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arXiv:2602.20269

Dissipative Time Crystals as Passively Protected Oscillating Qubits

Mert Esencan, A. I. Lvovsky, Berislav Buča

quant-phSubmitted Feb 23, 2026• Announced Feb 25, 2026• 0 citations• Revised Oct 22, 2026 (v2)
v1 · Feb 23, 2026v2 · Oct 22, 2026
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Abstract

Passive error correction schemes have so far been limited to static memories rather than dynamical qubits. We demonstrate that a driven-dissipative bosonic system, the Bose-Hubbard dimer (BHD), can encode a persistently oscillating qubit within a dynamical noiseless subsystem (DNS). The strong parity symmetry of the system leads to degenerate stationary states, whose mutual coherence breaks the time translation symmetry, giving rise to a time crystal in the thermodynamic limit. This time crystal undergoes a dissipative phase transition controlled by the driving force, with the DNS present above the transition point. This noiseless subsystem, and hence the qubit, is resilient to collective loss and at most quadratically affected when the strong symmetry condition is weakened. The decoherence from collective dephasing also cancels in the leading order, with the cancellation being exact at a specific drive strength, set by the photon-number difference between the two logical states. Tuning the drive extends this cancellation to unbalanced dephasing. These results establish dissipative time crystals as a medium for autonomously stabilized oscillating qubits.

Comments
9 pages (including End Matter), 8 figures. Supplemental Material (22 pages) included

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Passive error correction schemes have so far been limited to static memories rather than dynamical qubits. We demonstrate that a driven-dissipative bosonic system, the Bose-Hubbard dimer (BHD), can encode a persistently oscillating qubit within a dynamical noiseless subsystem (DNS). The strong parity symmetry of the system leads to degenerate stationary states, whose mutual coherence breaks the time translation symmetry, giving rise to a time crystal in the thermodynamic limit. This time crystal undergoes a dissipative phase transition controlled by the driving force, with the DNS present above the transition point. This noiseless subsystem, and hence the qubit, is resilient to collective loss and at most quadratically affected when the strong symmetry condition is weakened. The decoherence from collective dephasing also cancels in the leading order, with the cancellation being exact at a specific drive strength, set by the photon-number difference between the two logical states. Tuning the drive extends this cancellation to unbalanced dephasing. These results establish dissipative time crystals as a medium for autonomously stabilized oscillating qubits.
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Dissipative time crystals can appear in spin systems, when the Z2{Z}_{2}Z2​ symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator S2{S}^{2}S2 is conserved. In this paper, we relax the latter condition and show that time-translation-symmetry-breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an ad hoc Lindbladian using power-law-decaying spin operators and show that time-translation-symmetry breaking appears when the decay exponent obeys $0<\ensuremath{\eta}\ensuremath{\le}1$. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation. We prove that this approximation is quantitatively accurate, when $0<\ensuremath{\eta}<1$ and the thermodynamic limit is taken, because the system does not develop sizable quantum fluctuations, if the Gaussian approximation is considered.
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We investigate an unconventional symmetry in time-periodically driven systems, the Floquet dynamical symmetry (FDS). Unlike the usual symmetries, the FDS gives symmetry sectors that are equidistant in the Floquet spectrum and protects quantum coherence between them from dissipation and dephasing, leading to two kinds of time crystals: the discrete time crystal and discrete time quasicrystal that have different periodicity in time. We show that these time crystals appear in the Bose- and Fermi-Hubbard models under ac fields and their periodicity can be tuned only by adjusting the strength of the field. These time crystals arise only from the FDS and thus appear in both dissipative and isolated systems and in the presence of disorder as long as the FDS is respected. We discuss their experimental realizations in cold atom experiments and generalization to the SU(N)-symmetric Hubbard models.
We elucidate the role that the dissipation in a bosonic channel plays in the prevalence and stability of time crystals (TCs) in a periodically driven spin-boson system described by the Dicke model. Here, the bosons are represented by photons, and they mediate the infinite-range interactions between the spin systems. For strong dissipation, we study the dynamics using an effective atom-only description and the closed Lipkin-Meshkov-Glick model. By mapping out the phase diagrams for varying dissipation strengths, ranging from zero to infinitely strong, we demonstrate that the area in the phase diagram, where a TC exists, grows with the dissipation strength but only up to an optimal point, beyond which most of the TCs become unstable. We find TCs in both closed-system and dissipative regimes, but dissipative TCs are shown to be more robust against random noise in the drive and are only weakly affected by the choice of initial state. We present the finite-sized behavior and the scaling of the lifetime of the TCs with respect to the number of spins and the interaction strength within a fully quantum mechanical description.