Changpeng Shao

Quantum vs. Classical Algorithms for Solving the Heat Equation

2022 · Communications in Mathematical Physics

Abstract Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE—the heat equation in a rectangular region—and compare in detail the complexities of ten …

Testing Quantum Satisfiability

2025 · Communications in Mathematical Physics

Abstract Quantum k -SAT (the problem of determining whether a k -local Hamiltonian is frustration-free) is known to be QMA $$_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>1</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> -complete for $$k\ge 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> …