Low-overhead fault tolerance for transversal quantum algorithms

We will discuss experimental and theoretical progress towards large-scale error-corrected quantum computation. First, we report recent advances in quantum information processing using dynamically reconfigurable arrays of neutral atoms. Using this logical processor with various types of error-correcting codes, we demonstrate that we can improve logical two-qubit gates by increasing code distance, create logical GHZ states, and perform computationally complex quantum simulation of information scrambling. In performing such circuits, we observe that the performance can be substantially improved by accounting for error propagation during transversal logical entangling gates and decoding the logical qubits jointly. We find that by using this correlated decoding technique and correctly handling feedforward operations, the number of noisy syndrome extraction rounds in universal quantum computation can be reduced from O(d) to O(1), where d is the code distance. These techniques result in new theories of fault-tolerance and in practical reductions to the cost of large-scale computation by over an order of magnitude.