Dynamically Generated Logical Qubits
Matthew B. Hastings, Jeongwan Haah
Abstract
We present a quantum error correcting code with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext class="MJX-tex-mathit" mathvariant="italic">dynamically generated logical qubits</mml:mtext></mml:mrow></mml:math>. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, our measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Our particular code gives a model very similar to the two-dimensional toric code, but each measurement is a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi><mml:mi>w</mml:mi><mml:mi>o</mml:mi></mml:math>-qubit Pauli measurement.
Topics & Concepts
Computer scienceCode (set theory)QubitAlgorithmPauli matricesQuantum error correctionTheoretical computer scienceQuantumToric codeLogical conjunctionQuantum computerPauli exclusion principleError detection and correctionQuantum algorithmTruth tableArithmeticMathematicsQuantum informationQuantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum-Dot Cellular Automata