Variational Circuits Model Complex Systems, Advancing Quantum Simulation

Researchers have developed a novel approach for computing the excitation spectra of quantum many-body systems using noisy quantum devices. This method, termed the tangent-space excitation ansatz, leverages the structural similarities between quantum circuits and classical tensor networks, offering a potentially efficient pathway for exploring complex quantum systems.

Investigating the energetic properties of quantum many-body systems represents a significant challenge for contemporary physics, particularly as computational demands increase with system size. Ji-Yao Chen, Bochen Huang et al. present a novel computational approach, the tangent space excitation ansatz, designed to efficiently determine these excitation spectra on existing, imperfect quantum hardware. The method leverages concepts from quasi-particle physics, where collective excitations behave as individual particles, and draws parallels with classical tensor networks, a technique used to represent many-body wavefunctions. By expanding a parametrised quantum circuit by a single layer, the researchers construct a ‘tangent space’ around the circuit’s optimal configuration, enabling the accurate capture of numerous low-energy states. Demonstrations across one and two-dimensional models, including the complex kagome Heisenberg antiferromagnet, suggest the ansatz is robust to measurement errors and scalable for larger systems, potentially offering a pathway to utilising near-term quantum devices for materials science and fundamental physics investigations.

The core principle builds upon the single-mode approximation (SMA) commonly used in many-body physics. Traditionally, SMA approximates excited states by applying local operators to a ground state. The researchers extend this concept by constructing a tangent space – a subspace derived from the variational optimum of a parametrized quantum circuit – to capture a broader range of low-energy states. This is achieved by increasing the depth of the quantum circuit by one layer, effectively creating a space where excited states can be represented as perturbations.

The approach draws a parallel to tensor network methods, where perturbations are localised within a single tensor, allowing for efficient computation of excited states. By applying this concept to quantum circuits, the researchers demonstrate the ability to accurately capture low-energy states in both one and two spatial dimensions, including the challenging kagome Heisenberg antiferromagnet.

Importantly, the method is implementable using a Hadamard test and exhibits stability in the presence of measurement noise, suggesting its robustness for near-term quantum devices. Furthermore, the researchers demonstrate the scalability of the approach to larger system sizes, indicating its potential for tackling increasingly complex quantum systems.

Motivated by the quasi-particle picture prevalent in condensed matter physics, the researchers validate the ansatz’s efficacy across both one and two-dimensional models. This offers a promising route towards utilising noisy intermediate-scale quantum computers for tasks beyond ground state estimation, specifically in the exploration of quantum excitation spectra.

Future work could focus on optimising the circuit depth and ansatz parameters to further enhance accuracy and reduce computational cost. Investigating the performance of this method on a wider range of materials and models, including those with strong correlations, would also be valuable. Furthermore, exploring the potential for combining this approach with other quantum algorithms, such as those designed for dynamical simulations, could unlock new avenues for understanding complex quantum phenomena.