Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.
Accurate digital quantum simulation at long times is limited by the accumulation of errors inherent to approximate simulation. Here we introduce RL-Trotter, a reinforcement-learning framework that treats unavoidable approximation errors as resources for error correction rather than merely imperfections to suppress. We show that low-dimensional information from conservation laws, such as the energy and energy variance, provides a sufficient learning signal to guide the agent, which learns to adapt a single scalar---the next Trotter step size---without access to the target wave function. By optimizing the entire long-time evolution rather than individual steps, RL-Trotter discovers self-correcting sequences in which later errors compensate for those accumulated earlier, increasing the accuracy of the long-time dynamics. The learned policies are intrinsically robust to measurement noise, substantially reducing measurement overhead. They also generalize to previously unseen, physically similar initial states and transfer from small, classically simulable systems to systems an order of magnitude larger. This enables a practical protocol based on classical pretraining followed by direct deployment or limited fine-tuning on quantum hardware. Our results establish a broader perspective for quantum algorithms: errors in approximate evolution can be orchestrated into resources for accurate and resource-efficient quantum dynamics.
Simulation of continuous-time evolution requires time discretization on both classical and quantum computers.A finer time step improves simulation precision but it inevitably leads to increased computational efforts.This is particularly costly for today's noisy intermediate-scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy.Classical adaptive solvers are well developed to save numerical computation times.However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps.Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables.The key conceptual element of our algorithm is a feedback loop that self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth.It even allows for a controlled asymptotic long-time error, where the usual Trotterized dynamics faces difficulties.Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has a potentially wide range of applicability.We demonstrate the capabilities by enforcing gauge invariance, which is crucial for a faithful and long-sought-after quantum simulation of lattice gauge theories.Our algorithm can potentially be useful on a more general level whenever time discretization is involved also concerning, e.g., numerical approaches based on time-evolving block-decimation methods.
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [H. Zhao et al., Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond, PRX Quantum 4, 030319 (2023).2691-339910.1103/PRXQuantum.4.030319]. We validate the algorithm for a time dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.
Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols enabling more efficient adaptive Trotter protocols, which have been shown to exhibit a controlled error in the dynamics of local observables and correlation functions. However, it has remained open to which extent the errors on the actual generator of the dynamics, i.e., the target many-body Hamiltonian, remain controlled. Here, we propose to use quantum Hamiltonian learning to numerically obtain the effective Hamiltonian and apply it on the recently introduced ADA-Trotter algorithm as a concrete demonstration. Our key observation is that deviations from the target generator remain bounded on all simulation times. This result suggests that the ADA-Trotter not only generates reliable digital quantum simulation of local dynamics, but also controllably approximates the global quantum state of the target system. Our proposal is sufficiently general and readily applicable to other adaptive time-evolution algorithms.
Abstract Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and, consequently, to devise reliable and robust optimal control protocols. Here we present a framework for efficiently controlling quantum many-body systems based on reinforcement learning (RL). We tackle the quantum-control problem by leveraging matrix product states (1) for representing the many-body state and (2) as part of the trainable machine learning architecture for our RL agent. The framework is applied to prepare ground states of the quantum Ising chain, including states in the critical region. It allows us to control systems far larger than neural-network-only architectures permit, while retaining the advantages of deep learning algorithms, such as generalizability and trainable robustness to noise. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states and of adapting control protocols on the fly when the quantum dynamics is subject to stochastic perturbations. Furthermore, we map our RL framework to a hybrid quantum–classical algorithm that can be performed on noisy intermediate-scale quantum devices and test it under the presence of experimentally relevant sources of noise.
Quantum Reinforcement Learning (QRL) integrates reinforcement learning with parameterized quantum circuits and is a promising approach to combinatorial optimization. On Noisy Intermediate-Scale Quantum (NISQ) devices, however, decoherence, gate imperfections, and measurement errors reduce policy quality and make learning less reliable. Existing error mitigation techniques are generally applied as fixed corrections that do not adapt to changing noise conditions or to the evolving state of training. This work presents Adaptive Policy-Guided Error Mitigation (APGEM) as a context-aware orchestration layer of the hybrid quantum-classical training loop that dynamically selects the most suitable mitigation strategy during QRL training. APGEM evaluates Zero-Noise Extrapolation (ZNE), Probabilistic Error Cancellation (PEC), Clifford Data Regression (CDR), and Readout Error Mitigation (REM) using policy-level indicators, including quantum-state fidelity, policy entropy, cumulative reward, and approximation ratio, and integrates the selected strategy directly into the reinforcement learning loop. The framework is evaluated on the Capacitated Vehicle Routing Problem (CVRP), a representative NP-hard problem in urban logistics, under a range of NISQ noise models and noise levels. APGEM consistently outperforms conventional static mitigation methods, reaches approximately 94% of the utility of an oracle strategy, maintains higher quantum-state fidelity as noise increases, and produces more stable learning behaviour throughout training. Ablation studies show that the framework learns context-aware mitigation policies that adapt to different noise environments and circuit execution conditions. These findings demonstrate that integrating adaptive error mitigation into the learning process substantially improves the robustness and reliability of QRL on NISQ hardware.
The convergence of quantum computing and artificial intelligence presents profound opportunities but faces significant hurdles, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. Quantum Machine Learning (QML) algorithms, while promising, exhibit sensitivity to noise and scalability challenges, hindering the demonstration of practical quantum advantage. Concurrently, Quantum Error Correction (QEC), essential for fault tolerance, imposes substantial resource overheads and is often developed generically, without specific adaptation to the target application's error sensitivity. This paper reviews the current state of the intersection of AI and quantum computing, examining both QML paradigms, e.g., Variational Quantum Algorithms, Quantum Kernels, and the burgeoning use of AI to enhance quantum computing itself, e.g., quantum control, QEC decoding, circuit design. A critical gap identified is the lack of frameworks that systematically co-design QML algorithms and QEC protocols adaptively. To address this, a novel framework is proposed based on Reinforcement Learning (RL). This framework employs an RL agent to dynamically adjust both the QML circuit architecture, e.g., VQC ansatz, and QEC parameters, e.g., decoding strategy, measurement frequency, based on observed application performance and estimated error characteristics. This adaptive co-design loop aims to optimize the trade-off between QML performance and QEC overhead, enhancing noise resilience and resource efficiency. The potential advantages, feasibility, and limitations of this approach are discussed, alongside with future research directions aimed at realizing robust and practical Quantum AI.