Autoparametric Resonance Extending the Bit-Flip Time of a Cat Qubit up to 0.3 s
Antoine Marquet, Antoine Essig, Joachim Cohen, Nathanaël Cottet, Anil Murani, Emanuele Albertinale, Simon Dupouy, Audrey Bienfait, Théau Peronnin, S. Jezouin, R. Lescanne, Benjamin Huard
Abstract
Cat qubits, for which logical <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">|</a:mo><a:mn>0</a:mn><a:mo stretchy="false">⟩</a:mo></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo stretchy="false">|</e:mo><e:mn>1</e:mn><e:mo stretchy="false">⟩</e:mo></e:math> are coherent states <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mo stretchy="false">|</i:mo><i:mo>±</i:mo><i:mi>α</i:mi><i:mo stretchy="false">⟩</i:mo></i:math> of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo stretchy="false">|</m:mo><m:mi>α</m:mi><m:msup><m:mo stretchy="false">|</m:mo><m:mn>2</m:mn></m:msup></m:math>. A large two-photon dissipation rate <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>κ</q:mi><q:mn>2</q:mn></q:msub></q:math> ensures fast qubit manipulation and short error-correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here, we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump, and it reaches a rate <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>κ</s:mi><s:mn>2</s:mn></s:msub><s:mo>/</s:mo><s:mn>2</s:mn><s:mi>π</s:mi><s:mo>≈</s:mo><s:mn>2</s:mn><s:mtext> </s:mtext><s:mtext> </s:mtext><s:mi>MHz</s:mi></s:math>. With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. In addition, we illustrate how the phase of a quantum superposition between <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mo stretchy="false">|</u:mo><u:mi>α</u:mi><u:mo stretchy="false">⟩</u:mo></u:math> and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mo stretchy="false">|</y:mo><y:mo>−</y:mo><y:mi>α</y:mi><y:mo stretchy="false">⟩</y:mo></y:math> can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active. Published by the American Physical Society 2024