New Method Enables Long-Term Quantum Simulation of Topological States, Promises Future Applications

The study of topological properties of matter is a current frontier of physics, with potential applications in high-performance transistors, quantum sensors, and transport devices. However, the role of topology in quantum systems remains unclear, particularly in the time-domain. Quantum computers could help simulate these systems, but current models are limited by readout noise, gate-error rates, and short coherence times. A new method has been introduced that uses contemporary quantum hardware to simulate the long-time quantum dynamics of topological matter, potentially opening up new avenues for research and applications in quantum science.

What is the Role of Topology in Quantum Systems?

The study of topological properties of matter is a current frontier of physics. Chiral phenomena, which are characterized by their unique emergent behaviors, have been observed in various systems such as acoustic and mechanical systems, photonics, and magnetic materials. Symmetry-protected topological (SPT) phases, the paradigmatic models for realizing such chiral states, are characterized by their protection via global symmetries. A consequence of topological symmetry protection is the predicted robustness of SPT phases against local noise and perturbations. This opens avenues for foundational research and numerous device applications in quantum science, such as novel high-performance transistors, quantum sensors, and protected room-temperature transport devices.

However, the investigation of chiral topological modes within the time-domain remains ambiguous, especially within the context of open system time evolution. Understanding the role of topology in the dynamics of quantum systems is a timely endeavor, which has been exceptionally challenging to realize and control due to the inherent difficulty of accessing sensitive many-body quantum states. As intrinsically quantum platforms, a pioneering application of quantum computers is the physical simulation of many-body systems, where in special-use cases practical quantum advantage has recently been shown to be achievable.

How Can Quantum Computers Simulate Many-Body Systems?

Quantum computers have the potential to physically simulate many-body systems. This potential is currently being explored using photonic simulators, ultracold atoms, hybrid-quantum simulation, and periodically driven quantum simulators. While these provide a promising route to investigate condensed matter systems, many-body interactions that would otherwise be intractable for analog quantum simulators are well suited for digital quantum simulation. This provides universal capability to realize any finite-dimensional local Hamiltonian using sequences of quantum circuits.

Although topological states have been prepared and observed using digital quantum simulation, the analysis of transient behavior of topological modes in the time-domain presents a particular set of challenges. A primary reason is the effect of readout noise and gate-error rates, which have sharply limited reliable quantum simulation of interacting many-body systems. The computational power and effectiveness of current noisy intermediate-scale quantum (NISQ) computers is restricted by the number and quality of qubits.

What are the Limitations of Current Quantum Computers?

Current NISQ-era qubits have short coherence times and high gate-error rates, which demand the requirement for noise mitigation and error correction schemes. Moreover, quantum simulations for generic Hamiltonians require that the circuit depth scales linearly at minimum with the number of simulation time steps according to the No-Fast-Forwarding Theorem. These restraints make prolonged time evolution of many-body systems exceedingly challenging for conventional approaches.

To date, a reliable method to realize the long-time dynamics of topological phases of matter using digital quantum simulation is not available due to these limitations. Prior simulations are largely restricted in the number and width of time-step intervals, making the analysis of transient dynamics, which is non-negligible when interaction with the environment is present, unreachable.

How Can Long-Time Quantum Dynamics of Topological Matter be Realized?

A method to realize the long-time quantum dynamics of topological matter using contemporary quantum hardware has been introduced. This positions NISQ computation as an adequate environment to probe novel phases of matter. In comparison to previous methods, which have been limited in the total time duration or restricted entirely to the space-domain, this protocol enables the quantum simulation of topological states in one spatial dimension, nominally up to arbitrarily long times.

This one-dimensional protocol can be extended to higher dimensions with larger system implementations and mathematical developments. A subset of Hamiltonians with novel topological properties that are now tractable with this result has been identified. Its ability to predict physical results does not rely on employing readout error mitigation or post-processing techniques, though the output precision can benefit from such techniques.

What is the Future of Quantum Simulation of Topological States?

The future of quantum simulation of topological states looks promising with the introduction of this new method. By engineering interactions between qubits, the long-time quantum dynamics of topological matter can be realized using contemporary quantum hardware. This positions NISQ computation as an adequate environment to probe novel phases of matter.

This new protocol enables the quantum simulation of topological states in one spatial dimension, nominally up to arbitrarily long times. This one-dimensional protocol can be extended to higher dimensions with larger system implementations and mathematical developments. A subset of Hamiltonians with novel topological properties that are now tractable with this result has been identified. Its ability to predict physical results does not rely on employing readout error mitigation or post-processing techniques, though the output precision can benefit from such techniques. This opens up new avenues for foundational research and numerous device applications in quantum science.