Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-qubit interactions and challenging driving protocols that are difficult with other existing methods. We demonstrate this for a time-dependent Hamiltonian on the IBM Quantum Experience cloud quantum computer by showing superior performance of the quantum assisted simulator compared to Trotterization and variational quantum simulation. Further, we demonstrate the capability to simulate the dynamics of Hamiltonians consisting of 10000 qubits. Our results indicate that quantum assisted simulator is a promising algorithm for current term quantum hardware.
Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-qubit interactions and challenging driving protocols that are difficult with other existing methods. We demonstrate this for a time-dependent Hamiltonian on the IBM Quantum Experience cloud quantum computer by showing superior performance of the quantum assisted simulator compared to Trotterization and variational quantum simulation. Further, we demonstrate the capability to simulate the dynamics of Hamiltonians consisting of 10000 qubits. Our results indicate that quantum assisted simulator is a promising algorithm for current term quantum hardware.
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.
Noise in quantum devices is generally considered detrimental to computational accuracy. However, the recent proposal of noise-assisted simulation has demonstrated that noise can be an asset in digital quantum simulations of open systems on noisy intermediate-scale quantum (NISQ) devices. In this context, we introduce an optimized decoherence rate control scheme that can significantly reduce computational requirements by multiple orders of magnitude, in comparison to the original noise-assisted simulation. We further extend this approach to encompass Lindblad equations with time-dependent coefficients, using only quantum error characterization and mitigation techniques. This extension allows for the perturbative simulation of non-Markovian dynamics on NISQ devices, eliminating the need for ancilla qubits or midcircuit measurements. Our contributions are validated through numerical experiments on an emulated IBM Quantum device. Overall, our paper offers valuable optimizations that bring current quantum processors closer to effectively simulating realistic open systems.
Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm. We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm.
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.
We investigate how to simulate a quantum many body system using near term device known as noisy intermediate scale quantum (NISQ) hardware. We explore the two different types of hardware, analog and digital device, and discuss their potential for quantum many body simulation. For instance, one of the applications is to use the analog device to simulate the slow dynamics under a strong staggered field. However, noise is a major challenge for quantum hardware. Hence, we discuss the quantum error mitigation methods which are suitable for NISQ hardware. We apply the most commonly-used quantum error mitigation techniques to our many body simulation. We simulate quantum body scar dynamics using zero noise extrapolation techniques, Pauli twirling, and dynamical decoupling. We also calculate the corresponding correlation function using direct measurement without resorting to ancilla qubits. Furthermore, we use the same error mitigation techniques to explore dynamics of energy correlators. As additional error mitigation technique, we divide the noisy correlation results by their sum, which is ideally constant due to energy conservation. By doing so, we significantly improve our result. Finally, we consider another NISQ friendly quantum algorithm for imaginary time evolution. With enough samples from minimally entangled typical thermal state algorithms, we can obtain the thermal expectation value of observable and explore their thermodynamics. In chapter 2, we provide the background knowledge for the following 4 chapters. We introduce the rydberg atom system as the analog system and their special parameter regime for interesting physics. Moreover, we introduce the digital quantum hardware and trotterization that enable one to simulate many body dynamics on the quantum hardware. We also introduce the quantum error mitigation techniques to reduce the the impact of noise from the results. Finally, we introduce the variation quantum dynamics method for the dynamics simulation. In chapter 3, we explore the Rydberg blockade regime with a strong staggered field. With the strong staggered field, any computational basis states are thermalized. Here, we investigate the slow dynamics using a Schrieffer-Wolff (SW) transformation, which is similar to perturbation theory in calculating the different-order effective Hamiltonian in terms of energy scale. As numerical result shown, the naive Schrieffer-Wolff transformation is not enough to explain the some dynamics' relaxation time. Hence, here, we also consider another conservative quantity to perform the SW transformation. The corresponding analytical result agrees with the numerical result. In chapter 4, we simulate quantum many body scarred dynamics in IBM quantum superconducting hardware. We also use custom pulse gates, quantum error mitigation techniques, and quantum error suppression methods to help us handle the noise. The error mitigated result outperforms the raw result. With the all techniques, we also explore non-trivial correlation function which also manifest the long lived oscillation in the rydberg blockade regime. In chapter 5, we use the same quantum error mitigation techniques, which we used in ch. 5, to study the energy transport properties of the mixed Ising model at infinite temperature. Here, instead of using some random state to evaluate the necessary two point energy density correlations, we use Y basis product state sampling to evaluate them. Surprisingly, few samples are enough to estimate the correlation. In addition to the quantum error mitigation techniques, we also use the fact that sum of all correlation functions is constant to renormalize the noisy results. With this trick, we are able to extract an effective dynamical exponent, which enables us to classify the transport properties. In chapter 6, we combine a variational quantum algorithm and the minimally entangled typical thermal states approach to investigate the thermodynamics of 1+1-dimensional Z2 lattice gauge theory. In particular, with a confining field, the 1+1-dimensional Z2 lattice gauge theory cannot be solved exactly. We estimate the corresponding thermal particle number density and energy density to distinguish the confined and deconfined regime. Chapter 7 provides a short review of the main results described in the thesis and a discussion of future research directions that they motivate. We mainly give insight into the recent experimental breakthrough in quantum error correction. We also clarify that quantum error mitigation methods do not become totally useless when a fault-tolerant quantum computer is realized. Finally, we also comment on variational quantum algorithms and their potential applications.
Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.