Events

Research Advancement Centre, 475 Wes Graham Way, Room RAC 2009, Waterloo, ON, CA N2L 6R2

Graph-Theoretic Techniques for Optimizing NISQ Algorithms

Supervisor: Dr. Michele Mosca. Thesis available from mgo@uwaterloo.ca. Oral defence Friday, February 2, 9:00 a.m., online.

IQC Colloquium - Sisi Zhou, The Perimeter Institute

Quantum-Nano Centre, 200 University Ave West, Room QNC 0101 Waterloo, ON CA N2L 3G1

 Quantum metrology studies estimation of unknown parameters in quantum systems. The Heisenberg limit of estimation precision 1/N, with N being the number of probes, is the ultimate sensing limit allowed by quantum mechanics that quadratically outperforms the classically-achievable standard quantum limit 1/√N. The Heisenberg limit is attainable using multi-probe entanglement in the ideal, noiseless case. However, in presence of noise, many quantum systems only allow a constant factor of improvement over the standard quantum limit. To elucidate the noise effect in quantum metrology, we prove a necessary and sufficient condition for achieving the Heisenberg limit using quantum controls. We show that when the condition is satisfied, there exist quantum error correction protocols to achieve the Heisenberg limit; when the condition is violated, no quantum controls can break the standard quantum limit (although quantum error correction can be used to maximize the constant-factor improvement). We will also discuss the modified sensing limits when only restricted types of quantum controls can be applied. 

IQC Seminar - Zahra Khanian, Technical University of Munich

200 University Ave W. Waterloo On Can QNC 1201

In the seminal 1948 paper "a mathematical theory of communication", Shannon introduced the concept of a classical source as a random variable and established its optimal compression rate, given by Shannon entropy. Nearly five decades later, Schumacher rigorously defined the notion of a quantum source and its compressibility. Schumacher's definition involved a quantum system and correlations with a purifying reference system. In our work, we build upon Schumacher's quantum source model, extending it to the most general form allowed by quantum mechanics. This extension involves considering the source and the reference in a mixed state, along with the presence of additional systems treated as side information. We address and solve various problems posed by these modifications, determining the optimal compression rates. While our work contributes significant progress in quantum source compression, we point out remaining open questions that require further exploration.

A quick introduction to Clifford theory

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

Clifford theory studies the connection between representations of a group and those of its normal subgroups. In recent work, I examined the Clifford theory of the Clifford group to determine parts of its character table for future applications. The goal of this talk is to introduce the representation theory and Clifford theory of finite groups sufficiently to understand next week's talk when I will explain the Clifford theory of the n-qubit Clifford group. Note that these are two distinct Cliffords. I may also briefly discuss the applications of Clifford theory in quantum error correction, time permitting.

The Clifford theory of the n-qubit Clifford group

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply the tools of (the coincidentally named) Clifford theory to examine the representation theory of the Clifford group using the much simpler representation theory of the Pauli group. We find an unexpected correspondence between irreducible characters of the n-qubit Clifford group and those of the (n + 1)-qubit Clifford group. This talk will rely on the explanation of Clifford theory given last week.

CS/Math Seminar - Kunal Marwaha - University of Chicago

200 University Ave. Waterloo ON. QNC 1201 + ZOOM

We study a variant of QMA where quantum proofs have non-negative amplitudes in both completeness and soundness. This class was introduced by Jeronimo and Wu [STOC '23] to understand QMA(2). We show that this variant is very powerful even without considering multiple unentangled quantum provers. In fact, QMA+ with some constant gap is equal to NEXP, even though QMA+ with some other constant gap is equal to QMA.

IQC Special Colloquium - Aziza Suleymanzade, Harvard University

200 University Ave W. Waterloo ON - ZOOM only

The experimental development of quantum networks marks a significant scientific milestone, poised to enable secure quantum communication, distributed quantum computing, and entanglement-enhanced nonlocal sensing. In this talk, I will discuss the recent advancements in the field along with the outstanding challenges through my work on two different platforms: Silicon Vacancy defects in diamond nanophotonic cavities and Rydberg atoms coupled to hybrid cavities. First, I will present our recent results on distributing entanglement across a two-node network with on-chip solid-state defects in cavities which we built at Harvard. We demonstrated high-fidelity entanglement between communication and memory qubits and showed long-distance entanglement over the 35 km of deployed fiber in the Cambridge/Boston area. Second, I will describe our work at the University of Chicago on using Rydberg atoms as transducers of quantum information between optical and microwave photons, with the goal of integrating Rydberg platforms with superconducting circuits and paving the way for advanced quantum network architectures. The talk will conclude with a perspective on the potential of this hybrid platform approach in constructing quantum networks, highlighting the uncharted scientific and technological opportunities it could unlock.

CS/Math Seminar - Nolan Coble - University of Maryland, College Park

200 University Ave. Waterloo ON. QNC 1201 + ZOOM

The recent resolution of the NLTS Conjecture [ABN22] establishes a prerequisite to the Quantum PCP (QPCP) Conjecture through a novel use of newly-constructed QLDPC codes [LZ22]. Even with NLTS now solved, there remain many independent and unresolved prerequisites to the QPCP Conjecture, such as the NLSS Conjecture of [GL22]. In this talk we focus on a specific and natural prerequisite to both NLSS and the QPCP Conjecture, namely, the existence of local Hamiltonians whose low-energy states all require ω(log n) T gates to prepare. In fact, we will show a stronger result which is not necessarily implied by either conjecture: we construct local Hamiltonians whose low-energy states require Ω(n) T gates. We further show that our procedure can be applied to the NLTS Hamiltonians of [ABN22] to yield local Hamiltonians whose low-energy states require both Ω(log n)-depth and Ω(n) T gates to prepare. This result represents a significant improvement over [CCNN23] where we used a different technique to give an energy bound which only distinguishes between stabilizer states and states which require a non-zero number of T gates.

Special Colloquium - Zhi Li, Perimeter Institute

University of Waterloo 200 University Ave. W Waterloo QNC 0101

Quantum error-correcting codes play a pivotal role in enabling fault-tolerant quantum computation. These codes protect quantum information through intricately designed redundancies that encode the information in a global manner. Unlike classical objects, in a quantum error-correcting code, the knowledge of individual subregions, even when combined, reveals nothing about the overall state.

In this talk, we explore the quantification of how far quantum error-correcting code are from classical states. We examine this question from three different perspectives: circuit complexity (the mimimal number of circuit depth needed to prepare a quantum state), expansion number (the minimal number of terms needed to expand the wavefunction), and a quantity we termed product overlap, which characterizes the maximal overlap between a given state and any product state. We will demonstrate why any quantum error-correcting code states must exhibit exponentially small product overlap, and how it implies lower bounds for the circuit complexity and the expansion number.