We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field—the Hubbard atom. These problems are solved using IBM quantum computers, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware. Our two examples show promise that the driven-dissipative quantum many-body problem can eventually be solved on quantum computers.
We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field—the Hubbard atom. These problems are solved using IBM quantum computers, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware. Our two examples show promise that the driven-dissipative quantum many-body problem can eventually be solved on quantum computers.
Many-body physics is one very well suited field for testing quantum algorithms and for finding working heuristics on present quantum computers. We have investigated the non-equilibrium dynamics of one- and two-electron systems, which are coupled to an environment that introduces decoherence and dissipation. In our approach, the electronic system is represented in the framework of a two-site Hubbard model while the environment is modelled by a spin bath. To simulate the non-equilibrium population probabilities of the different states on a quantum computer we have encoded the electronic states and environmental degrees of freedom into qubits and ancilla qubits (bath), respectively. The total evolution time was divided into short time intervals, during which the system evolves. After each of these time steps, the system interacts with ancilla qubits representing the bath in thermal equilibrium. We have specifically studied spin baths leading to both, unital and non-unital dynamics of the electronic system and have found that electron correlations clearly enhance the electron transfer rates in the latter case. For short time periods, the simulation on the quantum computer is found to be in very good agreement with the exact results if error mitigation methods are applied. Our method to simulate also non-unitary time-evolution on a quantum computer can be well extended to simulate electronic systems in correlated spin baths as well as in bosonic and fermionic baths.
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.
Abstract Many-body physics is one very well suited field for testing quantum algorithms and for finding working heuristics on present quantum computers. We have investigated the non-equilibrium dynamics of one- and two-electron systems, which are coupled to an environment that introduces decoherence and dissipation. In our approach, the electronic system is represented in the framework of a two-site Hubbard model while the environment is modelled by a spin bath. To simulate the non-equilibrium population probabilities of the different states on a quantum computer we have encoded the electronic states and environmental degrees of freedom into qubits and ancilla qubits (bath), respectively. The total evolution time was divided into short time intervals, during which the system evolves. After each of these time steps, the system interacts with ancilla qubits representing the bath in thermal equilibrium. We have specifically studied spin baths leading to both, unital and non-unital dynamics of the electronic system and have found that electron correlations clearly enhance the electron transfer rates in the latter case. For short time periods, the simulation on the quantum computer is found to be in very good agreement with the exact results if error mitigation methods are applied. Our method to simulate also non-unitary time-evolution on a quantum computer can be well extended to simulate electronic systems in correlated spin baths as well as in bosonic and fermionic baths.
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.
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.
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.