Noisy Intermediate Scale Quantum (NISQ) devices have been proposed as a versatile tool for simulating open quantum systems. Recently, the use of NISQ devices as simulators for non-Markovian open quantum systems has helped verify the current descriptions of non-Markovianity in quantum physics. In this work, convex mixtures of channels are simulated using NISQ devices and classified as either Markovian or non-Markovian using the CP-divisibility criteria. Two cases are considered: two Markovian channels being convexly mixed to form a non-Markovian channel and vice versa. This work replicates the experiments performed in a linear optical setup, using NISQ devices, with the addition of a convex mixture of non-Markovian channels that was designed to address some of the problems faced in the experiments performed in the linear optical setup. The NISQ devices used were provided by the IBM Quantum Experience (IBM QE). The results obtained show that, using NISQ devices and within some error, convex mixtures of Markovian channels lead to a non-Markovian channel and vice versa.
Noisy Intermediate Scale Quantum (NISQ) devices have been proposed as a versatile tool for simulating open quantum systems. Recently, the use of NISQ devices as simulators for non-Markovian open quantum systems has helped verify the current descriptions of non-Markovianity in quantum physics. In this work, convex mixtures of channels are simulated using NISQ devices and classified as either Markovian or non-Markovian using the CP-divisibility criteria. Two cases are considered: two Markovian channels being convexly mixed to form a non-Markovian channel and vice versa. This work replicates the experiments performed in a linear optical setup, using NISQ devices, with the addition of a convex mixture of non-Markovian channels that was designed to address some of the problems faced in the experiments performed in the linear optical setup. The NISQ devices used were provided by the IBM Quantum Experience (IBM QE). The results obtained show that, using NISQ devices and within some error, convex mixtures of Markovian channels lead to a non-Markovian channel and vice versa.
Abstract Quantum algorithms for simulating quantum systems provide a clear and provable advantage over classical algorithms in fault-tolerant settings. There is also interest in quantum algorithms and their implementation in Noisy Intermediate Scale Quantum (NISQ) settings. In these settings, various noise sources and errors must be accounted for when executing any experiments. Recently, NISQ devices have been verified as versatile testbeds for simulating open quantum systems and have been used to simulate simple quantum channels. Our goal is to solve the more complicated problem of simulating convex mixtures of single qubit Pauli channels on NISQ devices. We consider two specific cases: mixtures of Markovian channels that result in a non-Markovian channel (M + M = nM) and mixtures of non-Markovian channels that result in a Markovian channel (nM + nM = M). For the first case, we consider mixtures of Markovian single qubit Pauli channels; for the second case, we consider mixtures of Non-Markovian single qubit depolarising channels, which is a special case of the single qubit Pauli channel. We show that efficient circuits, which account for the topology of currently available devices and current levels of decoherence, can be constructed by heuristic approaches that reduce the number of CNOT gates used in our circuit. We also present a strategy for regularising the process matrix so that the process tomography yields a completely positive and trace-preserving (CPTP) channel. Key points This work simulates the convex mixtures of single qubit Markovian and non-Markovian quantum channels on NISQ devices provided by the IMBQE. The circuits used to implement the channels take into account the topolgy of the quantum device used as well as the number of CNOT gates used. We present a strategy for regularising the process matrix to ensure the quantum process tomography yields a CPTP channel. Something that is not correctly implemented in Qiskit. A method is outlined for finding mixtures of non-Markovian depolarising channels that yield a Markovian depolarising channel. It is also shown that, one cannot convexly mix two Markovian depolarising channels that leads to a non-Markovian depolarising channel.
The study of memory effects in quantum channels helps in developing characterization methods for open quantum systems and strategies for quantum error correction. Two main sets of channels exist, corresponding to system dynamics with no memory (Markovian) and with memory (non-Markovian). Interestingly, these sets have a nonconvex geometry, allowing one to form a channel with memory from the addition of memoryless channels and vice versa. Here, we experimentally investigate this nonconvexity in a photonic setup by subjecting a single qubit to a convex combination of Markovian and non-Markovian channels. We use both divisibility and distinguishability as criteria for the classification of memory effects, with associated measures. Our results highlight some practical considerations that may need to be taken into account when using memory criteria to study system dynamics given by the addition of Markovian and non-Markovian channels in experiments.
Abstract The advent of noisy intermediate-scale quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. Here, we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum systems theory. During the last decade an increasing number of experiments have successfully tackled the task of simulating open quantum systems in different platforms, from linear optics to trapped ions, from nuclear magnetic resonance (NMR) to cavity quantum electrodynamics. Generally, each individual experiment demonstrates a specific open quantum system model, or at most a specific class. Our main result is to prove the great versatility of the IBM Q Experience processors. Indeed, we experimentally implement one and two-qubit open quantum systems, both unital and non-unital dynamics, Markovian and non-Markovian evolutions. Moreover, we realise proof-of-principle reservoir engineering for entangled state generation, demonstrate collisional models, and verify revivals of quantum channel capacity and extractable work, caused by memory effects. All these results are obtained using IBM Q Experience processors publicly available and remotely accessible online.
The advent of noisy intermediate-scale quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics.NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe.Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems.Here, we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum systems theory.During the last decade an increasing number of experiments have successfully tackled the task of simulating open quantum systems in different platforms, from linear optics to trapped ions, from nuclear magnetic resonance (NMR) to cavity quantum electrodynamics.Generally, each individual experiment demonstrates a specific open quantum system model, or at most a specific class.Our main result is to prove the great versatility of the IBM Q Experience processors.Indeed, we experimentally implement one and two-qubit open quantum systems, both unital and non-unital dynamics, Markovian and non-Markovian evolutions.Moreover, we realise proof-of-principle reservoir engineering for entangled state generation, demonstrate collisional models, and verify revivals of quantum channel capacity and extractable work, caused by memory effects.All these results are obtained using IBM Q Experience processors publicly available and remotely accessible online.
This experimental study aims to investigate the convex combinations of Pauli semigroups with arbitrary mixing parameters to determine whether the resulting dynamical map exhibits Markovian or non-Markovian behavior. Specifically, we consider the cases of equal as well as unequal mixing of two Pauli semigroups, and demonstrate that the resulting map is always non-Markovian. Additionally, we study three cases of three-way mixing of the three Pauli semigroups and determine the Markovianity or non-Markovianity of the resulting maps by experimentally determining the decay rates. To simulate the nonunitary dynamics of a single-qubit system with different mixing combinations of Pauli semigroups on an NMR quantum processor, we use an algorithm involving two ancillary qubits. The experimental results align with the theoretical predictions.
Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems. The circuits use ancilla qubits to simulate the environment, and memory effects are induced by storing information about the system on extra qubits. We simulate the amplitude damping channel and dephasing channel as examples of the framework and infer (Non-)Markovianity from the (non-)monotonic behaviour of the dynamics. Further, we develop a method to optimize simulations by decomposing complex open quantum dynamics into smaller parts, that can be simulated using a small number of qubits. We show that this optimization reduces quantum space complexity from O(l) to O(1) for simulating the environment.