Spring 2023

Abstract: Can the current generation quantum computers solve science problems that conventional computers cannot? The jury is still out on this, but key to achieving this goal is the ability to perform robust quantum computation on near-term hardware. In this talk, I will describe three different types of robust computation that we have successfully completed: (i) computing topological properties (ii) simulating driven-dissipative systems and (iii) performing coherent time evolution with constant depth circuits.

Hamiltonian simulation is one of the most promising applications of quantum computing. Recent experimental results suggest that continuous-time analog quantum simulation would be advantageous over gate-based digital quantum simulation in the Noisy Intermediate-Size Quantum (NISQ) machine era. However, programming such analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software, and the only few known examples are all hardware-specific.

Abstract: Over the past 6 years, a series of works have shown unconditional separations between the computational power of constant depth quantum and classical circuits. This talk will begin with a review of these circuit classes and separations. Then we'll discuss some tips and tricks -- essentially circuit identities -- which are useful when constructing constant depth quantum circuits with superclassical computational power.

Abstract: Quantum query complexity is a fundamental model in quantum computation, which captures known quantum algorithms such as Grover's search algorithm, and also enables rigorous comparison between classical and quantum models of computation. The polynomial method has become one of the main paradigms for proving lower bounds on quantum query complexity.

Abstract: Fabry-Perot based refractometry is a powerful technique for pressure assessments that, due to the recent redefinition of the SI system, offers a new route to realizing the SI unit of pressure, the Pascal. In the talk, I will provide a short introduction to pressure metrology and attempt to explain the basics of Fabry-Perot based refractometry and how it can be used to realize the Pascal.

Abstract: A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description.

Dissertation Committee Chair: Mohammad Hafezi

Committee: 

Abstract: I will discuss mesoscopic topological superconductors that can be used to realize quantum impurity models with orthogonal or symplectic symmetries. The first one uses a topological superconductor that hosts many (M>2) Majorana zero modes. Such an "M-Majorana island" coupled to normal metal leads realizes a novel type of topological Kondo effect, where the effective impurity "spin" transforms under the orthogonal group SO(M) stemming from the non-local topological ground state degeneracy of the island.

Abstract: While quantum walk frameworks make it easy to design quantum algorithms, as evidenced by their wide application across domains, the major drawback is that they can achieve at most a quadratic speedup over the best classical algorithm.  In this work, we generalise the electric network framework – the most general of quantum walk frameworks, into a new framework that we call the multidimensional quantum walk framework, which no longer suffers from the aforementioned drawback, while still maintaining the original classical walk intuition.