Emergent Discrete Time Crystals on Digital Quantum Computers: Boundary-Protected and Ancilla-Induced Disorder Mechanisms of Thermalization Slowdown

TL;DR

This work investigates Floquet prethermal dynamics and discrete time crystals on 2D Kagome and Lieb lattices implemented on IBM heavy-hex devices by using ancilla qubits to realize complex connectivity. It identifies two distinct DTC classes: type-I, boundary-protected DTCs stabilized by symmetry-charge pumping and robust to some quantum noise, and type-II, noise-induced DTCs that arise even without boundary pumping when ancilla noise is present. The authors combine error mitigation, ancilla-noise modeling, and noisy MPS simulations to reproduce experimental magnetization dynamics and OTOCs, revealing a boundary-localized, π-paired Floquet structure and a quantum-information blockade mechanism. The results highlight a novel role for quantum noise and ancilla qubits in engineering and observing exotic nonequilibrium phases on real quantum hardware, with potential implications for disorder- and topology-assisted dynamical control in higher dimensions.

Abstract

Periodically driven (Floquet) systems typically evolve toward an infinite-temperature thermal state due to continuous energy absorption. Before reaching equilibrium, however, they can transiently exhibit long-lived prethermal states that host exotic nonequilibrium phenomena, such as discrete time crystals (DTCs). In this study, we investigate the relaxation dynamics of periodically driven product states in a kicked Ising model implemented on the IBM Quantum Eagle and Heron processors. By using ancilla qubits to mediate interactions, we construct Kagome and Lieb lattices on superconducting qubits with heavy-hex connectivity. We identify two distinct types of noise-induced DTCs on Kagome and Lieb lattices, both arising from quantum noise in ancilla qubits. Type-I DTCs originate from robust boundary-mode period-doubling oscillations, stabilized by symmetry charge pumping, that are redistributed into the bulk due to ancilla noise. Type-II DTCs, in contrast, emerge in systems without charge-pumped qubits, where quantum noise unexpectedly stabilizes period-doubling oscillations that would otherwise rapidly decay. On the noisier Eagle device (ibm_kyiv), we observe both type-I and type-II DTCs on 53-qubit Kagome lattices with and without charge-pumped qubits, respectively. In contrast, on the lower-noise Heron device (ibm_marrakesh), period-doubling oscillations are confined to boundary-localized oscillations on 82-qubit Kagome and 40-qubit Lieb lattices, as redistribution into the bulk is suppressed. These experimental findings are supported by noisy matrix-product-state simulations, in which ancilla noise is modeled as random sign flips in the two-qubit gate rotation angles. Our results demonstrate that quantum noise in ancilla qubits can give rise to novel classes of prethermal dynamical phases, including boundary-protected and noise-induced DTCs.

Figures (24)

