Shor's Algorithm, Part I (of II)
In 1994, the field of quantum computing had a significant breakthrough when Peter Shor introduced a quantum algorithm that factors integers in (probabilistic) polynomial time. In these talks, I'll explain the mathematical aspects of Shor's algorithm.
Part II will follow on 3/5.
A cryogenic optical cavity for trapped Yb+ quantum networking
One approach to ion-photon entanglement relies on transitions from 2P3/2 to the low-lying 2D3/2 and 2D5/2 states at 1345 nm and 1650 nm in Yb+ [1]. Here Purcell enhancement is crucial for achieving good performance in the context of quantum networking. In support of this effort, we developed a monolithic, fiber-coupled Fabry–Pérot cavity integrated with a blade trap that operates at cryogenic temperatures. One of the cavity mirrors is bonded to a metalens that mode-matches cavity light to a single-mode fiber.
A cryogenic optical cavity for trapped Yb+ quantum networking
Abstract: One approach to ion-photon entanglement relies on transitions from 2P3/2 to the low-lying 2D3/2 and 2D5/2 states at 1345 nm and 1650 nm in Yb+ [1]. Here Purcell enhancement is crucial for achieving good performance in the context of quantum networking. In support of this effort, we developed a monolithic, fiber-coupled Fabry–Pérot cavity integrated with a blade trap that operates at cryogenic temperatures. One of the cavity mirrors is bonded to a metalens that mode-matches cavity light to a single-mode fiber.
The Rayleigh-Taylor instability in a binary quantum fluid
Instabilities, where initially small fluctuations seed the formation of large-scale structures, govern the dynamics in various fluid flows. The Rayleigh-Taylor instability (RTI) is an iconic example that leads to the development of mushroom-shaped incursions when immiscible fluids are accelerated into each other. RTI drives structure formation throughout science and engineering including table-top oil and water mixtures; supernova explosions; and inertial confinement fusion. Despite its ubiquity, controlled laboratory RTI experiments are technically challenging.
The Rayleigh-Taylor instability in a binary quantum fluid
Abstract: Instabilities, where initially small fluctuations seed the formation of large-scale structures, govern the dynamics in various fluid flows. The Rayleigh-Taylor instability (RTI) is an iconic example that leads to the development of mushroom-shaped incursions when immiscible fluids are accelerated into each other. RTI drives structure formation throughout science and engineering including table-top oil and water mixtures; supernova explosions; and inertial confinement fusion. Despite its ubiquity, controlled laboratory RTI experiments are technically challenging.
A Constructive Approach to Zauner’s Conjecture via the Stark Conjectures
Abstract: In this talk, I will present a construction of symmetric informationally complete POVMs (SIC-POVMs), a special class of quantum measurements whose existence in all dimensions was conjectured by Zauner in 1999. Equivalently, these are maximal sets of d^2 equiangular lines in ℂ^d. Our approach introduces an explicit mathematical object, the ghost SIC, built from number-theoretic properties of a special modular function, and we show that it is Galois conjugateto an actual SIC.
Glasses: From Physical Hamiltonians to Neural Networks and Back
Abstract: This talk will review our recent work on classical and quantum glasses. I will start with a discussion of spin glasses from the perspective of chaos theory.
Conditional lower bounds for algorithms with pre-processed advice
Abstract: Unlike the traditional study of algorithms which attempts to solve a certain task using minimal space and time resources, I will discuss data structures to solve certain algorithmic tasks after an initial pre-processing phase. The interest here is to study the tradeoffs between the resources such as the space and time required to perform the algorithmic task when asked a query; and the resources in the pre-processing phase such as the time required to prepare the data structure or its size.
Universal Adapters between quantum LDPC codes
Abstract: Error-correction is key to building a quantum computer. This includes both storage of quantum information as well as computing on it. Quantum low- density parity check (LDPC) codes offer a route to build these devices with low space overhead. The next question is - how do we fault-tolerantly com- pute on these codes? Existing proposals (Cohen et al. [2110.10794], Cross et al. [2407.18393]) rely on ancilla systems appended to the original LDPC code.
Permutation-invariant quantum error correction codes: from theory to practice
Abstract: Permutation-invariant quantum error correction codes that are invariant under any permutation of the underlying particles. These codes could have potential applications in quantum sensors and quantum memories. Here I will review the field of permutation-invariant codes, from code constructions to applications.
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*