Full-Permutation Dynamical Decoupling in Triple-Quantum-Dot Spin Qubits

Dynamical decoupling of spin qubits in silicon can increase fidelity and can be used to extract the frequency spectra of noise processes. We demonstrate a full-permutation dynamical decoupling technique that cyclically exchanges the spins in a triple-quantum-dot qubit. This sequence not only suppresses both low-frequency charge-noise-induced and magnetic-noise-induced errors; it also refocuses leakage errors to first order, which is particularly interesting for encoded exchange-only qubits. For a specific construction, which we call “NZ1y,” the qubit is isolated from error sources to such a degree that we measure a remarkable exchange pulse error of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mn>2.8</a:mn><a:mo>×</a:mo><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>5</a:mn></a:mrow></a:msup></a:math>. This sequence maintains a quantum state for roughly 18,000 exchange pulses, extending the qubit coherence from <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:msubsup><d:mi>T</d:mi><d:mn>2</d:mn><d:mo>∗</d:mo></d:msubsup><d:mo>=</d:mo><d:mn>2</d:mn><d:mspace width="0.2em"/><d:mtext>μ</d:mtext><d:mspace width="-0.5pt"/><d:mrow><d:mi mathvariant="normal">s</d:mi></d:mrow></d:math> to <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><j:msub><j:mi>T</j:mi><j:mn>2</j:mn></j:msub><j:mo>=</j:mo><j:mn>720</j:mn><j:mspace width="0.2em"/><j:mtext>μ</j:mtext><j:mspace width="-0.5pt"/><j:mrow><j:mi mathvariant="normal">s</j:mi></j:mrow></j:math>. We experimentally validate an error model that includes <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><p:mn>1</p:mn><p:mo>/</p:mo><p:mi>f</p:mi></p:math> charge noise and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><s:mn>1</s:mn><s:mo>/</s:mo><s:mi>f</s:mi></s:math> magnetic noise in two ways: by direct exchange-qubit simulation and by integration of the assumed noise spectra with derived filter functions, both of which reproduce the measured error and leakage with respect to a change of the repetition rate. Published by the American Physical Society 2024