21 citations · 41 across the 5 of their papers we have counts for
5 papers
A Class of Cyclic Quantum Codes
Matthew B. Hastings
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at leas…
A Sparse Chain Complex Without a Sparse Lift
Matthew B. Hastings
We construct a sparse chain complex (with three different degrees, so that it corresponds to a quantum code) which does not admit a sparse lift to the integers, answering a q…
Improving Perturbation Theory with the Sum-of-Squares: Third Order
M. B. Hastings
The sum-of-squares method can give rigorous lower bounds on the energy of quantum Hamiltonians. Unfortunately, typically using this method requires solving a semidefinite program,…
Topology and Phases in Fermionic Systems
M. B. Hastings
There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstruction…
Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity
M. B. Hastings
We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonre…