission, in a collaboration with researchers at the University of Illinois Urbana-Champaign, the Jet Propulsion Laboratory, ADVR Inc, and the National University of Singapore

#### Pagination

- Page 1
- Next page