We show that a self-correcting Gottesman-Kitaev-Preskill (GKP) qubit can be realized with a high-impedance L C circuit coupled to a resistor and a Josephson junction via a controllable switch. When activating the switch in a particular stepwise pattern, the resonator relaxes into a subspace of GKP states that encode a protected qubit. Under continued operation, the resistor dissipatively error corrects the qubit against bit flips and decoherence by absorbing noise-induced entropy. We show that this leads to an exponential enhancement of the coherence time ( T 1 and T 2 ), even in the presence of extrinsic noise, imperfect control, and device-parameter variations. We show that the qubit supports exponentially robust single-qubit Clifford gates, implemented via appropriate control of the switch, and readout and/or initialization via supercurrent measurement. The self-correcting properties of the qubit allow it to operate at approximately 1-K temperatures and resonator Q factors down to approximately 1000 for realistic parameters, and make it amenable to parallel control through global control signals. We discuss how the effects of quasiparticle poisoning—potentially, though not necessarily, a limiting factor—might be mitigated. We finally demonstrate that a related device supports a self-correcting magic T gate.We show that a self-correcting Gottesman-Kitaev-Preskill (GKP) qubit can be realized with a high-impedance L C circuit coupled to a resistor and a Josephson junction via a controllable switch. When activating the switch in a particular stepwise pattern, the resonator relaxes into a subspace of GKP states that encode a protected qubit. Under continued operation, the resistor dissipatively error corrects the qubit against bit flips and decoherence by absorbing noise-induced entropy. We show that this leads to an exponential enhancement of the coherence time ( T 1 and T 2 ), even in the presence of extrinsic noise, imperfect control, and device-parameter variations. We show that the qubit supports exponentially robust single-qubit Clifford gates, implemented via appropriate control of the switch, and readout and/or initialization via supercurrent measurement. The self-correcting properties of the qubit allow it to operate at approximately 1-K temperatures and resonator Q factors down to approximately 1000 for realistic parameters, and make it amenable to parallel control through global control signals. We discuss how the effects of quasiparticle poisoning—potentially, though not necessarily, a limiting factor—might be mitigated. We finally demonstrate that a related device supports a self-correcting magic T gate.

arXiv:2405.05671PRX QuantumJul 14, 20258 citations

A macroscopic qubit

Laura Fattaruso

Physics TodayJan 1, 20252 citations

Subsystem self-correction of the GKP qubit

Brian Chung Hang Cheung, Lasse Bjørn Kristensen, Frederik Nathan +1 more

Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories. In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian, manifested in the Arrhenius type scaling of the logical lifetime, from a quantum-information perspective based on the subsystem code decomposition. When coupling through the physical quadrature $q$ and $p$ , the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories. In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian, manifested in the Arrhenius type scaling of the logical lifetime, from a quantum-information perspective based on the subsystem code decomposition. When coupling through the physical quadrature $q$ and $p$, the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.

quant-pharXiv:2609.07702Sep 8, 20260 citations

One-qubit manipulations

Lajos Diósi

Springer eBooksFeb 18, 20071 citation

Self-correcting quantum teleportation protocol

Bayu Dwi Hatmoko, Muhammad Taufiqi, Agus Purwanto +2 more

In this work, we propose a self-correcting quantum teleportation protocol capable of transmitting a three-qubit Greenberger-Horne-Zeilinger-type (GHZ-type) state through a four-qubit quantum state in the presence of collective Bit-Flip Noise. We show that the protocol can self-correct the noise effect on the teleportation process, resulting in perfect state transfer with unit fidelity and probability. We also show that the proposed protocol has up to 33.3% lower quantum gate resource cost than a conventional combination of quantum error correction and teleportation protocols. Furthermore, we discuss the protocol’s generalization in teleporting [Formula: see text]-qubit GHZ-type state, with [Formula: see text] being any integer. Lastly, we simulate the proposed protocol under the noise in Qiskit and show that it can be implemented well.In this work, we propose a self-correcting quantum teleportation protocol capable of transmitting a three-qubit Greenberger-Horne-Zeilinger-type (GHZ-type) state through a four-qubit quantum state in the presence of collective Bit-Flip Noise. We show that the protocol can self-correct the noise effect on the teleportation process, resulting in perfect state transfer with unit fidelity and probability. We also show that the proposed protocol has up to 33.3% lower quantum gate resource cost than a conventional combination of quantum error correction and teleportation protocols. Furthermore, we discuss the protocol’s generalization in teleporting [Formula: see text]-qubit GHZ-type state, with [Formula: see text] being any integer. Lastly, we simulate the proposed protocol under the noise in Qiskit and show that it can be implemented well.

International Journal of Quantum InformationJul 30, 20250 citations

One-Qubit Manipulations

Lajos Diósi

Lecture notes in physicsJan 1, 20110 citations

q

and

p

, the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.