Quantum Simulations Reveal More Stable Paths to Complex Calculations

Leonard Logarić and colleagues at the Department of Physics, Trinity College Dublin, in collaboration with the Trinity Quantum Alliance, Algorithmiq Limited (Finland), and the Dublin Institute for Advanced Studies, investigate the behaviour of complex quantum systems using digital quantum processors, revealing mechanisms that defy typical thermalisation. A connection between gapless excitations and a recently discovered form of these mechanisms, asymptotic quantum many-body scars, is demonstrated, becoming more stable as system size increases. By preparing these states on Quantinuum’s H1-1 processor with circuits containing up to 418 entangling gates across 20 qubits, the team observed slower thermalisation times with increasing system size, providing the first experimental evidence of asymptotic scars and furthering understanding of ergodicity violation in quantum systems.

Experimental observation of stable quantum states beyond conventional scarring limits

Thermalisation times slowed to beyond 418 entangling ZZ gates, a scale previously unattainable for observing asymptotic quantum many-body scars. Prior methods struggled to probe beyond conventional scars due to limitations in circuit depth and qubit control. A clear link between gapless excitations and these asymptotic scars has been demonstrated, confirming theoretical predictions about their stability as quantum systems increase in size. By constructing a model hosting both conventional and asymptotic scars, and implementing it on the Quantinuum H1-1 trapped-ion processor, the first experimental signatures of these unusual, stable states have been established.

The predicted behaviour of asymptotic quantum many-body scars, or AQMBS, was confirmed by observing slowed thermalisation times extending beyond 418 entangling ZZ gates; these gates are fundamental operations in quantum computing that link qubits together. ZZ gates enact a controlled-Z operation, flipping the phase of a target qubit only if the control qubit is in the |1⟩ state, and are crucial for creating entanglement. The inability to reliably execute many of these gates, maintaining qubit coherence throughout, has historically limited the exploration of long-timescale quantum dynamics. States initially exhibiting non-scar behaviour rapidly lost information, characteristic of typical chaotic quantum systems where energy spreads throughout the many-body Hilbert space. Conventional quantum many-body scars showed decay independent of system size, a known phenomenon where specific initial states retain memory of their initial configuration. Notably, when initialised in an asymptotic scar, the relaxation time increased alongside system size, approaching a stable state as the number of qubits, reaching N = 20, grew. This behaviour aligns with theoretical predictions stemming from gapless excitations, where energy levels converge as the system expands, becoming zero-energy ground states in larger systems. The Quantinuum H1-1 trapped-ion processor was instrumental in preparing these states with logarithmic circuit depth, a measure of computational efficiency, meaning the number of gates required grows proportionally to the logarithm of the system size, rather than linearly.

Experimental validation confirms durability of quantum system stability with increasing size

A slowdown in quantum system chaos is now understood, representing a vital step towards building more stable and reliable quantum computers. Previous work explored ergodicity violating mechanisms like many-body localisation and conventional quantum scars, but this study focused on asymptotic scars, which theoretically become more stable as a system grows. Ergodicity, in this context, refers to the tendency of a closed quantum system to explore all accessible states over time. Violations of ergodicity, such as those induced by many-body localisation or quantum scars, prevent this complete exploration, leading to non-thermal behaviour. This represents a major advance, as it demonstrates the first experimental evidence of these scars using a digital quantum processor, specifically observing slower decay rates in larger systems and confirming the theoretical prediction that these scars become more durable with increased complexity.

This finding strengthens efforts to build robust and reliable quantum computers, capable of tackling complex simulations. The demonstration of asymptotic quantum many-body scars, or AQMBS, establishes a key link between energy levels and the stability of these unusual states within growing quantum systems. Slower decay rates were observed for these scars as system complexity increases when utilising a 20-qubit trapped-ion processor; this challenges the expectation of typical quantum systems becoming chaotic over time. The all-to-all connectivity of the Quantinuum H1-1 processor proved essential in preparing these states with a computationally efficient approach known as Floquet dynamics, repeatedly applying quantum operations to probe system behaviour. Floquet dynamics involves periodically driving the quantum system, effectively creating a time-crystal-like behaviour and allowing for the observation of long-term dynamics that would otherwise be obscured by decoherence. The choice of a trapped-ion system is significant; these qubits exhibit long coherence times and high fidelity gate operations, crucial for maintaining the quantum information throughout the complex simulations. Furthermore, the ability to individually address and control each ion allows for the precise implementation of the required quantum circuits.

The implications of this research extend beyond fundamental quantum physics. Understanding and harnessing ergodicity-breaking mechanisms could lead to the development of more robust quantum algorithms and error correction schemes. Conventional quantum computation relies on the ability to manipulate and entangle qubits, but these operations are susceptible to noise and decoherence. By exploiting the stability offered by AQMBS, it may be possible to create quantum states that are less vulnerable to these errors, paving the way for more practical quantum technologies. Future research will focus on exploring the properties of AQMBS in different quantum systems and investigating their potential applications in quantum information processing and materials science. The ability to simulate complex quantum systems, previously limited by computational resources, is now becoming increasingly accessible through the use of digital quantum processors, opening up new avenues for scientific discovery.

The research demonstrated the first experimental signatures of asymptotic quantum many-body scars in a system of up to 20 qubits. These scars represent a mechanism that hinders the typical chaotic behaviour of quantum systems, leading to slower thermalisation times as the system grows. This finding matters because understanding these ergodicity-breaking mechanisms may contribute to the development of more stable quantum states. Researchers prepared these states using the Quantinuum H1-1 processor and up to 418 entangling gates, and plan to explore AQMBS properties in different quantum systems.