JQI

In this talk I will describe Decoded Quantum Interferometry (DQI), a quantum algorithm for reducing classical optimization problems to classical decoding problems by exploiting structure in the Fourier spectrum of the objective function. (See: https://arxiv.org/abs/2408.08292.) For a regression problem called optimal polynomial intersection, which has been previously studied in the contexts of coding theory and cryptanalysis, we believe DQI achieves an exponential quantum speedup.

Quantum sensing leverages the principles of quantum mechanics to provide ``quantum-enhanced'' measurement sensitivity, thereby amplifying our ability to observe interesting physical phenomena. It employs a rich arsenal of techniques, including squeezing, photon counting, entanglement assistance, and distributed quantum sensing to achieve unprecedented sensitivity.

Aaronson, Atia, and Susskind established that swapping quantum states |ψ〉 and |ϕ〉 is computationally equivalent to distinguishing their superpositions |ψ〉 ± |ϕ〉. We extend this to a general duality principle: manipulating quantum states in one basis is equivalent to extracting values in a complementary basis. Formally, for any group, implementing a unitary representation is computationally equivalent to Fourier subspace extraction from its irreducible representations.

The spin-boson model, involving spins interacting with a bath of quantum harmonic oscillators, is a widely used representation of open quantum systems that describe many dissipative processes in physical, chemical and biological systems. Trapped ions present an ideal platform for simulating the quantum dynamics of such models, by accessing both the high-quality internal qubit states and the motional modes of the ions for spins and bosons, respectively.

D. Carney et al. [https://doi.org/10.1103/PRXQuantum.2.030330] suggest the use of a trapped atom interferometer combined with a mechanical oscillator to test certain theories combining quantum mechanics with gravity. We construct an entanglement witness applicable to the stated interferometer-oscillator setup. We also investigate the effects of atomic dephasing and thermal noise on the practical use of this entanglement witness in an experimental implementation of such a system.

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. I will discuss two approaches to better understand the role of quantum complexity in many-body physics. First, we'll consider random circuits, a model for chaotic dynamics. In such circuits, the quantum complexity grows linearly until it saturates at a value exponential in the system size.