



02121nas a2200181   4500008004100000245006900041210006800110260001400178520156100192100001901753700002201772700001901794700001901813700002401832700002501856700002101881856003701902       2023                        eng d00aFault-tolerant hyperbolic Floquet quantum error correcting codes0 aFaulttolerant hyperbolic Floquet quantum error correcting codes  c9/18/20233 a<p>A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call &quot;hyperbolic Floquet codes.&quot; These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in n. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a [[400,52,8]] code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.</p>1 aFahimniya, Ali1 aDehghani, Hossein1 aBharti, Kishor1 aMathew, Sheryl1 aKollár, Alicia, J.1 aGorshkov, Alexey, V.1 aGullans, Michael  uhttps://arxiv.org/abs/2309.10033