Revealing the quantum nature of memory in non-Markovian dynamics on IBM Quantum

TL;DR

The paper addresses whether current quantum hardware can simulate non-Markovian dynamics with verifiably quantum memory. It combines collision-model simulations, ancilla-assisted tomography, and a map-based, concurrence-based witness to distinguish quantum memory from classical memory in both single- and two-qubit settings. The authors implement a non-Markovian amplitude-damping model on IBM Quantum and demonstrate quantum memory via the concurrence-based criteria, despite hardware noise, and extend the approach with a tractable toy model for the two-qubit case. This work shows that practical quantum memory witnesses are feasible on NISQ devices and highlights the potential for more advanced, multi-time characterizations like process-tensor tomography in future experiments. The methods provide a pathway to validate quantum memory as a resource in quantum simulations and open avenues for more complex open-system dynamics on near-term quantum computers.

Abstract

We investigate memory effects in non-Markovian dynamics on superconducting quantum processors provided by IBM Quantum. We use a collision-model approach to implement suitable single- and two-qubit dynamics with a gate-based quantum circuit. Coupling the system of interest to an ancilla allows for a characterization of the process with respect to non-Markovian memory effects in general, as well as concerning the quantumness of that memory. We demonstrate that current noisy quantum hardware is capable of verifying quantum memory in single-qubit dynamics. We then discuss why a generalization of this dynamics to the two-qubit case cannot directly be simulated in a way that allows quantum memory to be observed. Nevertheless, we present an alternative toy example that demonstrates how quantum memory of two-qubit dynamics can be witnessed using current noisy quantum computers.

Figures (7)

• Figure 1: Classification of quantum dynamics with respect to the absence or presence of memory (Markovian and non-Markovian) as well as the type of memory (quantum and classical).
• Figure 2: Time-discrete implementation of the dynamics described by Eq. \ref{['eq:nMadthLindblad']} according to Eq. \ref{['eq:coll_mod']}. All qubits are by default initialized in the $\vert{0}\rangle$ state. First, system and ancilla are prepared in a maximally entangled state and the environment is left in the $\vert{0}\rangle$-state. Then the unitary $U_{\delta}$ is applied to the system-environment state sequentially up to $N$ times, here we depict the circuit for $N=3$ collisions. Finally, quantum state tomography is performed on the system-ancilla state $\rho_{\mathcal{S} \mathcal{A}}^{(3)}$. The actual implementation of the Bell state as well as of the unitary $U_{\delta}$ in terms of the fundamental basis gates of the quantum hardware can be found in App. \ref{['sec:app-implementation']}.
• Figure 3: Concurrence of formation $\mathcal{C}$ and concurrence of assistance $\mathcal{C}^\sharp$ of the system-ancilla state under the system dynamics realized via the collision model as described in Eq. \ref{['eq:coll_mod']} where we chose $g \delta t=\pi/4$. The quantum simulation (subscript qs) was run on 2025/05/28 on the IBM Quantum computer ibm_sherbrooke with 4096 shots for each of the nine tomography settings in each circuit. The dashed curves corresponds to a local simulation (subscript ls) on fake_sherbrooke and the dot-dashed curve represents the analytical results without any additional noise or noise models (subscript t). The concurrence of assistance at $t_1$ (2 collisions) is lower than the concurrence of formation at $t_2$ (4 collisions) implying that the memory is necessarily quantum according to Eq. \ref{['eq:theorem']}. The error bars shown for those two points reflect the fluctuating performance of ibm_sherbrooke and have been obtained by collecting statistics for the corresponding circuits at different times within a period of two weeks. The average of several runs of $\mathcal{C}^\sharp$ and $\mathcal{C}$ for two and four collisions lies in the middle of the error bars while the curves themselves represent the average of only one example run per circuit under identical conditions.
• Figure 4: Lower bound of concurrence of assistance $\mathcal{C}_<^\sharp$ and upper bound of concurrence of formation $\mathcal{C}_>$ of the three-qubit system-ancilla state under the system dynamics described by the Hamiltonian from Eq. \ref{['eq:h_u_2qub']}. The quantum simulation was executed on 2025/05/19 on ibm_sherbrooke with 4096 shots for each of the 27 tomography settings in each circuit.
• Figure 5: Quantum circuit implemented for the purpose of witnessing quantum memory in a two-qubit dynamics. The system as well as the environment consist of two qubits each and system and ancilla are prepared in a maximally entangled state. We run this circuit both, until time $t_1$ and until time $t_2$ on ibm_sherbrooke on 2025/06/27 for 4096 shots for each of the 81 tomography settings and the two additional settings for readout-error mitigation. At time $t_2$ this model in theory returns to the initially entangled system-ancilla state by construction.