Michael Jarret
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View article: On the stability of solutions to Schrödinger's equation short of the adiabatic limit
On the stability of solutions to Schrödinger's equation short of the adiabatic limit Open
We prove an adiabatic theorem that applies at timescales short of the typical adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturbation. We directly characterize cross-subspace effects of p…
View article: A QUANTUM-AI FRAMEWORK FOR EXTREME WEATHER PREDICTION
A QUANTUM-AI FRAMEWORK FOR EXTREME WEATHER PREDICTION Open
The frequency and intensity of extreme weather events in North America will likely increase with a changing climate. High resolution simulations are necessary to advance process-based understanding of weather events at local scales accompa…
View article: Effective Gaps Are Not Effective: Quasipolynomial Classical Simulation of Obstructed Stoquastic Hamiltonians
Effective Gaps Are Not Effective: Quasipolynomial Classical Simulation of Obstructed Stoquastic Hamiltonians Open
All known examples suggesting an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (StoqAQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. Th…
View article: Quantum adiabatic optimization without heuristics
Quantum adiabatic optimization without heuristics Open
Quantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian $H(s)$ with spectral gap $γ(s)$. Assuming the existence of an oracle $Γ$ such that $γ_\min = Θ\left(\min_sΓ(s)\right)$, we provide an algorithm that relia…
View article: Quantum algorithms for connectivity and related problems
Quantum algorithms for connectivity and related problems Open
An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formula evaluation problems. Th
View article: Hamiltonian surgery: Cheeger-type gap inequalities for nonpositive (stoquastic), real, and Hermitian matrices
Hamiltonian surgery: Cheeger-type gap inequalities for nonpositive (stoquastic), real, and Hermitian matrices Open
Cheeger inequalities bound the spectral gap $γ$ of a space by isoperimetric properties of that space and vice versa. In this paper, I derive Cheeger-type inequalities for nonpositive matrices (aka stoquastic Hamiltonians), real matrices, a…
View article: Improved quantum backtracking algorithms using effective resistance estimates
Improved quantum backtracking algorithms using effective resistance estimates Open
We investigate quantum backtracking algorithms of a type previously\nintroduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of\nunknown structure, and in certain cases exponentially outperform classical\nprocedures (suc…
View article: Quantum Algorithms for Connectivity and Related Problems
Quantum Algorithms for Connectivity and Related Problems Open
An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formula evaluation problems. The complexity of the resulting alg…
View article: Substochastic Monte Carlo Algorithms
Substochastic Monte Carlo Algorithms Open
In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algori…
View article: Adiabatic optimization versus diffusion Monte Carlo methods
Adiabatic optimization versus diffusion Monte Carlo methods Open
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods…
View article: Yang–Baxter operators need quantum entanglement to distinguish knots
Yang–Baxter operators need quantum entanglement to distinguish knots Open
Any solution to the Yang-Baxter equation yields a family of representations\nof braid groups. Under certain conditions, identified by Turaev, the\nappropriately normalized trace of these representations yields a link\ninvariant. Any Yang-B…