Tensor Networks Achieve Faster Ground State Energy Estimation for Quantum Algorithms
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Estimating the ground state energy of complex systems represents a fundamental challenge in computational science, and verifying a quantum advantage for this task remains a key goal. Hidetaka Manabe from The University of Osaka, Takanori Sugimoto from RIKEN, and Keisuke Fujii, also from The University of Osaka, present a new approach to dequantized algorithms that tackles the computational hurdles currently limiting progress. Their work introduces a tensor network formulation which eliminates the need for computationally expensive sampling procedures, instead leveraging the structure of entanglement and locality within the system to manage complexity. This innovative method allows for the efficient construction of high-degree polynomials for Hamiltonians with a significant number of qubits, explicitly revealing the boundary between classically solvable problems and those where a quantum advantage may emerge, and providing a crucial step towards rigorously demonstrating quantum computational power.
Tensor Networks Simulate Quantum System Dynamics Scientists are continually investigating the boundary between what computers can efficiently calculate using classical methods and what requires a quantum computer.
This research explores how tensor networks, a powerful class of classical data structures, can simulate quantum systems.
The team demonstrates that, for certain quantum computations, classical algorithms leveraging tensor networks can achieve performance comparable to, or even exceeding, naive quantum algorithms. This challenges the assumption that quantum speedup is guaranteed for all problems and highlights the importance of developing improved classical algorithms. The work significantly refines our understanding of quantum computational complexity and guides the development of both quantum and classical algorithms. Tensor networks efficiently represent many-body quantum states, particularly effective for systems with limited entanglement. Quantum simulation involves using computers, either classical or quantum, to model the behavior of quantum systems, crucial for fields like materials science and drug discovery. Dequantization is the process of finding efficient classical algorithms that mimic quantum algorithms, helping to understand the limits of quantum speedup. Techniques like Chebyshev expansion and the kernel polynomial method approximate functions, often used with tensor networks to solve quantum problems.
This research contributes to complexity theory, the study of resources required to solve computational problems. The authors present and analyze improved classical algorithms for quantum simulation based on tensor networks. They demonstrate that, for specific quantum algorithms related to short-time dynamics and certain types of Hamiltonians, classical algorithms using tensor networks can achieve comparable or even better performance. This challenges the notion that quantum computers are always necessary for these tasks. The paper emphasizes the role of entanglement in determining the efficiency of both quantum and classical algorithms, as systems with limited entanglement are more amenable to classical simulation using tensor networks.
The team compares their tensor network-based algorithms with other classical methods, highlighting the advantages of their approach. They investigate various tensor network architectures, including Matrix Product States, Projected Entangled Pair States, and Tensor Trains, and their suitability for different quantum problems. The authors provide implementations and benchmark their algorithms on various quantum systems, demonstrating their practical feasibility. The research shows that tensor networks can efficiently simulate the time evolution of quantum systems for short times, even in two dimensions. They present a classical algorithm based on tensor networks that efficiently solves the guided local Hamiltonian problem.
The team demonstrates that tensor networks can simulate 2D quantum systems with limited entanglement. They investigate the complexity of computing functions of matrices using quantum and classical algorithms and explore the use of tensor networks to solve impurity models in condensed matter physics.
The team utilized Quimb, a Python package for quantum information and many-body calculations, and TeNPy, a Python package for tensor network simulations. They also employed CVXPY, a Python-embedded modeling language for convex optimization, alongside various numerical libraries. In essence, this paper contributes to the ongoing debate about the power of quantum computation by demonstrating that classical algorithms, when cleverly designed and implemented using tensor networks, can often achieve surprisingly good performance on problems previously thought to require a quantum computer. It’s a valuable contribution to quantum information science and provides insights into the limits of quantum speedup.
Tensor Networks Enable Deterministic Ground State Estimation Scientists have developed a novel dequantization algorithm for ground state energy estimation, a central problem in quantum computing, that eliminates the prohibitive computational overheads of previous classical approaches. This work introduces a tensor network-based framework that classically simulates quantum algorithms without relying on Monte Carlo sampling. By representing key computational elements as tensor networks, the team achieved a deterministic method for calculating essential quantities, bypassing the need for statistical estimation and preserving the theoretical complexity scaling of prior algorithms. The breakthrough delivers a practical algorithm capable of constructing high-degree polynomial filters, reaching a degree of 104, a scale fundamentally inaccessible to sampling-based methods. Experiments demonstrate the ability to perform ground state energy estimation for systems with up to 100 qubits, revealing a clear pathway toward rigorously verifying quantum advantage in realistic many-body systems. The method reframes the computational challenge, shifting the bottleneck from statistical variance to the entanglement growth of Chebyshev vectors, and allowing for efficient computation by leveraging the locality inherent in the Hamiltonian. Measurements confirm that one-dimensional transverse-field Ising models can be fully dequantized using tensor networks to high precision, while two-dimensional models exhibit limitations with current bond dimensions, explicitly visualizing the crossover between classically tractable and quantum-advantaged regimes.
The team employed Matrix Product States to represent these vectors, demonstrating the power of tensor network approximations in tackling complex quantum simulations.
This research provides a crucial tool for quantitatively probing the boundary between classical and quantum computation and offers a pathway toward validating quantum advantage in practical scenarios.
Tensor Networks Simplify Quantum Energy Estimation This research presents a novel tensor network-based framework for dequantizing algorithms used in ground state energy estimation, a key challenge in computational theory.
The team successfully eliminated the need for computationally expensive sampling procedures, a limitation of previous dequantized algorithms, while maintaining comparable computational complexity. This was achieved by representing mathematical functions as tensor networks, allowing for efficient computation and reflecting inherent physical structures like entanglement and locality within the computational cost. Numerical simulations demonstrate the practical application of this method, efficiently constructing high-degree polynomials for Hamiltonians with up to 100 qubits. These results reveal a clear crossover point between classically tractable problems and regimes where quantum computation may offer an advantage. The authors acknowledge limitations in fully dequantizing certain models with the bond dimensions used in their experiments, but importantly, this limitation itself provides valuable insight into the boundary between classical and quantum computational power. Future work will focus on comparing this dequantized algorithm against established classical heuristics, such as DMRG, and exploring classical simulations of quantum circuits.
The team intends to refine the understanding of when quantum computation genuinely outperforms classical methods by characterizing the difficulty of approximating key mathematical functions, offering a single parameter to define the boundary between classical and quantum regimes.
This research provides a crucial tool for rigorously identifying and quantifying the potential advantages of quantum computation in realistic scenarios. 👉 More information 🗞 Tensor Network Formulation of Dequantized Algorithms for Ground State Energy Estimation 🧠 ArXiv: https://arxiv.org/abs/2512.13548 Tags: