  In the quantum optimisation setting, we build on a scheme introduced by Young
et al [PRA 88, 062314, 2013], where physical qubits in multiple copies of a
problem encoded into an Ising spin Hamiltonian are linked together to increase
the logical system's robustness to error. We introduce several innovations that
improve this scheme significantly. First, we note that only one copy needs to
be correct by the end of the computation, since solution quality can be checked
efficiently. Second, we find that ferromagnetic links do not generally help in
this "one correct copy" setting, but anti-ferromagnetic links do help on
average, by suppressing the chance of the same error being present on all of
the copies. Third, we find that minimum-strength anti-ferromagnetic links
perform best, by counteracting the spin-flips induced by the errors. We have
numerically tested our innovations on small instances of spin glasses from
Callison et al [NJP 21, 123022, 2019], and we find improved error tolerance for
three or more copies in configurations that include frustration. Interpreted as
an effective precision increase, we obtain several extra bits of precision for
three copies connected in a triangle. This provides proof-of-concept of a
method for scaling quantum annealing beyond the precision limits of hardware, a
step towards fault tolerance in this setting.
