Circuits Unlock Elusive Chiral Spin Liquid States

Scientists are increasingly utilising quantum circuits to simulate complex states of matter, yet realising and characterising chiral topological phases has proven particularly challenging. Zi-Yang Zhang from Sun Yat-sen University, Donghoon Kim from RIKEN, and Ji-Yao Chen, also of Sun Yat-sen University, demonstrate the variational preparation and characterisation of chiral spin liquids within quantum circuits, achieved through a collaborative effort between the Center for Neutron Science and Technology, Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics at Sun Yat-sen University, and the Analytical Quantum Complexity RIKEN Hakubi Research Team, RIKEN Center for Quantum Computing (RQC). This research is significant because it employs the variational eigensolver framework and a novel tangent space excitation ansatz to not only create these elusive chiral spin liquids but also to reliably identify key signatures of their topological order, including ground state degeneracy and chiral edge modes, offering a promising route towards exploring more exotic quantum phases of matter.

This work demonstrates a new method for building and analysing complex magnetic materials with unusual properties within these circuits, bringing us closer to understanding and potentially utilising these quantum states for future technologies.

Quantum circuits are proving to be a powerful platform for realising complex phases of matter, but creating and characterising chiral topological phases has remained a significant challenge. These chiral states, exhibiting unique properties like unidirectional edge modes, differ fundamentally from their non-chiral counterparts and lack a straightforward path to creation using standard quantum circuit techniques.

Researchers have now demonstrated a method for preparing and characterising chiral topological phases, specifically chiral spin liquids, within quantum circuits using a variational quantum eigensolver (VQE) framework. This approach leverages a recently proposed tangent space excitation ansatz to reveal the signatures of chiral topological order, efficiently preparing the ground state of a quantum system and probing its properties through its low-energy excitations.

By employing the VQE, the researchers moved beyond the limitations of purely unitary circuits and achieved highly accurate results for the Kitaev honeycomb model, a well-known system exhibiting topological order. The study demonstrates the ability to faithfully capture both the topological ground state degeneracy and the chiral edge mode, defining features of these systems.

The team validated their approach by comparing the low-energy excitation spectrum obtained from the quantum circuits with the exact analytical solution for the Kitaev honeycomb model across all topological sectors, finding excellent agreement. Extending this methodology to a more complex chiral spin liquid model on a square lattice, one without a known exact solution, yields promising results, suggesting the robustness and broad applicability of this technique.

This advancement opens new avenues for exploring and understanding exotic quantum states of matter using near-term quantum devices. The research introduces a novel method for characterising these chiral states by examining their low-energy spectrum on quantum devices, offering a potentially efficient alternative to traditional methods like entanglement spectrum measurements. By focusing on the excited states of the system, the researchers provide a means of identifying and revealing experimental signatures of chiral topological phases, paving the way for future investigations and potential applications in quantum information science.

Quantum circuit validation of chiral topological phases and ground state properties

Kitaev honeycomb model circuits demonstrated excellent agreement between low-energy excitation spectra obtained on the quantum circuits and those from exact solutions across all topological sectors, validating the approach and confirming its ability to accurately represent the system’s behaviour. Further application of this method to a chiral spin liquid model on a square lattice suggests the technique’s robustness and wider applicability even when topological sectors remain unknown.

The variational eigensolver (VQE) framework successfully prepared generic chiral topological states, showcasing a versatile platform for exploring these complex phases of matter. Ground state degeneracy, a hallmark of topological order, was faithfully captured by the circuits, confirming the presence of multiple, distinct ground states. The chiral edge mode, another key signature of chiral topological phases, was also accurately reproduced within the computational framework.

Employing the tangent space excitation ansatz for quantum circuits allowed for efficient computation of the low-energy excitation spectrum, scaling with a low-order polynomial relationship to both circuit depth and system size. This computational efficiency is particularly advantageous for implementation on near-term quantum devices. The research successfully prepared all representative models within Kitaev’s 16-fold way, achieving machine precision in the preparation of degenerate ground states with minimal circuit depth.

Analysis of the excitation spectrum on both torus and disk geometries provided further evidence supporting the chiral topological order. This approach offers a novel means of characterising chiral states on quantum devices, circumventing the limitations of traditional methods like stabilizer formalism and entanglement spectrum measurements.

Variational Eigensolver Simulations of Chiral Topological Phases in Spin Systems

A variational eigensolver (VQE) framework underpinned the preparation and characterisation of chiral topological phases within spin systems explored in this work. Leveraging this computational approach, the research circumvented the challenges associated with directly observing these phases in physical materials, instead simulating their behaviour using quantum circuits.

The core of the methodology involved finding the ground state of a specific spin model, the Kitaev honeycomb model, and a chiral spin liquid model on a square lattice, using the VQE algorithm. This algorithm iteratively refines an initial guess for the ground state, minimising its energy until a stable solution is reached. To probe the topological order inherent in these states, a tangent space excitation ansatz was implemented.

This ansatz constructs excited states by applying carefully chosen operators to the VQE ground state, effectively simulating low-energy excitations within the system, focusing on excitations that reveal the presence of chiral edge modes and topological ground state degeneracy. The researchers meticulously validated this approach by comparing the calculated low-energy excitation spectrum of the Kitaev model with its known exact solution across all topological sectors, confirming the accuracy of the simulation.

This approach was further extended to a more complex, non-exactly solvable chiral spin liquid model on a square lattice, broadening the scope of the technique to less-understood topological phases. The study systematically examined vortex sectors, beginning with a (3, 2) system size. It then moved on to examine (3, 3) and (4, 3) before focusing on the (3, 3) case for detailed analysis, with energy errors minimised to 1 × 10−12 for the 100 lowest energy states and below 1 × 10−13 for the ground states themselves.

Simulating chiral spin liquids with programmable quantum circuits advances topological material design

Scientists are edging closer to building genuinely useful quantum materials, not just demonstrating fleeting quantum behaviour. This work represents a significant step forward in simulating exotic states of matter, specifically chiral spin liquids, using programmable quantum circuits. For years, the challenge has been to move beyond simple model systems and tackle materials exhibiting complex, topological order, where the arrangement of electrons dictates unusual properties.

Chiral spin liquids are particularly elusive, possessing a ‘handedness’ that could underpin novel forms of quantum computation and information storage. The ability to prepare and characterise these chiral phases within a circuit framework is noteworthy because it bypasses the difficulties of creating them in real materials, offering a clean, virtual laboratory.

The researchers have demonstrated that key signatures of this topological order, ground state degeneracy and chiral edge modes, can be reliably captured, even in systems where the underlying topological structure isn’t fully known. However, the method isn’t without limitations. The excitation ansatz struggles with accurately representing states involving multiple particle excitations, suggesting that while the ground state properties are well-defined, understanding the full range of dynamic behaviour remains a challenge.

Scaling these simulations to larger, more realistic systems will demand substantial computational resources and algorithmic improvements. Looking ahead, this work could inspire new hybrid approaches, combining circuit simulations with insights from materials science. The insights gained from these virtual experiments could guide the design of actual materials exhibiting similar properties, and the broader effort will likely see the development of more sophisticated ansatzes and the integration of machine learning techniques to accelerate the search for novel topological phases.