Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.
The complexity of quantum spin systems on a two-dimensional square lattice
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA, see quant-ph/0406180. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.
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For non-critical systems, analogue quantum simulation via perturbative gadgets requires only polylogarithmic interaction strengths through extrapolation within phases of matter.
Deep Boltzmann Quantum States with natural-gradient optimization and annealing-like training match exact or best-known solutions for large infinite-range Ising spin glasses and solve job shop scheduling instances.
The succinct state 2-local Hamiltonian problem for qubit Hamiltonians is promise-MA-complete.
citing papers explorer
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Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra
Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.
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Analogue quantum simulation with polylogarithmic interaction strengths by extrapolating within phases of matter
For non-critical systems, analogue quantum simulation via perturbative gadgets requires only polylogarithmic interaction strengths through extrapolation within phases of matter.
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Solving Classical and Quantum Spin Glasses with Deep Boltzmann Quantum States
Deep Boltzmann Quantum States with natural-gradient optimization and annealing-like training match exact or best-known solutions for large infinite-range Ising spin glasses and solve job shop scheduling instances.
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On the Complexity of the Succinct State Local Hamiltonian Problem
The succinct state 2-local Hamiltonian problem for qubit Hamiltonians is promise-MA-complete.