StoqMa(k) equals StoqMa for any polynomial k via a positive value-based de Finetti theorem that approximates nonnegative product values with symmetric extensions.
Merlin-Arthur Games and Stoquastic Complexity
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
abstract
MA is a class of decision problems for which `yes'-instances have a proof that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete problem which we call the stoquastic k-SAT problem. This is a matrix-valued analogue of the satisfiability problem in which clauses are k-qubit projectors with non-negative matrix elements, while a satisfying assignment is a vector that belongs to the space spanned by these projectors. Stoquastic k-SAT is the first non-trivial example of a MA-complete problem. We also study the minimum eigenvalue problem for local stoquastic Hamiltonians that was introduced in quant-ph/0606140, stoquastic LH-MIN. A new complexity class StoqMA is introduced so that stoquastic LH-MIN is StoqMA-complete. Lastly, we consider the average LH-MIN problem for local stoquastic Hamiltonians that depend on a random or `quenched disorder' parameter, stoquastic AV-LH-MIN. We prove that stoquastic AV-LH-MIN is contained in the complexity class \AM, the class of decision problems for which yes-instances have a randomized interactive proof with two-way communication between prover and verifier.
citation-role summary
method 1
citation-polarity summary
roles
method 1polarities
use method 1representative citing papers
The Guided Local Hamiltonian problem for stoquastic Hamiltonians is promise BPP-hard (even 2-local on lattices), BQP-hard under fixed local constraints, and admits a deterministic classical approximation algorithm when promise gap, overlap, and spectral gap are constant with constant-depth local-pre
StoqMA(2) contains NP via Õ(√n)-qubit unentangled stoquastic proofs (nearly perfect completeness) and is contained in EXP, with ETH-optimal parameters matching a refined BKS Sum-of-Squares bound.
Stoquastic Sparse Hamiltonians is StoqMA-complete and its separable version is StoqMA(2)-complete.
citing papers explorer
-
The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
StoqMa(k) equals StoqMa for any polynomial k via a positive value-based de Finetti theorem that approximates nonnegative product values with symmetric extensions.
-
The Guided Local Hamiltonian Problem for Stoquastic Hamiltonians
The Guided Local Hamiltonian problem for stoquastic Hamiltonians is promise BPP-hard (even 2-local on lattices), BQP-hard under fixed local constraints, and admits a deterministic classical approximation algorithm when promise gap, overlap, and spectral gap are constant with constant-depth local-pre
-
The power of unentanglement without destructive interference
StoqMA(2) contains NP via Õ(√n)-qubit unentangled stoquastic proofs (nearly perfect completeness) and is contained in EXP, with ETH-optimal parameters matching a refined BKS Sum-of-Squares bound.
-
The Complexity of Stoquastic Sparse Hamiltonians
Stoquastic Sparse Hamiltonians is StoqMA-complete and its separable version is StoqMA(2)-complete.