Effective gaps are not effective: quasipolynomial classical simulation of obstructed stoquastic Hamiltonians

by   Jacob Bringewatt, et al.

All known examples confirming the possibility of an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (AQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. The symmetries produce large effective eigenvalue gaps, which in turn make adiabatic computation efficient. We present a classical algorithm to efficiently sample from the effective subspace of a k-local stoquastic Hamiltonian H, without a priori knowledge of its symmetries (or near-symmetries). Our algorithm maps any k-local Hamiltonian to a graph G=(V,E) with | V | = O(poly(n)) where n is the number of qubits. Given the well-known result of Babai, we exploit graph isomorphism to study the automorphisms of G and arrive at an algorithm quasi-polynomial in | V| for producing samples from the effective subspace eigenstates of H. Our results rule out exponential separations between stoquastic AQC and classical computation that arise from hidden symmetries in k-local Hamiltonians. Furthermore, our graph representation of H is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in non-stoquastic cases, or be useful in studying additional properties of k-local Hamiltonians.


page 1

page 2

page 3

page 4


(Sub)Exponential advantage of adiabatic quantum computation with no sign problem

We demonstrate the possibility of (sub)exponential quantum speedup via a...

Spectral sparsification of matrix inputs as a preprocessing step for quantum algorithms

We study the potential utility of classical techniques of spectral spars...

Direct Application of the Phase Estimation Algorithm to Find the Eigenvalues of the Hamiltonians

The eigenvalue of a Hamiltonian, H, can be estimated through the phase e...

Time-dependent Hamiltonian simulation with L^1-norm scaling

The difficulty of simulating quantum dynamics depends on the norm of the...

On skew-Hamiltonian Matrices and their Krylov-Lagrangian Subspaces

It is a well-known fact that the Krylov space K_j(H,x) generated by a sk...

Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States

Recently it was shown that the so-called guided local Hamiltonian proble...

Please sign up or login with your details

Forgot password? Click here to reset