Can one considerably shorten a proof for a quantum problem by using a protocol with a constant number of unentangled provers? We consider a frustration-free variant of the QCMA -complete ground state connectivity (GSCON) problem for a system of size n with a proof of superlinear size. We show that we can shorten this proof in QMA(2): There exists a two-copy, unentangled proof with length of order n, up to logarithmic factors, while the completeness–soundness gap of the new protocol becomes a small inverse polynomial in n.

We present a collection of results about the clock in Feynman's computer construction and Kitaev's local Hamiltonian problem. First, by analyzing the spectra of quantum walks on a line with varying end-point terms, we find a better lower bound on the gap of the Feynman Hamiltonian, which translates into a less strict promise gap requirement for the quantum-Merlin-Arthur–complete local Hamiltonian problem. We also translate this result into the language of adiabatic quantum computation. Second, introducing an idling clock construction with a large state space but fast Cesaro mixing, we provide a way for achieving an arbitrarily high success probability of computation with Feynman's computer with only a logarithmic increase in the number of clock qubits. Finally, we tune and thus improve the costs (locality and gap scaling) of implementing a (pulse) clock with a single excitation.