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Nondegenerate Noise-Resilient Superconducting Qubit

Max Hays1,*, Junghyun Kim1,2, and William D. Oliver1,2,3

  • *Contact author: maxhays@mit.edu
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PRX Quantum 6, 040321 – Published 30 October, 2025

DOI: https://doi.org/10.1103/dd96-gcb6

Abstract

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation EJ1cosφ and EJ2cos2φ. By constructing a circuit such that EJ2 is negative and |EJ1|≪|EJ2|, 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.

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Popular Summary

Superconducting circuits are among the most promising building blocks for quantum computers. Yet today’s leading designs—transmons and fluxoniums—still suffer from environmental noise that causes qubits to lose information. A central challenge is creating qubits that are naturally protected from both “bit-flip” errors (where a 0 turns into a 1) and “phase-flip” errors (where the coherence of a superposition is lost).

We introduce a new qubit design, which we call the “harmonium,” that tackles this challenge by carefully engineering the quantum energy landscape of the circuit. Instead of relying on a single periodic potential, harmonium combines two different “harmonics” of the Josephson energy, corresponding to tunneling of Cooper pairs one-by-one and two-by-two, respectively. Together, these harmonics produce two stable, nondegenerate wells. The quantum states of the qubit are confined to separate wells, which suppresses bit-flip errors, while a symmetry between the wells suppresses phase-flip errors.

Our simulations show that harmonium can support single- and two-qubit gate operations in roughly 100 ns, approaching the operation speed of today’s fastest superconducting qubits. More importantly, we predict error rates orders of magnitude lower: bit-flip times of seconds and dephasing times of tens of milliseconds, well beyond current devices. Heating into unwanted higher states remains possible, but these events can be flagged and corrected as “erasure errors” using standard readout techniques.

In short, harmonium offers a realistic path to superconducting qubits with intrinsic noise protection—an important step toward building large-scale, fault-tolerant quantum computers.

Article Text

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PRX Quantum 6, 040321– Published 30 October, 2025
  • Received 14 April 2025
  • Revised 25 July 2025
  • Accepted 9 September 2025
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