Abstract As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through classical simulation fails. However, we can classically simulate small scale quantum computations and hence we are able to test that devices behave as expected in this domain. This constitutes the first step towards obtaining confidence in the anticipated quantum-advantage when we extend to scales that can no longer be simulated. Realistic devices have restrictions due to their architecture and limitations due to physical imperfections and noise. Here we extend the usual ideal simulations by considering those effects. We provide a general methodology for constructing realistic simulations emulating the physical system which will both provide a benchmark for realistic devices, and guide experimental research in the quest for quantum-advantage. We exemplify our methodology by simulating a networked architecture and corresponding noise-model; in particular that of the device developed in the Networked Quantum Information Technologies Hub (NQIT) (Networked Quantum Information Technologies Hub 2018 https://nqit.ox.ac.uk/ ; 2016 private communication. The error model was based on communication with Chris Balance and Tom Harty, mediated through Niel de Beaudrap, early on the NQIT project. Continued collaboration and communication with experimentalists could lead in refinement of the error model, which could be subject for future work.). For our simulations we use, with suitable modification, the classical simulator of Bravyi and Gosset 2016 ( Phys. Rev. Lett. 116 250501). The specific problems considered belong to the class of instantaneous quantum polynomial-time ( IQP ) problems (Shepherd and Bremner 2009 Proc. R. Soc. A 465 141339), a class believed to be hard for classical computing devices, and to be a promising candidate for the first demonstration of quantum-advantage. We first consider a subclass of IQP , defined in Bermejo-Vega et al 2018 ( Phys. Rev. X 8 021010), involving two-dimensional dynamical quantum simulators, before moving to more general instances of IQP , but which are still restricted to the architecture of NQIT.
Abstract As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through classical simulation fails. However, we can classically simulate small scale quantum computations and hence we are able to test that devices behave as expected in this domain. This constitutes the first step towards obtaining confidence in the anticipated quantum-advantage when we extend to scales that can no longer be simulated. Realistic devices have restrictions due to their architecture and limitations due to physical imperfections and noise. Here we extend the usual ideal simulations by considering those effects. We provide a general methodology for constructing realistic simulations emulating the physical system which will both provide a benchmark for realistic devices, and guide experimental research in the quest for quantum-advantage. We exemplify our methodology by simulating a networked architecture and corresponding noise-model; in particular that of the device developed in the Networked Quantum Information Technologies Hub (NQIT) (Networked Quantum Information Technologies Hub 2018 https://nqit.ox.ac.uk/ ; 2016 private communication. The error model was based on communication with Chris Balance and Tom Harty, mediated through Niel de Beaudrap, early on the NQIT project. Continued collaboration and communication with experimentalists could lead in refinement of the error model, which could be subject for future work.). For our simulations we use, with suitable modification, the classical simulator of Bravyi and Gosset 2016 ( Phys. Rev. Lett. 116 250501). The specific problems considered belong to the class of instantaneous quantum polynomial-time ( IQP ) problems (Shepherd and Bremner 2009 Proc. R. Soc. A 465 141339), a class believed to be hard for classical computing devices, and to be a promising candidate for the first demonstration of quantum-advantage. We first consider a subclass of IQP , defined in Bermejo-Vega et al 2018 ( Phys. Rev. X 8 021010), involving two-dimensional dynamical quantum simulators, before moving to more general instances of IQP , but which are still restricted to the architecture of NQIT.
Abstract Complex quantum networks are not only hard to establish, but also difficult to simulate due to the exponentially growing state space and noise-induced imperfections. In this work, we propose an alternative approach that leverages quantum computers and noisy intermediate-scale quantum (NISQ) devices as simulators for quantum networks, including noisy devices, channels, and protocols. Rather than treating noise as an undesired feature to be mitigated, we show how imperfections in quantum hardware can be exploited to simulate real-world communication devices under realistic conditions beyond classical simulation capabilities. Our approach allows NISQ devices with modest noise to simulate more imperfect devices, enabling large-scale, detailed quantum network simulations with exact error models. It also improves over direct implementation and benchmarking of real networks, as waiting times, locality, and memory restrictions do not apply. This framework offers flexibility, scalability, and precision, showing that NISQ devices can serve as natural testbeds for complex quantum networks.
