Related papers: Quantum simulation with sum-of-squares spectral am…
Quantum sensing encompasses highly promising techniques with diverse applications including noise-reduced imaging, super-resolution microscopy as well as imaging and spectroscopy in challenging spectral ranges. These detection schemes use…
We study the Sum of Squares (SoS) Hierarchy with a view towards combinatorial optimization. We survey the use of the SoS hierarchy to obtain approximation algorithms on graphs using their spectral properties. We present a simplified proof…
Spectroscopy is an indispensable tool in understanding the structures and dynamics of molecular systems. However computational modelling of spectroscopy is challenging due to the exponential scaling of computational complexity with system…
For spin rotational symmetric models with a positive-definite high-temperature expansion of the partition function, a stochastic sampling of the series expansion upon partial resummation becomes logically equivalent to sampling an…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
Surface-enhanced Raman scattering (SERS) is a critical tool for chemical sensing and spectroscopy, and a key question is how to optimally design nanostructures for maximizing SERS. We present fundamental limits on spatially-averaged SERS…
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical…
We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations.…
The quantum many-body problem in condensed phases is often simplified using a quasiparticle description, such as effective mass theory for electron motion in a periodic solid. These approaches are often the basis for understanding many…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…
In the context of energy storage at the nanoscale, exploring the notion of \textit{quantum advantage} implies walking on the thin line at the boundary between quantum mechanics and thermodynamics, which underpins our conventional…
The Sum-of-Squares (SoS) hierarchy is a powerful framework for polynomial optimization and proof complexity, offering tight semidefinite relaxations that capture many classical algorithms. Despite its broad applicability, several works have…
We show how to achieve full spectral characterization of general multiaxis additive noise. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable even to models where a large…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
As quantum technology advances, quantum simulation becomes increasingly promising, with significant implications for quantum many-body physics and quantum chemistry. Despite being one of the most accessible simulation methods, the product…
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…