Seminar

Circuit quantum electrodynamics (circuit QED) has become one of the main platforms for quantum simulation and computation. One of its notable advantages is its ability to facilitate the study of new regimes of light-matter interactions. This is achieved due to the native strong coupling between superconducting qubits and microwave resonators, and the ability to lithographically define a large variety of resonant microwave structures, for example, photonic crystals.

The task of quantum position verification (QPV) deploys quantum information with the aim to use a party's position as a cryptographic credential. One well-studied proposed protocol for this task, f-routing, involves a mixture of classical information and a single quantum bit that has to be routed somewhere as a function of the classical information.

This presentation introduces a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023].

In this talk, I will describe a significant open problem in post-quantum cryptography: specifically the quantum security of the sponge construction with invertible permutations (which, among other things, underlies the international hash standard SHA-3). I will motivate the query model in which this problem is usually stated, and give intuition for why it is hard. Then we'll explore some recent progress on this question based on applying the theory of Young subgroups, explained in a beginner-friendly way.

Quantum computing promises to transform our approach to solving significant computational challenges, such as factorization and quantum system simulation. Harnessing this quantum power in real life necessitates software stack support. This talk focuses on the critical challenges encountered in the software for quantum computing, aiming to shape high-assurance software stacks for controlling quantum computing devices in the immediate future and beyond.

At the heart of math, physics, and computing is Arithmetic, a field that has been around throughout all of human history. However, today quantum computers provide a completely new landscape for the field. The requirements of quantum systems means that many of the standard operations one would find on a classical ALU cannot be easily implemented on quantum circuits. In this talk, I will speak on some of the new ways programmers and researchers must think when implementing arithmetic operations on quantum computers.

Nagaoka ferromagnetism (NF) is a long-predicted example of itinerant ferromagnetism in the Hubbard model and has been studied theoretically for many years. NF occurs when there is one hole in a half-filled band and a large onsite Coulomb repulsion, which does not arise naturally in materials. Quantum dots systems like dopant arrays in Si, can be fabricated with atomically precise complex geometries to create highly controllable systems. This makes them good candidates to study itinerant ferromagnetism in different array geometries.

In this talk, I will discuss a general formalism for detecting and correcting faults in a Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code. From the outcome code we construct a corresponding stabilizer code, the spacetime code. Our construction extends the circuit-to-code construction of Bacon, Flammia, Harrow and Shi, revisited recently by Gottesman.

Theories whose fluctuating degrees of freedom live on extended loops as opposed to points, are abundant in nature. One example is the action obtained upon eliminating the redundant gauge fields in a gauge theory. Formulating a Renormalization Group (RG) procedure for such a theory is an open problem. In this work, we outline a procedure that in principle computes the outcome of coarse-graining and rescaling of such a theory. We make estimates that lead to qualitative agreement with known results of phase transitions in gauge theories and the XY-model.

Minimizing the energy of a many-body system is a fundamental problem in many fields. Although we hope a quantum computer can help us solve this problem faster than classical computers, we have a very limited understanding of where a quantum advantage may be found. In this talk, I will present some recent theoretical advances that shed light on quantum advantages in this domain. First, I describe rigorous analyses of the Quantum Approximate Optimization Algorithm applied to minimizing energies of classical spin glasses.