Simulating the Anisotropic XY-model on a Trapped Ion Quantum Simulator
Location: QNC 1201
Efficient Circuit-Based Quantum State Tomography via Sparse Entry Optimization
Location: QNC 1201 and Online on Zoom
Quantum sensing of light with sub-wavelength resolution
Nonclassicality of Propagating States from 3-Photon Interactions in a Parametric Cavity
Quantum Error Characterization and Benchmarking
QNC building, 200 University Ave. Room 1201, Waterloo
An overview of quantum harmonic oscillators is given. The phase space picture of quantum mechanics is discussed with a special focus on Wigner functions. An overview of Gaussian states and channels is discussed. Non-classical states and their phase-space signatures are explored. Some examples of non-classical states used for encoding logical quantum information and their properties are explored. If the time permits, current research directions and popular implementation platforms will be discussed.
QNC building, 200 University Ave. Online only, Waterloo
A basic question in the PAC model of learning is whether proper learning is harder than improper learning. In the classical case, there are examples of concept classes with VC dimension d that have sample complexity Ω(d/ϵ log (1/ϵ)) for proper learning with error ϵ, while the complexity for improper learning is O(d/ϵ). One such example arises from the Coupon Collector problem.
Motivated by the efficiency of proper versus improper learning with quantum samples, Arunachalam, Belovs, Childs, Kothari, Rosmanis, and de Wolf (TQC 2020) studied an analogue, the Quantum Coupon Collector problem. Curiously, they discovered that for learning size k subsets of [n] the problem has sample complexity Θ(k log (min{k,n−k+1})), in contrast with the complexity of Θ(k log k) for Coupon Collector. This effectively negates the possibility of a separation between the two modes of learning via the quantum problem, and Arunachalam et al. posed the possibility of such a separation as an open question.
In this work, we first present an algorithm for the Quantum Coupon Collector problem with sample complexity that matches the sharper lower bound of (1−o(1)) k ln( min{k,n−k+1} ) shown recently by Bab Hadiashar, Nayak, and Sinha (IEEE TIT 2024), for the entire range of the parameter k. Next, we devise a variant of the problem, the Quantum Padded Coupon Collector. We prove that its sample complexity matches that of the classical Coupon Collector problem for both modes of learning, thereby exhibiting the same asymptotic separation between proper and improper quantum learning as mentioned above.
QNC building, 200 University Ave. Room 1201, Waterloo
Quantum entanglement can be quantified in many ways, some of which bear clear operational meanings. The Distillable Entanglement and DIQKD rate are two such measures, speculated to be equivalent as stated by the Revised Peres Conjecture (Friedman and Leditzky, 21). Our research lays foundations to the conjecture’s proof, most notably using the notion of ‘private states’, a family of quantum states that arise naturally in the context of QKD. Asking questions such as “what kind of private state can be resulted from a certain DIQKD protocol?”, we were able to provide simple sufficient conditions for the Revised Peres Conjecture to hold.
RAC building, 475 Wes Graham Way, Waterloo Room 3003
This week's summer tutorial session will cover quantum error correction, starting from an overview of early successes in the field before introducing stablizer codes.
QNC building, 200 University Ave. Room 1201, Waterloo
As we move towards the era of quantum computers with 1000+ qubits, the most promising application able to harness the potential of such devices is quantum simulation. Simulating fermionic systems is both a well-formulated problem with clear real-world applications and a computationally challenging task. In order to simulate a system of fermions on a quantum computer, one has to map the fermionic Hamiltonian to a qubit Hamiltonian. The most popular such mapping is the Jordan-Wigner encoding, which suffers from inefficiencies caused by the non-locality of the encoded operators. As a result, alternative local mappings have been proposed that solve the problem of long encoded operators at the expense of constant factor of qubits. Some of these alternative mappings end up possessing non-trivial stabilizer structure akin to popular quantum error correction (QEC) codes.
In this talk, I will introduce the problem of mapping fermionic operators to qubit operators and how the selection of an encoding could affect resource requirements in near-term simulations. I will also talk about error mitigation approaches utilizing the stabilizer structure of certain encodings as well as using stabilizer simulation to assess the effectiveness of such approaches.