Digital quantum computers are potentially an ideal platform for simulating open quantum many-body systems beyond the digital classical computers. Many studies have focused on obtaining the ground state by simulating time dynamics or variational approaches of closed quantum systems. However, dynamics of open quantum systems has not been given much attention with a reason being their non-unitary dynamics not natural to simulate on a set of unitary gate operations in quantum computing. Here we study prototypical models in open quantum systems with Trotterisations for the modified stochastic Schr{ö}dinger equation (MSSE). Minimising the leading error in MSSE enables to optimise the quantum circuits, and we run the optimised circuits with the noiseless \textit{quantum assembly language (QASM) simulator} and the noisy IBM Quantum devices. The \textit{QASM simulator} enables to study the reachable system size that is comparable to the limits of classical computers. The results show that the nonequilibrium critical phenomena in open quantum systems are successfully obtained with high precision. Furthermore, we run the algorithm on the IBM Quantum devices, showing that the current machine is challenging, to give quantitatively accurate time dynamics due to the noise. Despite errors, the results by IBM devices qualitatively follow the trend of critical behaviour and include a possibility to demonstrate quantum advantage when the noise is reduced. We discuss how much noise should be reduced for a certain fidelity using the noise model, which will be crucial to demonstrate quantum advantage from future quantum devices.
Digital quantum computers are potentially an ideal platform for simulating open quantum many-body systems beyond the digital classical computers. Many studies have focused on obtaining the ground state by simulating time dynamics or variational approaches of closed quantum systems. However, dynamics of open quantum systems has not been given much attention with a reason being their non-unitary dynamics not natural to simulate on a set of unitary gate operations in quantum computing. Here we study prototypical models in open quantum systems with Trotterisations for the modified stochastic Schr{ö}dinger equation (MSSE). Minimising the leading error in MSSE enables to optimise the quantum circuits, and we run the optimised circuits with the noiseless \textit{quantum assembly language (QASM) simulator} and the noisy IBM Quantum devices. The \textit{QASM simulator} enables to study the reachable system size that is comparable to the limits of classical computers. The results show that the nonequilibrium critical phenomena in open quantum systems are successfully obtained with high precision. Furthermore, we run the algorithm on the IBM Quantum devices, showing that the current machine is challenging, to give quantitatively accurate time dynamics due to the noise. Despite errors, the results by IBM devices qualitatively follow the trend of critical behaviour and include a possibility to demonstrate quantum advantage when the noise is reduced. We discuss how much noise should be reduced for a certain fidelity using the noise model, which will be crucial to demonstrate quantum advantage from future quantum devices.
Abstract Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics—we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous-time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid advances in recent years. Yet, current quantum devices remain noisy and limited in scale. Hence, it is essential to identify classically hard problems of practical interest and tractable with existing quantum devices. Among potential applications, the real-time simulation of quantum systems is one of the most promising to deliver an early, practical quantum advantage. This doctoral thesis is therefore centered around simulating quantum dynamics on quantum devices. We first present an overview of the most relevant quantum algorithms for quantum dynamics, highlighting respective advantages and limitations. Further, we identify relevant problems within quantum dynamics that could benefit from quantum simulation in the near future. Second, we propose a method for benchmarking hardware and error mitigation algorithms that is based on well-understood theoretical results and suffers from no scaling issues. The resulting quality metric is intuitive and transferable to other applications. We successfully implement the scheme on up to 133 qubits, demonstrating coherent evolution up to a two-qubit gate depth of 28, featuring 1396 two-qubit gates, before noise becomes prevalent. Third, we propose a novel variant of probabilistic error amplification to implement open quantum dynamics, relying on characterizing and altering hardware noise to mimic the system-environment interaction under study. Lastly, we present two studies on state preparation and phase classification: first, a hybrid algorithm to prepare ground states of electron-phonon systems; second, a quantum machine learning-based approach to distinguish phases in previously prepared quantum states.
