A Qudit-native Framework for Discrete Time Crystals

Abstract

We introduce a qudit-native framework for engineering robust discrete time crystals (DTCs) by leveraging their internal multilevel structure. Our approach confines the periodic drive to specified on-site subspaces, creating an embedded kick that suppresses heating by preventing population leakage to inactive levels. We underpin DTC stability with a normal-form analysis that decomposes the effective dynamics into distinct components: the carrier locks the subharmonic frequency, neutral terms govern the slow decay and dephasing of the subharmonic response, and charged terms scatter spectral weight away from the locked modes. This framework's predictive power is demonstrated across various qudit platforms: in spin-1 chains, we enhance the stability of DTC by confining the drive to a subspace; in spin-3/2 systems, we show that robustness is dictated by the symmetry of the subspace partition; and in spin-2 platforms, we realize concurrent 2T and 3T DTCs under a unified drive. These findings establish a systematic, hardware-efficient methodology for designing stable and multifunctional Floquet phases of matter on modern qudit-based quantum processors.

Figures (5)

• Figure 1: (a) Qudit Floquet architecture. Each period factors as $Ke^{-iH_z}$: a diagonal phase layer generated by disordered on-site $Z_i$ fields and disordered nearest-neighbor $Z_i Z_{i+1}$ couplings, followed by a site-factorized kick $K$ that reshuffles populations. (b) Global-kick realization of a $2T$ DTC in a $d$-level system via a single rotation with angle $\pi$ acting on the full on-site multiplet. (c) Embedded-kick realization confined to an active subspace (e.g., the doublet $\ket{0},\ket{d-1}$), leaving the complement inert. For a $2T$ DTC, the kick is compiled from a short sequence of two-level rotations within the active block.
• Figure 2: Resistance to thermalization in spin-1 chains ($N=8$). (Left) Average adjacent-gap ratio $\langle r \rangle$ versus drive imperfection $\varepsilon$. Embedded 2T and 3T drives (lower curves) remain pinned to the Poisson value ($\approx 0.39$), indicating that the effective Hamiltonian remains localized or integrable-like. In contrast, global drives (upper curves) flow toward the GOE limit ($\approx 0.53$), marking the onset of many-body chaos. (Right) Level spacing distributions $P(s)$. While global drives (left column) develop Wigner-Dyson level repulsion at high $\varepsilon$, embedded drives (right column) retain Poissonian statistics across the full range of errors, confirming that subspace selectivity effectively suppresses sector mixing.
• Figure 3: Robustness of spin-1 DTCs ($N{=}14$). (a) Subharmonic weight $C_m$ vs. imperfection $\varepsilon$. The embedded 2T protocol (squares) yields a broad plateau, whereas the global 2T drive (circles) decays rapidly due to leakage into the idle $\ket{1}$ state. For 3T, the embedded cycle (diamonds) produces a stable response, while the global drive (triangles) fails to maintain order due to basis mixing. (b) Comparison with a qubit baseline. The embedded 2T data tracks the response of an ideal qubit system mapped to the $\{\ket{0}, \ket{2}\}$ subspace, confirming that the protocol successfully hides the extra dimension. The global drive deviates significantly, highlighting the detrimental cost of unselective addressing.
• Figure 4: $d=4$ embedded protocols splitting the four-level space into two independent doublets ($N=10$). Left: symmetric partition $\{0,3\}\oplus\{1,2\}$: broad near-unity $C_2$ plateau. Contiguous partition $\{0,1\}\oplus\{2,3\}$: less stability and the subharmonic weight drops for smaller $\varepsilon$. Right: corresponding Fourier spectra at various $\varepsilon$, the contiguous partition exhibits significant broadening and lower peak with increasing imperfection.
• Figure 5: Mixed trimer-doublet protocol on $N=10$ and $d=5$ qudits. Dynamics and Fourier spectra of $M_z$ show single-line locking at $1/3$ (for trimer-only preparations) or $1/2$ (for doublet-only preparations), and concurrent $1/3$ and $1/2$ components for initial states of cross-block superpositions, with relative weights determined by the initial support.