Ivan Bardet

Abstract With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge overhead imposed by quantum error correction itself. We propose a fault-tolerant quantum computing scheme that can nonetheless be assembled from a small number of experimental components, potentially dramatically reducing the engineering challenges associated with building a large-scale fault-tolerant quantum computer. Our scheme has a threshold of $0.39\%$ for depolarising noise, assuming that memory errors are negligible. In the presence of memory errors, the logical error rate decays exponentially with $\sqrt{T/\tau}$, where $T$ is the memory coherence time and $\tau$ is the timescale for elementary gates. Our approach is based on a novel procedure for fault-tolerantly preparing three-dimensional cluster states using a single actively controlled qubit and a pair of delay lines. Although a circuit-level error may propagate to a high-weight error, the effect of this error on the prepared state is always equivalent to that of a constant-weight error. We describe how the requisite gates can be implemented using existing technologies in quantum photonic and phononic systems. With continued improvements in only a few components, we expect these systems to be promising candidates for demonstrating fault-tolerant quantum computation with a comparatively modest experimental effort. Session 1B Stage B 8:30 - 9:00 On the entropic convergence of quantum Gibbs samplers Abstract Given a uniform, frustration-free family of local Lindbladians defined on a quantum lattice spin system in any spatial dimension, we prove a strong exponential convergence in relative entropy of the system to equilibrium under a condition of spatial mixing of the stationary Gibbs states and the rapid decay of the relative entropy on finite-size blocks. Our result leads to the first examples of the positivity of the modified logarithmic Sobolev inequality for quantum lattice spin systems independently of the system size. Moreover, we show that our notion of spatial mixing is a consequence of the recent quantum generalization of Dobrushin and Shlosman's complete analyticity of the free-energy at equilibrium. The latter typically holds above a critical temperature $T_c$. Our results have wide applications in quantum information processing. As an illustration, we discuss three of them: first, using techniques of quantum optimal transport, we show that a quantum annealer subject to a finite range classical noise will output an energy close to that of the fixed point after constant annealing time. Second, we prove a finite blocklength refinement of the quantum Stein lemma for the task of asymmetric discrimination of two Gibbs states of commuting Hamiltonians satisfying our conditions. In the same setting, our results imply the existence of a local quantum circuit of logarithmic depth to prepare Gibbs states of a class of commuting Hamiltonians.