The new quantum era is expected to have an unprecedented social impact, enabling the research of tomorrow in several pivotal fields. These perspectives require a physical system able to encode, process and store for a sufficiently long amount of time the quantum information. However, the optimal engineering of currently available quantum computers, which are small and flawed by several non-ideal phenomena, requires an efficacious methodology for exploring the design space. Hence, there is an unmet need for the development of reliable hardware-aware simulation infrastructures able to efficiently emulate the behaviour of quantum hardware that commits to looking for innovative systematic ways, with a bottom-up approach starting from the physical level, moving to the device level and up to the system level. This article discusses the development of a classical simulation infrastructure for semiconductor quantum-dot quantum computation based on compact models, where each device is described in terms of the main physical parameters affecting its performance in a sufficiently easy way from a computational point of view for providing accurate results without involving sophisticated physical simulators, thus reducing the requirements on CPU and memory. The effectiveness of the involved approximations is tested on a benchmark of quantum circuits — in the expected operating ranges of quantum hardware — by comparing the corresponding outcomes with those obtained via numeric integration of the Schrödinger equation. The achieved results give evidence that this work is a step forward towards the definition of a classical simulator of quantum computers.
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.
The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identify the level of error expected in quantities we extract from experiments. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators. We also identify the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. Verification techniques are already available to test the assumptions we make here, and demonstrating these in experiments will be an important next step.
Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work, we make progress on this problem for noisy analogue quantum simulators computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics. We first formulate a system-size independent notion of stability against extensive errors, which we prove for Gaussian fermion models, as well as for a restricted class of spin systems. Remarkably, for the Gaussian fermion models, our analysis shows the stability of critical models which have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limit of many-body models, in the presence of a constant error rate and without any explicit error correction.
Context: The main obstacle of quantum computing on its way to scalability is the noisy nature of current hardware. Various types of errors lead to incorrect computational results,and measures such as quantum error mitigation are needed to counteract these errors. Many error mitigation techniques require a thorough understanding of the noise and its impact on computations. Therefore, accurate noise models are indispensable to facilitate meaningful quantum computing in the near future. They also enable realistic simulations of quantum devices. Since these devices are currently limited and quantum computing is expensive, researchers typically rely on simulations for testing their algorithms.Objective: In this thesis, we aim to construct a realistic noise model for quantum computing and optimise its model parameters. The model construction should build on the underlying physical processes, and the number of parameters should scale well with the system size. We also address the evaluation and comparison of different noise models by benchmarks using quantum circuits specific to real-world applications. Finally, we aim to develop useful graphical representations of noise models based on the existing quantum circuit model.Method: We present a benchmarking framework for quantum computing noise models and evaluate it based on benchmarking quality attributes from the literature. Moreover, we construct a quantum computing noise model and develop a training procedure for its parameters. We analyse the parameters of the trained noise model and the impact ofdifferent types of errors on computations. We benchmark the noise model with the above approach and compare it to a noise model provided by IBM’s software development kit Qiskit. Finally, we develop an extension of the quantum circuit model to represent noise channels.Result: The benchmarks performed in this thesis show that our noise model predicts noisy hardware behaviour of IBM’s ibmq_manila quantum device equally well as the Qiskit model, if not better, based on quantum circuits commonly used for variational quantum algorithms. Within the trained noise model, readout error has the most detrimental impact on computations. Our benchmarking approach satisfies relevant quality criteria by choosing suitable quantum circuits and objective functions to compare model predictionsto hardware data. Moreover, the quantum circuit model can be extended meaningfully by noise channels.Conclusion: Our benchmarking approach is suitable for evaluating and comparing quantum computing noise models. In future work, volumetric benchmarks should be performed for various noise models and application contexts. The parameter optimisation based on learning with training circuits yields accurate noise models and shows the importance of mitigating measurement error. Different optimisation algorithms and quantum circuits should be explored, and more types of noise should be incorporated into the noise model.