Analytical solution for low energy state estimation by quantum annealing to arbitrary Ising spin Hamiltonian

We point to the existence of an analytical solution to a general quantum annealing (QA) problem of finding low energy states of an arbitrary Ising spin Hamiltonian HI by implementing time evolution with a Hamiltonian H(t) = HI + g(t)Ht. We will assume that the nonadiabatic annealing protocol is defined by a specific decaying coupling g(t) and a specific mixing Hamiltonian Ht that make the model analytically solvable arbitrarily far from the adiabatic regime. In specific cases of HI, the solution shows the possibility of a considerable quantum speedup of finding the Ising ground state. We then compare predictions of our solution to results of numerical simulations, and argue that the solvable QA protocol produces the optimal performance in the limit of maximal complexity of the computational problem. Our solution demonstrates for the most complex spin glasses a power-law energy relaxation with the annealing time T and uncorrelated from HI annealing schedule. This proves the possibility for spin glasses of a faster than ∼ 1/logβT energy relaxation.

Enhanced coherence of all-nitride superconducting qubits epitaxially grown on silicon substrate

Improving the coherence of superconducting qubits is a fundamental step towards the realization of fault-tolerant quantum computation. However, coherence times of quantum circuits made from conventional aluminum-based Josephson junctions are limited by the presence of microscopic two-level systems in the amorphous aluminum oxide tunnel barriers. Here, we have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on silicon substrates which promise to overcome the drawbacks of qubits based on Al/AlOx/Al junctions. The all-nitride qubits have great advantages such as chemical stability against oxidation, resulting in fewer two-level fluctuators, feasibility for epitaxial tunnel barriers that reduce energy relaxation and dephasing, and a larger superconducting gap of ~5.2 meV for NbN, compared to ~0.3 meV for aluminum, which suppresses the excitation of quasiparticles. By replacing conventional MgO by a silicon substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time $${T}_{1}=16.3\;{{\upmu }}{{{{{\rm{s}}}}}}$$ T 1 = 16.3 μ s and a spin-echo dephasing time $${T}_{2}=21.5\;{{\upmu }}{{{{{\rm{s}}}}}}$$ T 2 = 21.5 μ s . These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to the previously reported $${T}_{1}\approx {T}_{2}\approx 0.5\;{{\upmu }}{{{{{\rm{s}}}}}}$$ T 1 ≈ T 2 ≈ 0.5 μ s of NbN-based qubits on MgO substrates. These results are an important step towards constructing a new platform for superconducting quantum hardware.