2025/05/08 by Andreas Bauer, Julio C. Magdalena de la Fuente, Bauer, Andreas +2 · 5 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Quantum-Dot Cellular Automata
paper · pdf · doi:10.1103/p7c9-x1m9
We introduce a family of scalable planar fault-tolerant circuits that implement logical non-Clifford operations on a 2D color code, such as a logical <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>T</a:mi> </a:math> gate or a logical non-Pauli measurement that prepares a magic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mrow> <c:mo stretchy="false">|</c:mo> </c:mrow> <c:mi>T</c:mi> <c:mo fence="false" stretchy="false">⟩</c:mo> </c:mrow> </c:math> state. The circuits are relatively simple, consisting only of physical <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>T</h:mi> </h:math> gates, <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>C</j:mi> <j:mi>X</j:mi> </j:math> gates, and few-qubit measurements. They can be implemented with an array of qubits on a 2D chip with nearest-neighbor couplings and no wire crossings. The construction is based on a spacetime path integral representation of a non-Abelian 2+1D topological phase, which is related to the 3D color code. We turn the path integral into a circuit by expressing it as a spacetime <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>Z</l:mi> <l:mi>X</l:mi> </l:math> tensor network and then traversing it in some chosen time direction. We describe in detail how fault tolerance is achieved using a “just-in-time” decoding strategy, for which we repurpose and extend state-of-the-art color-code matching decoders.