Quantum Circuit Algorithm Achieves Topological Invariant Calculation for Many-Body Magnets

Understanding the fundamental properties of complex materials represents a significant challenge in modern physics, particularly when dealing with the interactions of many particles. Sebastián Domínguez-Calderón, Marcel Niedermeier, Jose L. Lado, and Pascal M. Vecsei, from Aalto University and the Lucerne University of Applied Science and Arts, now present a new method to determine key characteristics of these materials, specifically the topological invariants of complex magnetic systems. Their research introduces a quantum circuit algorithm that efficiently calculates these invariants, offering a pathway to characterise many-body matter previously hampered by computational complexity. This innovative approach relies on carefully controlling the evolution of quantum bits, or qubits, and reveals that the path taken during this evolution can influence the identified invariants, uncovering hidden properties of the material.

Simulating Topological Matter on Noisy Quantum Hardware

This research explores the use of quantum computing to investigate topological phases of matter, focusing on systems difficult to study with classical methods. The work acknowledges the limitations of current quantum hardware and aims to develop methods suitable for near-term devices, bridging the gap between theoretical predictions and experimental realization. Investigations center on higher-order topological insulators and spin systems, particularly Heisenberg models and bond-alternating chains, utilizing the Berry phase as a key indicator of topological order. The core methodology involves designing quantum circuits to simulate the Hamiltonian of spin systems and calculate relevant observables.

Variational Quantum Eigensolvers are employed to approximate the ground state, and circuits are implemented using Qiskit, with simulations performed using AerSimulator. Cross-entropy benchmarking assesses circuit performance, and Suzuki-Trotter decomposition approximates time evolution. Results demonstrate the feasibility of estimating the Berry phase, characterizing topological phases, identifying phase transitions, and simulating complex Hamiltonians, even on relatively small systems. Future work focuses on scaling up simulations to larger systems, exploring more complex materials, developing more efficient quantum algorithms, and validating theoretical predictions with experimental measurements.

The ultimate goal is to leverage quantum computing for quantum materials discovery, quantum sensing, and the development of fault-tolerant quantum computers. Specific systems studied include J1-J2 Heisenberg models, bond-alternating spin chains, K-Γ chains, and nanographene-based spin chains. This research represents a significant step towards understanding and characterizing topological quantum matter using quantum simulation.

Berry Phase Calculation via Adiabatic Quantum Circuits

Researchers have developed a quantum circuit methodology to compute topological invariants, crucial for classifying many-body matter and identifying higher-order symmetry protected topological phases. This approach leverages adiabatic quantum circuits to calculate quantized Berry phases in first and second-order SPT quantum magnets described by a Heisenberg spin-1/2 model, addressing a significant challenge in condensed matter physics. The technique simulates the time evolution of a quantum system along a closed path, extracting the Berry phase, a geometric property reflecting changes in the system’s quantum state. To isolate the Berry phase from the dynamical phase, the team implemented a time-reversal strategy, effectively canceling the dynamical contribution by evolving the system both forwards and backwards in time.

This allows for precise measurement of the Berry phase, which is quantized for systems possessing anti-unitary symmetry. The approach utilizes gate-based quantum circuits, carefully controlling the evolution and employing a Hadamard test to measure the accumulated Berry phase. This innovative method provides a powerful tool for classifying complex quantum materials and predicting novel phases of matter.

Quantum Circuits Reveal Topological Invariants of Matter

Scientists have achieved a breakthrough in characterizing complex quantum materials by developing a novel method to measure their fundamental topological invariants using quantum circuits. This work demonstrates a circuit capable of determining the many-body invariant of a second-order magnet, revealing hidden invariants dependent on the path of quantum evolution. The team’s algorithm leverages adiabatic evolution within transverse paths in parameter space, offering a new approach to characterize many-body matter. Experiments involved simulating time evolution via gate-based adiabatic quantum circuits and extracting the Berry phase using a Hadamard test.

Results demonstrate the ability to classify higher-order symmetry protected topological phases, highlighting the potential for discovering new phases of matter. Specifically, the team successfully quantified the Berry phase by evolving the system forward and backward in time, doubling the loop in parameter space and canceling the dynamical phase. The method was implemented on a dimerized one-dimensional Heisenberg spin-1/2 chain, revealing a clear distinction between strong and weak bonds and confirming the accuracy of the method. The quantum circuit was constructed by decomposing the Hamiltonian and utilizing a second-order Trotter-Suzuki decomposition to approximate the time evolution. Further experiments demonstrated the precision of the measurement, with results for lattice sizes of 4, 6, and 8 exhibiting strong agreement with exact calculations. The ability to distinguish between topological phases using this quantum circuit opens new avenues for materials discovery and the development of quantum technologies.

Berry Phase Defines Topological Invariants

Scientists have developed a new quantum algorithm to calculate topological invariants of higher-order topological quantum paramagnets. This achievement relies on a carefully controlled, high-dimensional evolution of the Berry phase, allowing for the calculation of these invariants in two-dimensional quantum many-body models. The research reveals that the path taken through the system’s parameter space influences the calculated value, requiring careful consideration when defining the invariant. This work represents a significant step towards harnessing the power of quantum computers to understand topology in complex quantum materials. The team uncovered that gauging a symmetry can be intricate, and the choice of path through the parameter space is crucial for accurate results. While the current implementation requires substantial computational resources and precise initial state preparation, future fault-tolerant or topological quantum computers hold the potential to fully realize its capabilities.