  For any local Hamiltonian H, I construct a local CPT map and stopping
condition which converges to the ground state subspace of H. Like any ground
state preparation algorithm, this algorithm necessarily has exponential
run-time in general (otherwise BQP=QMA), even for gapped, frustration-free
Hamiltonians (otherwise BQP is in NP). However, this dissipative quantum
eigensolver has a number of interesting characteristics, which give advantages
over previous ground state preparation algorithms.
  - The entire algorithm consists simply of iterating the same set of local
measurements repeatedly.
  - The expected overlap with the ground state subspace increases monotonically
with the length of time this process is allowed to run.
  - It converges to the ground state subspace unconditionally, without any
assumptions on or prior information about the Hamiltonian.
  - The algorithm does not require any variational optimisation over
parameters.
  - It is often able to find the ground state in low circuit depth in practice.
  - It has a simple implementation on certain types of quantum hardware, in
particular photonic quantum computers.
  - The process is immune to errors in the initial state.
  - It is inherently error- and noise-resilient, i.e. to errors during
execution of the algorithm and also to faulty implementation of the algorithm
itself, without incurring any computational overhead: the overlap of the output
with the ground state subspace degrades smoothly with the error rate,
independent of the algorithm's run-time.
  I give rigorous proofs of the above claims, and benchmark the algorithm on
some concrete examples numerically.
