Frederik Nathan

Self-correcting GKP qubit in a superconducting circuit with an oscillating voltage bias

  1. Max Geier,
  2. and Frederik Nathan
We propose a simple circuit architecture for a dissipatively error corrected Gottesman-Kitaev-Preskill (GKP) qubit. The device consists of a electromagnetic resonator with impedance
h/2e2≈12.91kΩ connected to a Josephson junction with a voltage bias oscillating at twice the resonator frequency. For large drive amplitudes, the circuit is effectively described by the GKP stabilizer Hamiltonian, whose low-energy subspace forms the code space for a qubit protected against phase-space local noise. The GKP states in the codespace can be dissipatively stabilized and error corrected by coupling the resonator to a bath through a bandpass filter; a resulting side-band cooling effect stabilizes the system in the GKP code space, dissipatively correcting it against both bit and phase flip errors. Simulations show that this dissipative error correction can enhance coherence time by factor ∼1000 with NbN-based junctions, for operating temperatures in the ∼100mK range. The scheme can be used to stabilize both square- and hexagonal-lattice GKP codes. Finally, a Josephson current based readout scheme, and dissipatively corrected single-qubit Clifford gates are proposed.
arxiv pdf

Self-correcting GKP qubit and gates in a driven-dissipative circuit

  1. Frederik Nathan,
  2. Liam O'Brien,
  3. Kyungjoo Noh,
  4. Matthew H. Matheny,
  5. Arne L. Grimsmo,
  6. Liang Jiang,
  7. and Gil Refael
We propose a circuit architecture for a dissipatively error-corrected GKP qubit. The device consists of a high-impedance LC circuit coupled to a Josephson junction and a resistor
via a controllable switch. When the switch is activated via a particular family of stepwise protocols, the resistor absorbs all noise-induced entropy, resulting in dissipative error correction of both phase and amplitude errors. This leads to an exponential increase of qubit lifetime, reaching beyond 10ms in simulations with near-feasible parameters. We show that the lifetime remains exponentially long in the presence of extrinsic noise and device/control imperfections (e.g., due to parasitics and finite control bandwidth) under specific thresholds. In this regime, lifetime is likely only limited by phase slips and quasiparticle tunneling. We show that the qubit can be read out and initialized via measurement of the supercurrent in the Josephson junction. We finally show that the qubit supports native self-correcting single-qubit Clifford gates, where dissipative error-correction of control noise leads to exponential suppression of gate infidelity.
arxiv pdf