Quantum Annealing Boosts Complex Simulations with Stable Optimisation Methods

Julian Schuhmacher of IBM Research, and colleagues, present a new method for optimising ground-state approximations in quantum systems. The approach combines non-parametric quantum states, generated via quantum annealing, with classical isometric tensor networks to overcome limitations in existing variational quantum algorithms. It uses the quantum component as a fixed resource, in the form of classical shadows, while variationally optimising the classical tensor network. Simulations on the transverse-field Ising model show strong performance against noise and key improvements in ground state approximation without increasing quantum circuit complexity, suggesting a pathway towards scalable and practical quantum computation.

Quantum annealing enhanced by tensor networks yields improved ground state accuracy

Ground state approximation accuracy improved by up to 20 per cent compared to standard quantum annealing alone, a result previously unattainable without sharply increasing quantum circuit complexity. The integration of quantum annealing, a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions, with a classical Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network achieved this improvement. MERA, a specific type of tensor network, efficiently represents complex quantum states by recursively coarse-graining the system, effectively capturing its entanglement structure and reducing computational demands. This allows for more accurate simulations of complex quantum systems, particularly those exhibiting strong correlations, and pushes beyond the limitations of current variational quantum algorithms which often struggle with scalability and expressivity. The transverse-field Ising model, a fundamental model in condensed matter physics used to study phase transitions and magnetism, served as the testbed for this research. Its relative simplicity allows for robust benchmarking against established methods while still capturing the essential challenges of quantum many-body systems.

Numerical simulations utilising the transverse-field Ising model revealed the approach consistently improves ground state approximation accuracy. It effectively matched results from slower, longer annealing schedules, typically requiring significantly more computational time on a quantum annealer, without increasing the depth of quantum circuits. This is crucial as circuit depth is a primary driver of error accumulation in near-term quantum devices. Classical shadows, a technique for efficiently extracting information about a quantum state by performing multiple measurements on randomly rotated copies of that state, were successfully integrated into the tensor network workflow, enabling this enhancement. The resulting classical data, representing the quantum state, is then used to train the parameters of the tensor network. The isometric tensor network employed, MERA, ensures proper normalisation of the overall quantum state representation, a critical requirement for physically meaningful results and stable optimisation. Normalisation prevents the wavefunction from artificially growing or shrinking during the iterative optimisation process.

Hybrid quantum-classical algorithms represent a vital step towards unlocking the potential of quantum computation for real-world problems. Current methods often struggle with optimising the quantum components within these systems, despite combining the strengths of both classical and quantum processing. Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimisation Algorithm (QAOA) are prominent examples, both relying on optimising parameters within a quantum circuit. A viable pathway around that bottleneck is now available, utilising a pre-defined quantum state generated via quantum annealing as a resource for classical computation, effectively turning quantum hardware into a computational asset. This differs from traditional variational approaches where the quantum circuit itself is the primary optimisation target. Although concerns remain about the practical scalability of hybrid methods, particularly regarding the overhead of data transfer between quantum and classical processors, this suggests a route to overcome these difficulties. The 20 per cent improvement in ground state accuracy, achieved without increasing circuit complexity, is a significant step towards demonstrating the potential of this hybrid approach.

Quantum annealing provides a fixed state for enhanced classical tensor network calculations

This method sidesteps the troublesome optimisation of quantum components, offering a strong and potentially faster route to improved results. Gate fidelity increased five-fold without increasing the computational demands on the quantum processor, circumventing a key limitation of existing hybrid algorithms. Gate fidelity, a measure of how accurately a quantum gate performs its intended operation, is a critical metric for assessing the quality of quantum computation. Improving fidelity without increasing computational cost is a major advancement. Quantum and classical computation combined offers a pathway towards solving complex problems beyond the reach of either alone. This presents a new method for approximating the ground state, the lowest energy state, of quantum systems, utilising quantum annealing to generate a fixed quantum state which then informs a classical tensor network, allowing for more efficient calculations. The quantum annealing process effectively explores the solution space to find a good initial state, which is then refined by the classical tensor network optimisation. This division of labour leverages the strengths of both quantum and classical resources.

The use of a non-parametric quantum state, generated through quantum annealing, is particularly noteworthy. Unlike parametric quantum circuits used in VQE or QAOA, the quantum annealer does not have adjustable parameters. Instead, it relies on the physical process of adiabatic evolution to find the ground state. This fixed state provides a robust and noise-resilient foundation for the subsequent classical tensor network calculations. The classical optimisation of the isometric tensor network, specifically MERA, focuses on refining the representation of the quantum state, effectively ‘cleaning up’ any imperfections introduced by the quantum annealing process. The combination of these two techniques results in a more accurate and efficient ground state approximation. Further research will focus on exploring the applicability of this method to more complex quantum systems and investigating the potential for scaling it to larger problem sizes. The ability to leverage existing quantum annealing hardware, coupled with the efficiency of tensor network methods, offers a promising avenue for advancing the field of quantum computation.

The researchers demonstrated a new method for approximating the ground state of quantum systems, combining a quantum state prepared through quantum annealing with a classical isometric tensor network. This approach improves the accuracy of ground state approximations compared to standard quantum simulation, without requiring more complex quantum circuits. By using a fixed quantum state generated via quantum annealing, the optimisation process remains robust even with noise. The authors intend to explore applying this method to more complex quantum systems and scaling it to larger problem sizes.