Accelerating qubit reset through the Mpemba effect

TL;DR

The paper tackles the slow passive reset of qubits by leveraging a quantum Mpemba effect in the regime $T_2 > T_1$. It shows that a single entangling gate with an incoherent ancilla can transfer local single-qubit coherences into fast-decaying global two-qubit coherences, effectively suppressing the slow Liouvillian mode and accelerating relaxation to the ground state. Theoretical analysis using Davies map and Markovian/non-Markovian models predicts an asymptotic speedup $S \to \frac{T_2}{T_1}$, corroborated by experimental demonstration on a superconducting processor achieving near-ideal speedups. The results indicate Mpemba-like accelerated relaxation is a practical tool for rapid qubit initialization, robust to finite temperature and moderate control imperfections, with potential extensions to broader dissipative tasks and other quantum platforms.

Abstract

Passive qubit reset is a key primitive for quantum information processing, whereby qubits are initialized by allowing them to relax to their ground state through natural dissipation, without the need for active control or feedback. However, passive reset occurs on timescales that are much longer than those of gate operations and measurements, making it a significant bottleneck for algorithmic execution. Here, we show that this limitation can be overcome by exploiting the Mpemba effect, originally indicating the faster cooling of hot systems compared to cooler ones. Focusing on the regime where coherence times exceed energy relaxation times ($T_2 > T_1$), we propose a simple protocol based on a single entangling two-qubit gate that converts local single-qubit coherences into fast-decaying global two-qubit coherences. This removes their overlap with the slowest decaying Liouvillian mode and enables a substantially faster relaxation to the ground state. For realistic parameters, we find that our protocol can reduce reset times by up to $50\%$ compared to standard passive reset. We analyze the robustness of the protocol under non-Markovian noise, imperfect coherent control and finite temperature, finding that the accelerated reset persists across a broad range of realistic error sources. Finally, we present an experimental implementation of our protocol on an IQM superconducting quantum processor. Our results demonstrate how Mpemba-like accelerated relaxation can be harnessed as a practical tool for fast and accurate qubit initialization.

Figures (9)

• Figure 1: Enhancing qubit reset via coherence delocalization. (a) In the regime $T_2 > T_1$, single-qubit coherences decay more slowly than populations, causing a coherent qubit $q_1$ (blue) to relax to the ground state more slowly than an incoherent qubit $q_2$ (red). (b) Applying an entangling two-qubit gate (e.g., CNOT or CRy$(\pi)$, see \ref{['sec:cnot:protocol']}) between $q_1$ and an incoherent ancilla converts local coherences of $q_1$ into global two-qubit coherences, which decay faster under local dissipation, thereby removing the slow relaxation bottleneck and accelerating the reset of $q_1$.
• Figure 2: Speeding up qubit reset in the presence of Markovian noise. Panel (a) and (b) show the Liouvillian spectra from \ref{['eq:2qubit:davies:map:T0:with:dephasing']}, along with the overlap $\langle\mspace{-3mu}\langle l_k | +0 \rangle\mspace{-3mu}\rangle$ between the initial state and the left eigenvectors before and after the application of the C-Ry gate, respectively. Panel (c) displays the asymptotic Mpemba speedup $|\mathrm{Re}(\lambda_3)|/|\mathrm{Re}(\lambda_2)|$ as a function of the $T_1$ and $T_2$ relaxation times. The red crosses represent the $T_1$ and $T_2$ values found in experimental setups. Finally, panel (d) shows the trace distance to the ground state as a function of time for $1000$ initial states, where the state of the system qubit $q_1$ is sampled from the Haar measure and the ancilla is initialized in the excited state ($p_2^1 = 1$). Results are shown with (red) and without (blue) application of the C-Ry gate. The inset shows the histogram of achieved speedups for $\epsilon=10^{-3}$ [see Eq. (\ref{['eq:speedup_gen']})].
• Figure 3: Markovian (a) and non-Markovian (b) descriptions of the system considered in \ref{['sec:non-markovian:case']}, where a flux-tunable transmon qubit of frequency $\omega_q$ is coupled, with strength $\nu_{zx}$, to a single TLS of frequency $\omega_t$. Both are subject to amplitude damping with rates $\Gamma_1$ and $\kappa$, respectively. Additionally, the qubit is subject to dephasing with a rate $\Gamma_\phi$/2. (a) Markovian description of the combined qubit-TLS system described by the Liouvillian $\mathcal{L}_{\mathrm{emb}}$ [Eq. (\ref{['eq:non-Markovian:model']})]. (b) Non-Markovian description of the qubit, where the damped TLS acts as a non-Markovian bath with finite memory time $1/\kappa$. The reduced dynamics of the qubit obtained after tracing out the TLS is well described by the Redfield Liouvillian $\mathcal{L}_{\mathrm{red}}$ [Eq. (\ref{['eq:reduced_liouv']})].
• Figure 4: (a) Spectra of the full Markovian embedding [Eq. (\ref{['eq:non-Markovian:model']})] (orange points) and of the reduced Liouvillian [Eq. (\ref{['eq:reduced_liouv']})] as a function of time (green lines) and for long times (green points). The lower plots show the time evolution of $\text{Re}(\lambda_2)$ as a function of time, with $\omega_q = 3.10^{5}$ Hz (left plot) and $3.10^{10}$ Hz (right plot), while $\kappa/\nu_{zx} = 0.05$. (b) Trace distance to the ground state of $1000$ two-qubit states as a function of time, where the system qubit $q_1$ is sampled from the Haar measure and the ancilla and the TLSs are initialized in their ground state. Results are shown with (red) and without (blue) application of the C-Ry gate. The inset shows the histogram of achieved speedups for $\epsilon=10^{-3}$. While $\kappa/\nu_{zx}$ is set to 0.05, $\omega_q$ and $\omega_t$ are set to small values to explicitly display the non-Markovian behavior (i.e., the oscillations), even though the speedups achieved are very similar for larger frequencies. We perform exponential fits following the curves' peaks, such that the speedup corresponds to the relative reduction of the time it takes the whole curve to cross the horizontal line defined by $\epsilon$.
• Figure 5: Comparison of the dynamics of the two-qubit state coherence [panel (a)] and purity [panel (b)], obtained from the Markovian embedding of \ref{['eq:non-Markovian:model']} (blue curves) and the reduced Redfield model of \ref{['eq:reduced_liouv']} (orange curves). Both are evaluated for $\omega_q = 10^5$ Hz (solid line) and $\omega_q = 10^7$ Hz (dashed line), while $\kappa/\nu_{zx} = 0.05$.