



@article {3362,
	title = {Quantum Lego Expansion Pack: Enumerators from Tensor Networks},
	year = {2023},
	month = {8/9/2023},
	abstract = {<p>We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. As a corollary, if a quantum code has a known tensor network construction of its encoding map, our method produces an algorithm that computes its distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can provide up to an exponential speed up compared to the current methods. We also introduce a few novel applications of different weight enumerators. In particular, for any code built from the quantum lego method, we use enumerators to construct its (optimal) decoders under any i.i.d. single qubit or qudit error channels and discuss their applications for computing logical error rates. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the 2d Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force.</p>},
	url = {https://arxiv.org/abs/2308.05152},
	author = {ChunJun Cao and Michael Gullans and Brad Lackey and Zitao Wang}
}
@article {2873,
	title = {Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks},
	journal = {PRX Quantum},
	volume = {3},
	year = {2022},
	month = {05/11/2022},
	pages = {020332},
	abstract = {<p>We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as non-stabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding/encoding circuit. To highlight the framework\&$\#$39;s range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a 3d stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the 2d Bacon-Shor code after \&quot;dualizing\&quot; its tensor network encoding map.</p>},
	doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.020332},
	url = {https://arxiv.org/abs/2109.08158},
	author = {ChunJun Cao and Brad Lackey}
}
