Nondegenerate Noise-Resilient Superconducting Qubit

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>E</a:mi> <a:mrow> <a:mi>J</a:mi> <a:mn>1</a:mn> </a:mrow> </a:msub> <a:mi>cos</a:mi> <a:mo></a:mo> <a:mi>φ</a:mi> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>E</c:mi> <c:mrow> <c:mi>J</c:mi> <c:mn>2</c:mn> </c:mrow> </c:msub> <c:mi>cos</c:mi> <c:mo></c:mo> <c:mn>2</c:mn> <c:mi>φ</c:mi> </c:math> . By constructing a circuit such that <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>E</e:mi> <e:mrow> <e:mi>J</e:mi> <e:mn>2</e:mn> </e:mrow> </e:msub> </e:math> is negative and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mo stretchy="false">|</g:mo> </g:mrow> <g:msub> <g:mi>E</g:mi> <g:mrow> <g:mi>J</g:mi> <g:mn>1</g:mn> </g:mrow> </g:msub> <g:mrow> <g:mo stretchy="false">|</g:mo> </g:mrow> <g:mo>≪</g:mo> <g:mrow> <g:mo stretchy="false">|</g:mo> </g:mrow> <g:msub> <g:mi>E</g:mi> <g:mrow> <g:mi>J</g:mi> <g:mn>2</g:mn> </g:mrow> </g:msub> <g:mrow> <g:mo stretchy="false">|</g:mo> </g:mrow> </g:math> , we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.