Quantinuum H2-2 Demonstrates Energy-Resolved Transport and 8×7 Lattice Localization

Researchers are tackling the challenge of understanding how energy affects the movement of particles within complex systems. Melody Lee (College of Computing, Georgia Institute of Technology & Institute for Quantum Information and Matter, California Institute of Technology) and Roland C Farrell (Institute for Quantum Information and Matter, California Institute of Technology & Department of Physics) et al demonstrate a novel technique using ‘wavepackets’ to precisely measure energy-resolved transport on quantum computers. Their work overcomes limitations of previous methods by preparing states with much finer energy control, allowing them to identify a crucial ‘mobility edge’ in the Anderson model on Quantinuum’s H2-2, a key indicator of how easily particles can move through a material. Significantly, the team also developed an error mitigation strategy improving data accuracy by up to fivefold, and extended this approach to simulate multiple interacting particles, paving the way for exploring complex transport phenomena in near-term quantum devices.

This breakthrough reveals a clear distinction in behaviour between low-energy and high-energy wavepackets, with the former remaining spatially localised and the latter delocalising, a direct consequence of the mobility edge. Crucially, the team implemented an error mitigation strategy based on maximum-likelihood estimation, which infers the noiseless output bit string distribution and reduces statistical uncertainty by up to a factor of 5 when compared to post-selection techniques.

The study unveils a method for preparing states with tunable energy and minimal energy variance, overcoming limitations inherent in previous approaches that relied on quench dynamics of simple initial states. Existing techniques often suffer from limited energy resolution due to the energy variance of computational basis states scaling with system size, hindering precise analysis of transport properties. By employing wavepackets, superpositions of low-energy excitations, the researchers achieved a significant improvement in energy resolution, particularly in lower dimensions, where the energy variance scales as O(N−2/D). This allows for a more detailed investigation of phenomena like mobility edges, which separate localised and extended eigenstates and govern energy-dependent transport behaviour.

The experiments successfully identified this transition in the Anderson model, confirming the theoretical prediction of a critical energy separating these distinct states. Furthermore, the research establishes a quantum algorithm for preparing quasiparticle wavepackets in a one-dimensional model of interacting fermions, extending the methodology to the many-particle regime. This algorithm, applied to the XXZ model, combines variational ground state preparation with the use of W states for efficient wavepacket creation, requiring modest quantum resources. The resulting wavepackets represent superpositions of low-energy quasiparticle excitations, enabling the study of transport properties over an energy interval independent of system size. This work opens exciting possibilities for near-term quantum computers to investigate complex many-body systems and address challenges intractable for classical computation, potentially revolutionising our understanding of material properties and quantum phenomena. The team’s error mitigation strategy, utilising maximum-likelihood estimation, proved instrumental in achieving accurate results and reducing statistical errors, paving the way for more reliable quantum simulations.

Wavepacket Probing Reveals Anderson Localisation Edge in Disordered

Scientists engineered a novel methodology employing wavepackets to probe energy-dependent transport in quantum simulators, addressing limitations inherent in existing techniques that rely on quench dynamics of basis states. These initial states, far from energy eigenstates, restrict achievable energy resolution, prompting the development of this wavepacket-based approach to enhance precision. The research team prepared and evolved wavepackets on Quantinuum’s H2-2 device to identify a finite-size mobility edge within the Anderson model on an 8×7 lattice, demonstrating the utility of their technique. Crucially, the study observed that a low-energy wavepacket remained spatially localized during time evolution, while a high-energy counterpart delocalized, confirming the presence of the mobility edge and validating the method’s sensitivity.

To achieve this, researchers meticulously crafted wavepackets, superpositions of low-energy excitations forming Gaussian-shaped energy distributions, allowing for tunable momentum and access to a range of energies. The team harnessed the dispersion relation to precisely control the energy of the wavepackets, enabling targeted probing of transport properties. Experiments employed a custom algorithm for preparing quasiparticle wavepackets within a one-dimensional model of interacting fermions, significantly reducing quantum resource requirements and opening avenues for studying many-body systems. This innovative approach achieves a substantial improvement in energy resolution compared to traditional product states, where energy variance scales with system size N, as wavepacket energy variance scales as O(N−2/D) where D is the spatial dimension.

A pivotal aspect of the work involved an error mitigation strategy utilizing maximum-likelihood estimation to infer the noiseless output bit string distribution. This method, unlike post-selection, effectively removes systematic errors and reduces statistical uncertainty by up to a factor of 5, bolstering the reliability of the results. The team validated their quantum simulations through comparison with classical counterparts, achieving excellent agreement after applying the error mitigation protocol. This combination of precise wavepacket preparation, sophisticated error mitigation, and rigorous validation establishes a powerful new tool for investigating energy-dependent transport phenomena in quantum systems.

Wavepackets reveal Anderson model mobility edge behavior

Scientists achieved a breakthrough in probing energy-dependent transport in quantum simulators by utilizing wavepackets to prepare states with tunable energy and minimal energy variance. The team demonstrated this approach on Quantinuum’s H2-2 processor, identifying an energy-dependent localization transition within the Anderson model on an 8×7 lattice, effectively a finite-size mobility edge. Experiments revealed that a wavepacket initialized with low energy remained spatially localized during time evolution, whereas a high-energy wavepacket delocalized, confirming the presence of this mobility edge and providing direct evidence of energy-dependent behaviour. Crucially, the research incorporated an error mitigation strategy employing maximum-likelihood estimation to infer the noiseless output bit string distribution.

Measurements confirm this method removed systematic errors and reduced statistical uncertainty by up to a factor of 5, significantly enhancing the reliability of the results. The team measured the Inverse Participation Ratio (IPR) to quantify localization, finding that the IPR values clearly distinguished between localized and delocalized wavepackets at different energies. Data shows that for low energies, the IPR remained high, indicating strong localization, while at higher energies, the IPR decreased, signifying delocalization. Furthermore, the study extended beyond single wavepackets, investigating the IPR as a function of energy for various disorder strengths (W).

Results demonstrate a clear trend: the IPR decreases with increasing energy, indicating that higher-energy states are less localized. Specifically, the team observed that the magnitude of |h√E|√WPi|2, where Pi is the probability of finding the particle at a given location, varied significantly with momentum, highlighting the anisotropic nature of the localization. The researchers also explored the impact of different initial momenta on the wavepacket dynamics. They found that the IPR values were sensitive to the initial momentum, with wavepackets initialized at different momenta exhibiting distinct localization patterns. This provides further insight into the complex interplay between energy, momentum, and localization in disordered systems. These findings pave the way for more accurate and efficient simulations of complex quantum phenomena, offering a powerful tool for materials science and fundamental physics research.

Wavepackets reveal Anderson model mobility edge behavior

Scientists have developed a novel technique employing wavepackets to investigate energy-dependent transport phenomena in quantum simulators. This approach allows for improved energy resolution compared to traditional methods that utilise simple initial states, offering a more precise probe of system dynamics. Researchers successfully demonstrated this by identifying an energy-dependent localization transition, a finite-size mobility edge, in the Anderson model on Quantinuum’s H2-2 device. The key achievement lies in the preparation and evolution of wavepackets, revealing that low-energy wavepackets remain localised, while high-energy ones delocalise, confirming the presence of the mobility edge.

Furthermore, the team implemented an error mitigation strategy based on maximum-likelihood estimation, significantly reducing statistical uncertainty, by up to a factor of five, compared to post-selection techniques. They also extended their methodology to many-particle systems, devising an algorithm for creating quasiparticle wavepackets in a one-dimensional model of interacting fermions, suggesting potential for near-term applications.