Simultaneous sweet-spot locking of gradiometric fluxonium qubits

Efforts to scale up superconducting processors that employ flux qubits face numerous challenges, among which is the crosstalk created by neighboring flux lines, which are necessary to bias the qubits at the zero-field and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi mathvariant="normal">Φ</a:mi> <a:mn>0</a:mn> </a:msub> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:math> sweet spots. A solution to this problem is to use symmetric gradiometric loops, which incorporate a flux-locking mechanism that, once a fluxon is trapped during cooldown, holds the device at the sweet spot and limits the need for active biasing. We demonstrate this technique by simultaneously locking multiple gradiometric fluxonium qubits in which an aluminum loop retains the trapped fluxon indefinitely. By compensating the inductive asymmetry between the two loops of the design, we are able to lock the effective flux bias within <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi mathvariant="normal">Φ</d:mi> <d:mi>eff</d:mi> </d:msub> <d:mo>=</d:mo> <d:mrow> <d:mo>−</d:mo> <d:mn>3</d:mn> </d:mrow> <d:mo>×</d:mo> <d:msup> <d:mn>10</d:mn> <d:mrow> <d:mo>−</d:mo> <d:mn>4</d:mn> </d:mrow> </d:msup> <d:mrow/> <d:mspace width="0.1em"/> <d:msub> <d:mi mathvariant="normal">Φ</d:mi> <d:mn>0</d:mn> </d:msub> </d:math> from the target, corresponding to only <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>15</i:mn> <i:mrow> <i:mi mathvariant="normal">%</i:mi> </i:mrow> </i:math> degradation in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>T</l:mi> <l:mrow> <l:mn>2</l:mn> <l:mo>,</l:mo> <l:mi>E</l:mi> </l:mrow> </l:msub> </l:math> when operated in zero external field. The design strategy demonstrated here reduces integration complexity for flux qubits by minimizing crosstalk and potentially eliminating the need for local flux bias.