• Figure 1: Two-qubit gate connectivity and geometry of the Kagome82 lattice. (a) Kagome82 lattice constructed on the heavy-hex architecture of the ibm_marrakesh device with 156 qubits. White and black circles represent system qubits ($|i\rangle$ and $|j\rangle$) and ancilla qubits ($|a\rangle$), located at positions with coordination numbers two and three, respectively, on the heavy-hex lattice. The four layers of $\hat{R}_{Z_{i}Z_{j}}(\theta_{J})$ gates applied within a single Floquet cycle are colored red, blue, green, and yellow. (b) Geometry of the Kagome82 lattice showing only the system qubits, renumbered to define a one-dimensional path for MPS construction. Green circles indicate system qubits with coordination number three in the Kagome82 connectivity. Boundary qubits are located at sites 1, 2, 3, 4, 5, 6, 7, 10, 11, 17, 18, 21, 22, 28, 29, 32, 33, 39, 40, 43, 44, 50, 51, 54, 55, 61, 62, 65, 66, 72, 73, 76, 77, 78, 79, 80, 81, and 82. (c) Schematic representation of the single-cycle Floquet operator $\hat{U}_{\rm F}$. Red, blue, green, and yellow boxes correspond to the four layers of $\hat{R}_{Z_{i}Z_{j}}(\theta_{J})$ gates, applied in parallel as indicated in (a). White boxes represent the product of $\hat{R}_{X_i}$ gates. Horizontal lines correspond to qubits on which the gates act. Each $\hat{R}_{Z_{i}Z_{j}}(\theta_{J})$ gate acting on system qubits $i$ and $j$ is implemented in general using four CNOT gates along with a single-qubit $\hat{R}_{Z_{a}}(\theta_{J})$ gate acting on an ancilla qubit $|0_{a}\rangle$, or using three CNOT gates along with two phase gates $\hat{S}$ when $\theta_J=-\pi/2$.
• Figure 2: Two-qubit gate connectivity and geometry of the Lieb40 lattice. (a) The Lieb40 lattice constructed on the heavy-hex architecture of the ibm_marrakesh device with 156 qubits. White and black circles represent system qubits and ancilla qubits, located at positions with coordination numbers two and three, respectively, on the heavy-hex lattice. The four layers of $\hat{R}_{Z_{i}Z_{j}}(\theta_J)$ gates applied within a single Floquet cycle are colored red, blue, green, and yellow. (b) Geometry of the Lieb40 lattice showing only system qubits, renumbered to define a one-dimensional path used for MPS construction. Green circles indicate system qubits with coordination number three in the Lieb40 connectivity. Boundary qubits are located at sites 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 18, 19, 22, 23, 29, 30, 33, 34, 35, 36, 37, 38, 39, and 40.
• Figure 3: Error-mitigated dynamics of the magnetization $\langle \hat{Z}_{\rm avg}(t) \rangle$ on the Kagome82 lattice, realized on the ibm_marrakesh device. (a)--(c) Raw experimental data for the magnetization $\langle \hat{Z}_{\rm avg}(t) \rangle_{0}$ (blue circles), alongside $f(\theta_x=\pi)=|\langle \hat{Z}_{\rm avg}(t) \rangle_{0,\theta_x=\pi}|$ (black crosses). Error-mitigated results obtained via Eq. (\ref{['eq-norm']}) are shown as red diamonds. (d)--(f) Comparison of error-mitigated experimental data (red diamonds) with noiseless ($p=0$) MPS simulations using bond dimensions $\chi=300$ (brown crosses) and $\chi=600$ (blue squares). The transverse field parameters are: (a, d) $\theta_{x}=0.95\pi$, (b, e) $\theta_{x}=0.9\pi$, and (c, f) $\theta_{x}=0.85\pi$. Each $\hat{R}_{Z_{i}Z_{j}}$ gate is implemented using $M_\text{CNOT}=3$ native two-qubit gates (i.e., CNOT gates) in (a)--(c).
• Figure 4: Effect of quantum noise in ancilla qubits on the magnetization dynamics of the kicked Ising model on the Kagome82 lattice, realized on the ibm_marrakesh device. (a, b) Comparison between error-mitigated experimental data (red diamonds) and noisy MPS simulations with a noise parameter $p=0.02$, using bond dimensions $\chi=300$ (brown crosses) and $\chi=600$ (blue squares). (c, d) Magnetization averaged over all ancilla qubits, $\langle \hat{Z}_\text{ancilla}(t) \rangle$ (green diamonds), along with an exponential fitting curve $\eta^{t/T}$ (black line). These are raw experimental data without error mitigation. The transverse field parameters are: (a, c) $\theta_{x}=0.9\pi$ and (b, d) $\theta_{x}=0.85\pi$.
• Figure 5: Time evolution of magnetization in the kicked Ising model with $\theta_{x}=0.9\pi$ on the Kagome82 lattice. (a) Snapshots of error-mitigated local magnetization $\langle \hat{Z}_{j}(t) \rangle$ at $t/T=0$, 10, 20, and 30, measured on ibm_marrakesh. (b) Corresponding results obtained from MPS simulations with $p=0.02$ and bond dimension $\chi=600$. (c) Error-mitigated magnetization averaged over the boundary qubits $\langle \hat{Z}_\text{boundary}(t) \rangle$ (green diamonds) and over the bulk qubits $\langle \hat{Z}_\text{bulk}(t) \rangle$ (purple circles), measured on ibm_marrakesh. The locations of the boundary qubits are indicated in Fig. \ref{['fig:geometry_Kagome82']}(b), while the bulk consists of all interior system qubits excluding those at the boundary. (d) Same as (c), but from noisy MPS simulations with $p=0.02$ and $\chi=600$.