no code implementations • 23 Dec 2020 • James D. Watson, Johannes Bausch, Sevag Gharibian
It is known that three fundamental questions regarding local Hamiltonians -- approximating the ground state energy (the Local Hamiltonian problem), simulating local measurements on the ground space (APX-SIM), and deciding if the low energy space has an energy barrier (GSCON) -- are $\mathsf{QMA}$-hard, $\mathsf{P}^{\mathsf{QMA}[log]}$-hard and $\mathsf{QCMA}$-hard, respectively, meaning they are likely intractable even on a quantum computer.
Quantum Physics Strongly Correlated Electrons Mathematical Physics Mathematical Physics
1 code implementation • 12 Sep 2019 • Sevag Gharibian, Stephen Piddock, Justin Yirka
Perhaps surprisingly, [Ambainis, CCC 2014] showed that the related, but arguably more natural, problem of simulating local measurements on ground states of local Hamiltonians (APX-SIM) is likely harder than QMA.
Quantum Physics Computational Complexity
1 code implementation • 28 May 2018 • Sevag Gharibian, Miklos Santha, Jamie Sikora, Aarthi Sundaram, Justin Yirka
The polynomial-time hierarchy ($\mathrm{PH}$) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as $\mathrm{PH}$ does not collapse).
Computational Complexity Quantum Physics 68Q12, 68Q15, 81P68, 03D15 F.1.3
1 code implementation • 17 Jun 2016 • Sevag Gharibian, Justin Yirka
An important task in quantum physics is the estimation of local quantities for ground states of local Hamiltonians.
Quantum Physics Strongly Correlated Electrons Computational Complexity
