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.
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.
Hamiltonian dynamics have been widely implemented on noisy intermediate-scale quantum devices in recent years. In contrast, experimental demonstrations of Markovian quantum dynamics remain limited, because implementing nonunitary evolution on quantum computers is challenging. Quantum collision models provide a natural approach to this problem by coupling the system to ancillas to realize dissipation. However, previous implementations of quantum collision models on quantum computers have typically been restricted to one or two system qubits and fewer than 12 time steps, owing to noise, circuit depth, the overhead of ancilla reset, and limited qubit resources. In this work, we experimentally simulate Markovian quantum processes with local and nonlocal dissipation on both trapped-ion and superconducting quantum computers. By employing hardware-specific ancilla strategies, we realize simulations with up to seven system qubits, corresponding to 13 qubits in total, and 40 time steps. Our results demonstrate that, even for the same physical model, the optimal implementation strategy depends strongly on the hardware characteristics of the quantum computer.
A Markov assumption considers a physical system memoryless to simplify its dynamics. Whereas memory effect or the non-Markovian phenomenon is more general in nature. In the quantum regime, it is challenging to define or quantify the non-Markovianity because the measurement of a quantum system often interferes with it. We simulate the open quantum dynamics in a superconducting processor, then characterize and quantify the non-Markovian process. With the complete set of intervening projections and the final measurement of the qubit, a restricted process tensor can be determined to account for the qubit-environment interaction. We apply the process tensor to predict the quantum state with memory effect, yielding an average fidelity of $99.86\%\pm 1.1\unicode{x2030}$. We further derive the Choi state of the rest process conditioned on history operations and quantify the non-Markovianity with a clear operational interpretation.
A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.
The concept of non-Markovianity in open quantum systems is traditionally associated with the existence of information backflows from the environment to the system. Meanwhile, the mechanisms through which such backflows emerge are still a subject of debate. In this work, we use collision models to study memory effects in the dynamics of a qubit system in contact with a thermal bath made up of few ancillas, in which system-ancilla and ancilla-ancilla interactions are considered. In the single-ancilla limit case, we show that the system-bath information flow exhibits an interesting mixture of chaotic and regular oscillatory behavior, which depends on the interaction probabilities. In parallel, our results clearly indicate that the information backflows decrease when new ancillas are added to the bath, which sheds light on the nature of the Markovian to non-Markovian transition.
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or whether they might equally be modeled by a classical memory. In this contribution, we propose a criterion to test locally for a truly quantum memory. The approach is agnostic with respect to the environment, as it solely depends on the local dynamics of the system of interest. Experimental realizations are particularly easy, as only single-time measurements on the system itself have to be performed. We study memory in a variety of physically motivated examples, both for a time-discrete case, and for time-continuous dynamics. For the latter, we are able to provide an interesting class of non-Markovian master equations with classical memory that allows for a physically measurable quantum trajectory representation.
Quantum non-Markovianity represents memory during system dynamics, which is typically weakened by temperature. We study here the effects of environmental temperature on the non-Markovianity of an open quantum system by virtue of collision models. The environment is simulated by a chain of ancillary qubits that are prepared in thermal states with a finite temperature T. Two distinct non-Markovian mechanisms are considered via two types of collision models, one where the system S consecutively interacts with ancillas and a second where S collides only with an intermediate system ${S}^{\ensuremath{'}}$, which in turn interacts with the ancillas. We show that in both models the relation between non-Markovianity and temperature is nonmonotonic. In particular, revivals of non-Markovianity may occur as temperature increases. We find that the physical reason behind this behavior can be revealed by examining a peculiar system-environment coherence exchange, leading to ancillary qubit coherence larger than system coherence, which triggers information backflow from the environment to the system. These results provide insights into the mechanisms underlying the counterintuitive phenomenon of temperature-enhanced quantum memory effects.