Tensor network is known as a powerful method to simulate quantum computation on a classical computer. Recently, the random quantum circuit used in the demonstration of quantum supremacy by Sycamore quantum computer have been simulated with tensor network method. Compared to the application of tensor networks to Discrete-Variable (DV) quantum computation, there are very few examples of application of tensor network to Continuous-Variable (CV) quantum computation. Therefore, we applied a tensor network structure called Matrix Product States (MPS) to CV quantum computation. Tensor network is expected to be useful for simulating Gaussian Boson Sampling (GBS), which is a promised near-term application of photonic quantum system. We outline the performance of tensor network-based simulation of CV quantum computation in GBS.
Tensor network is known as a powerful method to simulate quantum computation on a classical computer. Recently, the random quantum circuit used in the demonstration of quantum supremacy by Sycamore quantum computer have been simulated with tensor network method. Compared to the application of tensor networks to Discrete-Variable (DV) quantum computation, there are very few examples of application of tensor network to Continuous-Variable (CV) quantum computation. Therefore, we applied a tensor network structure called Matrix Product States (MPS) to CV quantum computation. Tensor network is expected to be useful for simulating Gaussian Boson Sampling (GBS), which is a promised near-term application of photonic quantum system. We outline the performance of tensor network-based simulation of CV quantum computation in GBS.
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical simulations, it has been suggested that the addition of non-linear elements to the experiment will help retain the quantum advantage. We propose a classical simulation tool for general continuous variable sampling problems, including Gaussian Boson Sampling and beyond. We reformulate the sampling problem as that of finding the ground state of a simple few-body Hamiltonian. This allows us to employ powerful variational methods based on tensor networks and to read off the simulation error directly from the expectation value of the Hamiltonian. We validate our method by simulating Gaussian Boson Sampling, where we achieve results comparable to the state of the art. We also consider a non-Gaussian sampling problem, for which we develop novel local basis optimization techniques based on a non-linear parameterization of the implicit basis, resulting in high effective cutoffs with diminished computational overhead.
Tensor networks are highly promising methods for efficiently simulating quantum systems using classical computers. In recent years, the efficiency of tensor networks has been eagerly harnessed to simulate NISQ devices in the era of quantum supremacy. However, as of now, quantum advantage with NISQ devices has not been clearly demonstrated in practical applications. This provide impetus for us to intensify our effort in fault tolerant quantum computation (FTQC). Various physical systems and schemes for FTQC have been proposed, with GKP encoding in bosonic systems being one such example. The preparation of GKP states serves as an important building block for realizing FTQC with the GKP code. We introduce tensor networks for simulating and optimizing the GKP state preparation circuit. It is known that the generation of approximated GKP states is achievable through photon counting and post-selection applied to properly prepared multimode Gaussian states. However, it requires optimization of numerous circuit parameters, which is typically computationally challenging on classical computers due to the involvement of the photon counting measurement process. We attempt to utilize tensor networks for more efficient parameter optimization. Additionally, we explore further efficient approach in terms of tensor network structure. We propose a multi-cutoff dimension approach combined with a tree tensor network structure.
The accurate simulation of quantum circuits remains a significant challenge due to the exponential scaling of computational resources with circuit size. This work explores the application of tensor network methods, specifically Matrix Product States (MPS), to provide a scalable approach for simulating quantum circuits. We demonstrate how tensor networks can efficiently represent and manipulate the states of quantum circuits, reducing the computational burden associated with traditional methods. The core claim of this research is that tensor networks offer a viable path to accurately simulating larger and more complex quantum systems. This research introduces a novel framework for symbolic simulation, leveraging the power of tensor network representations to overcome the limitations of conventional simulation techniques. The effectiveness of this approach is illustrated through theoretical analysis and conceptual examples.
Continuous-variable (CV) quantum computing offers a promising framework for scalable quantum machine learning, leveraging optical systems with infinite-dimensional Hilbert spaces. While discrete-variable (DV) quantum neural networks have shown remarkable progress in various computer vision tasks, CV quantum models remain comparatively underexplored. In this work, we present a feasibility study of continuous-variable quantum neural networks (CV-QCNNs) applied to biomedical image classification. Utilizing photonic circuit simulation frameworks, we construct CV quantum circuits composed of Gaussian gates, such as displacement, squeezing, rotation, and beamsplitters to emulate convolutional behavior. Our experiments are conducted on the MedMNIST dataset collection, a set of annotated medical image benchmarks for multiple diagnostic tasks. We evaluate CV-QCNN's performance in terms of classification accuracy, model expressiveness, and resilience to Gaussian noise, comparing against classical CNNs and equivalent DV quantum circuits. This study aims to identify trade-offs between DV and CV paradigms for quantum-enhanced medical imaging. Our results highlight the potential of continuous-variable models and their viability for future computer-aided diagnosis systems.
This paper explores the application of tensor network methods for simulating molecular dynamics on quantum computers. Traditional molecular dynamics simulations are computationally expensive, particularly for complex systems exhibiting strong quantum correlations. Tensor networks provide a powerful framework for representing and manipulating high-dimensional quantum states, potentially offering a pathway to efficiently simulate molecular dynamics by directly leveraging quantum computational resources. This work details the theoretical framework, outlining how tensor network techniques, specifically Matrix Product States (MPS) and Tree Tensor Networks (TTN), can be adapted for this purpose. We present a simplified model of a diatomic molecule to illustrate the core concept: the construction of a tensor network representation of the molecular wavefunction, followed by the application of time evolution operators to simulate dynamics. The focus is on demonstrating the potential of this approach rather than a fully optimized simulation, highlighting key challenges and future research directions. The efficiency gains compared to classical methods are discussed, acknowledging the significant technological hurdles involved in realizing this approach on near-term quantum devices. We investigate the scalability of the method, considering the limitations imposed by the bond dimension of the tensor network. The ultimate goal is to demonstrate how tensor networks can provide a viable strategy for tackling computationally intractable molecular dynamics problems, paving the way for a new era of quantum-enhanced molecular simulations.
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which provides an effective and efficient representation of one-dimensional quantum systems. Indeed, it lies at the heart of density matrix renormalization group (DMRG), a most common method for simulation of one-dimensional strongly correlated quantum systems. It has got attention from several areas varying from solid-state systems to quantum computing and quantum simulators. We have considered maximally entangled matrix product states (GHZ and W). Here, we designed the quantum circuits for implementing the matrix product states. In this paper, we simulated the matrix product states in customized IBM (2-qubit, 3-qubit and 4-qubit) quantum systems and determined the probability distribution among the quantum states.