



@article {3359,
	title = {Fault-tolerant hyperbolic Floquet quantum error correcting codes},
	year = {2023},
	month = {9/18/2023},
	abstract = {<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>},
	url = {https://arxiv.org/abs/2309.10033},
	author = {Ali Fahimniya and Hossein Dehghani and Kishor Bharti and Sheryl Mathew and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Michael Gullans}
}
