Simulating open quantum systems on digital quantum computers typically relies on the use of auxiliary qubits, resulting in overheads of noisy multi-qubit gates, that severely limit execution on near-term hardware. In this work, we explore the simulation of non-Markovian dynamics as well as memory channels leveraging the method of trajectory mixing, valid for mixed unitary channels. This allows to drastically reduce circuit depth, trading entangling gates for a statistical mixture of independent, pure state trajectories. Using a realistic noise model calibrated to modern quantum processors, we show the benefits of this approach, yielding higher state fidelity and better preservation of quantum correlations. This shows the possibility of simulating long-time non-Markovian evolutions with low noise and limited resources.
Simulating open quantum systems on digital quantum computers typically relies on the use of auxiliary qubits, resulting in overheads of noisy multi-qubit gates, that severely limit execution on near-term hardware. In this work, we explore the simulation of non-Markovian dynamics as well as memory channels leveraging the method of trajectory mixing, valid for mixed unitary channels. This allows to drastically reduce circuit depth, trading entangling gates for a statistical mixture of independent, pure state trajectories. Using a realistic noise model calibrated to modern quantum processors, we show the benefits of this approach, yielding higher state fidelity and better preservation of quantum correlations. This shows the possibility of simulating long-time non-Markovian evolutions with low noise and limited resources.
The advent of noisy intermediate-scale quantum (NISQ) devices has not only opened up new possibilities to studying quantum computational benefits, but it has also presented new challenges associated with noise and short coherence times. Entanglement is one of the inherent resources that can be used to perform quantum computation and implement the performance and reliability of quantum algorithms. This paper looks at entanglement dynamics in NISQ machines subjected to natural noises. The study focuses on the problem of examining the role of various noise channels in the creation, dynamics, and decay of the entanglement during quantum operations, such as depolarizing, amplitude damping, and phase damping. The study is based on theoretical modeling and numerical simulations of multi-qubit quantum circuits to determine the stability of entangled states with respect to circuit depth and intensity of noise. Concurrence and von Neumann entropy are examples of entanglement measures that are used to characterize correlations between qubits as well as to trace the dynamics of these correlations across computational interactions. The results show that noise has major impacts on entanglement distribution, which tends to cause rapid decays in highly entangled states with increase in circuit complexity. The findings, however, also show that there are some circuit architectures and error-mitigation schemes that can somewhat sustain entanglement with moderate levels of noise. The paper also emphasizes the relevance of minimalizing sequence of gates, and reduced circuit depth in an effort to preserve useful entanglement in present-day quantum hardware. These observations help in understanding the behaviour of quantum correlations better in real world quantum devices and provide a way of developing more resilient quantum algorithms that would work on NISQ systems. In general, the article offers a systematic view on entanglement behavior in disordered quantum systems and highlights its value in the development of quantum computing applications in the near term.
Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum XY model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.
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.
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.
Abstract Digital quantum simulation of open quantum systems has produced a range of methods for reproducing non-Markovian dynamics, including pseudomode embeddings, the hierarchical equations of motion, and collision models. These methods are validated against populations, coherences, or spectra. They are not validated against the quantities that define memory itself, and the behavior of those quantities under the pressures of a real simulation is largely unexamined. We study three such pressures. First, a single-qubit mode encoding misrepresents the Breuer-Laine-Piilo (BLP) measure with an error whose sign flips between regimes: it fabricates memory at strong coupling, by about a factor of 2.6 over the converged value, and it erases memory at moderate temperature. The Rivas-Huelga-Plenio (RHP) measure corroborates the temperature-driven destruction, while at strong coupling it is numerically unstable and does not track the BLP result. We derive a cross-validated rule for the required Fock dimension that collapses both regimes onto the occupied number extent, d req ≈ ⌈⟨n⟩+c σ n ⌉+1, and we show that the constant must be calibrated on super-Poissonian statistics. Second, using the exact noisy measure as computable ground truth, we show that the raw finite-shot estimate of the BLP measure can nearly double the true value under realistic noise. We provide a debiased estimator that is validated near-unbiased in that regime, together with a Markovian null-floor control that ports to hardware. Third, temporally correlated device noise is conflated with physical memory by the measure. A resource-fair comparison finds that a pseudomode and an ancilla-train collision model reach parity at equal qubit cost for a single-Lorentzian bath. Every result is simulator-based, validated against an exact reference, and reproducible from recorded data. We make no claim of quantum advantage.
Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects (non-Markovianity), system-environment hybridization, and the necessity for accuracy beyond the Born-Markov approximation form particular challenges. Approaches to meet these challenges have been introduced, originating from different fields, such as hierarchical equations of motion, Lindblad-pseudomode formulas, chain-mapping approaches, quantum Brownian motion master equations, stochastic unravelings, and refined quantum master equations. This diversity, while indicative of the field's relevance, has inadvertently led to a fragmentation that hinders cohesive advances and their effective cross-community application to current problems for complex systems. How are different approaches related to each other? What are their strengths and limitations? Here we give a systematic overview and concise discussion addressing these questions. We make use of a unified framework which very conveniently allows to link different schemes and, this way, may also catalyze further progress. In line with the state of the art, this framework is formulated not in a fully reduced space of the system but in an extended state space which in a minimal fashion includes effective reservoir modes. This in turn offers a comprehensive understanding of existing methods, elucidating their physical interpretations, interconnections, and applicability.