Effective Gaps Are Not Effective: Quasipolynomial Classical Simulation of Obstructed Stoquastic Hamiltonians.

All known examples suggesting an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (StoqAQC) 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 subexponentially sample from an effective subspace of any 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 [Graph isomorphism in quasipolynomial time, in Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing (2016), pp. 684-697], we exploit graph isomorphism to study the automorphisms of G and arrive at an algorithm quasipolynomial in |V| for producing samples from effective subspace eigenstates of H. Our results rule out exponential separations between StoqAQC and classical computation that arise from hidden symmetries in k-local Hamiltonians. Our graph representation of H is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in nonstoquastic cases, or be useful in studying additional properties of k-local Hamiltonians.

A large 12-month extension study of an 8-week trial to evaluate the safety and efficacy of triple combination (TC) cream in melasma patients previously treated with TC cream or one of its dyads.

This was a 12-month extension of a randomized, investigator-blinded, multicenter, 8-week trial with triple combination (TC) cream in facial melasma. A total of 585 patients were enrolled in the study and 569 patients received study medication. Three hundred eighty-nine patients completed 6 months of treatment and 327 patients completed 12 months of treatment. TC cream demonstrated a favorable safety profile: only 14 patients (2.5%) discontinued the study due to treatment-related adverse events (AEs). The 2 cases of skin atrophy were mild and did not lead to withdrawal. From the 23 cases of mild telangiectasia, only 2 resulted in discontinuation. All others were transient. Results confirmed those of a previous smaller study, with both physicians and patients reporting clinically significant improvements in melasma. By month 12, 80% of patients had lesions completely cleared or nearly cleared. Once daily application of TC cream applied intermittently over a long period is a safe, tolerable, and effective treatment for moderate to severe melasma of the face.