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.
Simulating quantum many-body systems is essential for understanding complex phenomena in condensed matter, chemistry, and materials science. Quantum computing offers a way to overcome the limitations of classical methods by operating directly in exponentially large Hilbert spaces. In particular, classical methods often fail to capture the dynamics of strongly correlated systems, which makes quantum algorithms a promising alternative for exploring these challenging regimes. This thesis uses quantum dynamics simulations to probe the behaviour of many-body systems. We first introduce a spectroscopy-based protocol to extract excitation spectra from the time evolution of observables and analyse its performance on near-term quantum devices. We show that the protocol requires only short evolution times and is resilient to errors, facilitating its implementation on real hardware. Building on this, we simulate fermionic excitation spectra using current quantum devices, introducing resource optimisations - including an approximate free-fermion initial state, a unitary quench without ancillae, and reduced Trotter steps - that significantly lower circuit depth. These improvements enable simulations at system sizes competitive with the state of the art, yielding results that match classical benchmarks. While most studies focus on unitary dynamics of isolated systems, open quantum dynamics is increasingly relevant for describing non-equilibrium processes across biology, materials science, and quantum control. We extend our scope to systems coupled to an environment and governed by Lindbladian evolution. By studying simulation complexity through physically meaningful quantities - such as correlation length and mixing time - we explore whether open-system dynamics can be as tractable as their unitary counterparts. These findings provide insights into the computational complexity landscape of open-system simulation and highlight regimes where quantum methods offer a clear advantage.
Many-body open quantum systems, described by Lindbladian master equations, are a rich class of physical models that display complex equilibrium and out-of-equilibrium phenomena which remain to be understood. In this paper, we theoretically analyze noisy analog quantum simulation of geometrically local open quantum systems and provide evidence that this problem both is hard to simulate on classical computers and could be approximately solved on near-term quantum devices. First, given a noiseless quantum simulator, we show that the dynamics of local observables and the fixed-point expectation values of rapidly mixing local observables in geometrically local Lindbladians can be obtained to a precision of ϵ in time that is poly ( ϵ − 1 ) and uniform in system size. Furthermore, we establish that the quantum simulator would provide a superpolynomial advantage, in run-time scaling with respect to the target precision and either the evolution time (when simulating dynamics) or the Lindbladian’s decay rate (when simulating fixed points), over any classical algorithm for these problems, assuming BQP ≠ BPP . We then consider the presence of noise in the quantum simulator in the form of additional geometrically local Lindbladian terms. We show that the simulation tasks considered in this paper are stable to errors; i.e., they can be solved to a noise-limited, but system-size independent, precision. Finally, we establish that, assuming BQP ≠ BPP , there are stable geometrically local Lindbladian simulation problems such that, as the noise rate on the simulator is reduced, classical algorithms must take time superpolynomially longer in the inverse noise rate to attain the same precision as the analog quantum simulator.
Abstract Quantum simulation represents the most promising quantum application to demonstrate quantum advantage on near-term noisy intermediate-scale quantum (NISQ) computers, yet available quantum simulation algorithms are prone to errors and thus difficult to realize with limited circuit depth on nowadays quantum devices. Herein, we propose a novel scheme to utilize intrinsic gate errors of NISQ devices to enable controllable simulation of open quantum system dynamics without ancillary qubits or explicit bath engineering, thus turning unwanted quantum noises into useful quantum resources. Specifically, we simulate the energy transfer process in a photosynthetic dimer system on IBM-Q cloud. By employing tailored decoherence-inducing gates, we show that quantum dissipative dynamics can be simulated efficiently across coherent-to-incoherent regimes with results comparable to those of the numerically exact classical method. Moreover, we demonstrate a calibration routine that enables consistent and predictive simulations of open-quantum system dynamics in the intermediate coupling regime. This work provides a new direction for quantum advantage in the NISQ era.