Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary evolution of closed quantum systems, dissipation and noise are vital in understanding the dynamics of practical quantum systems. In this work, we experimentally demonstrate a digital simulation of an open quantum system in a controllable Markovian environment with the assistance of a single ancillary qubit. By Trotterizing the quantum Liouvillians, the continuous evolution of an open quantum system is effectively realized, and its application in error mitigation is demonstrated by adjusting the simulated noise intensities. High-order Trotter for open quantum dynamics is also experimentally investigated and shows higher accuracy. Our results represent a significant step toward hardware-efficient simulation of open quantum systems and error mitigation in quantum algorithms in noisy intermediate-scale quantum systems.
Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary evolution of closed quantum systems, dissipation and noise are vital in understanding the dynamics of practical quantum systems. In this work, we experimentally demonstrate a digital simulation of an open quantum system in a controllable Markovian environment with the assistance of a single ancillary qubit. By Trotterizing the quantum Liouvillians, the continuous evolution of an open quantum system is effectively realized, and its application in error mitigation is demonstrated by adjusting the simulated noise intensities. High-order Trotter for open quantum dynamics is also experimentally investigated and shows higher accuracy. Our results represent a significant step toward hardware-efficient simulation of open quantum systems and error mitigation in quantum algorithms in noisy intermediate-scale quantum systems.
The goal of digital quantum simulation is to approximate the dynamics of a given target Hamiltonian via a sequence of quantum gates, a procedure known as Trotterization.The quality of this approximation can be controlled by the so-called Trotter step that governs the number of required quantum gates per unit simulation time.The stroboscopic dynamics generated by Trotterization is effectively described by a time-independent Hamiltonian, referred to as the Floquet Hamiltonian.In this work, we propose Floquet Hamiltonian learning to reconstruct the experimentally realized Floquet Hamiltonian order by order in the Trotter step.This procedure is efficient, i.e., it requires a number of measurements that scales polynomially in the system size, and can be readily implemented in state-of-the-art experiments.With numerical examples, we propose several applications of our method in the context of verification of quantum devices: from the characterization of the distinct sources of errors in digital quantum simulators to determining the optimal operating regime of the device.We show that our protocol provides the basis for feedback-loop design and calibration of new types of quantum gates.Furthermore, it can be extended to the case of nonunitary dynamics and used to learn Floquet Liouvillians, thereby offering a way of characterizing the dissipative processes present in noisy intermediate-scale quantum devices.
Digital quantum simulation (DQS) is one of the most promising applications of quantum computing. Trotterised DQS models quantum dynamics by decomposing the evolution into a sequence of gate-based Trotter steps. Using larger Trotter steps reduces the required gate count, but it is now understood that the Trotterisation step size cannot be increased beyond a certain threshold value, beyond which there is a sudden breakdown in simulation accuracy, due to the onset of quantum chaos. To date, this behaviour has only been studied for closed systems not subjected to the environmental noise and decoherence to which real-world quantum computers are highly sensitive. In this work, we study a range of experimentally relevant open-system quantum simulator models and show that Trotterisation thresholds persist even when open-system effects are included, even in the long-time, steady-state limit, once all coherence has been lost. We show that open DQS can accurately reproduce the dynamics of open target systems prior to the threshold, but still exhibits a sudden performance breakdown beyond it. We introduce new, statistical techniques to rigorously characterise the onset of quantum chaos beyond the Trotterisation threshold for both approximately unitary and genuine dissipative quantum chaos, based on random matrix theory (RMT), building on techniques developed for closed systems. Finally, we demonstrate that dissipative quantum chaos emerges when the dissipation is in balance with the presence of underlying unitary quantum chaos; the dissipation must be strong enough to induce genuinely dissipative behaviour, yet not so strong as to suppress the underlying chaotic structure.
Deep-circuit quantum computation, like Shor's algorithm, is undermined by error accumulation, and near-future quantum techniques are far from adequate for full-fledged quantum error correction. Instead of resorting to shallow-circuit quantum algorithms, recent theoretical research suggests that digital quantum simulation (DQS) of closed quantum systems are robust against the accumulation of Trotter errors, as long as local observables are concerned. In this paper, we investigate the error-mitigation problem of open systems via DQS. First, we prove that the deviation in the steady state obtained from digital quantum simulation depends only on the error in a single Trotter step, which indicates that error accumulation may not be disastrous. By numerical simulation of the quantum circuits for the DQS of the dissipative XYZ model, we then show that the correct results can be recovered by quantum error mitigation as long as the error rate in the DQS is below a sharp threshold. We explain this threshold behavior by the existence of a dissipation-driven quantum phase transition. Finally, we propose a error-mitigation technique based on the scaling behavior in the vicinity of the critical point of a quantum phase transition. Our results expand the territory of near-future available quantum algorithms and stimulate further theoretical and experimental efforts in practical quantum applications.
Quantum systems are inherently open and susceptible to environmental noise, which can have both detrimental and beneficial effects on their dynamics.This phenomenon has been observed in biomolecular systems, where noise enables novel functionalities, making the simulation of their dynamics a crucial target for digital and analog quantum simulation.Nevertheless, the computational capabilities of current quantum devices are often limited due to their inherent noise.In this work, we present a novel approach that capitalizes on the intrinsic noise of quantum devices to reduce the computational resources required for simulating open quantum systems.Our approach combines quantum noise characterization methods with quantum error mitigation techniques, enabling us to manipulate and control the intrinsic noise in a quantum circuit.Specifically, we selectively enhance or reduce decoherence rates in the quantum circuit to achieve the desired simulation of open-system dynamics.We provide a detailed description of our methods and report on the results of noise characterization and quantum error mitigation experiments conducted on both real and emulated IBM Quantum computers.Additionally, we estimate the experimental resource requirements for our techniques.Our approach holds the potential to unlock new simulation techniques in noisy intermediate-scale quantum devices, harnessing their intrinsic noise to enhance quantum computations.
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where quantum many-body spin dynamics of the transverse-field Ising model is simulated. While the work presents a pedagogical way to exploit a real quantum computer, the effectiveness of the symmetric Trotterization is evaluated in a prototype superconducting quantum device on IBM Quantum Experience. It turns out that the symmetric Trotterization does not provide higher accuracy than the first-order Trotterization in the testbed using the transverse-field Ising model. The result indicates that apart from the quantum errors, such as logical gate error and readout error, the use of a higher-order Trotterization should be circumspect, and the Trotter error would play an insignificant role in particular applications in an early stage of realized noisy intermediate-scale quantum (NISQ) devices.
We present an efficient algorithm for simulating open quantum systems dynamics described by the Lindblad master equation on quantum computers, addressing key challenges in the field. In contrast to existing approaches, our method achieves two significant advancements. First, we employ a repetition of unitary gates on a set of n system qubits and, remarkably, only a single ancillary bath qubit representing the environment. It follows that, for the typical case of m locality of the Lindblad operators, we reach an exponential improvement of the number of ancilla in terms of m and up to a polynomial improvement in ancilla overhead for large n with respect to other approaches. Although stochasticity is introduced, requiring multiple circuit realizations, the sampling overhead is independent of the system size. Second, we show that, under fixed accuracy conditions, our algorithm enables a reduction in the number of Trotter steps compared to other approaches, substantially decreasing circuit depth. These advancements hold particular significance for near-term quantum computers, where minimizing both width and depth is critical due to inherent noise in their dynamics. Published by the American Physical Society 2024