Simulating multi-dimensional condensed matter systems with NISQ hardware

Scientists have made a groundbreaking discovery that could revolutionize the field of quantum computing. By developing an approach to simulate higher-order topological lattices using noisy intermediate-scale quantum (NISQ) hardware, researchers have found a potential route to useful quantum advantage in simulating complex condensed matter systems.

This breakthrough has significant implications for various fields, including chemistry and materials science, where simulating complex systems is crucial for understanding their behavior. The projected resource requirements for this approach scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to outperforming classical computers in certain tasks.

The realization of higher-order topological phases in high-dimensional lattices using NISQ hardware has the potential to provide a new platform for quantum computing and quantum simulation. Researchers can use this approach to simulate complex chemical reactions and material properties, leading to breakthroughs in these areas.

Further research is needed to fully explore the capabilities and limitations of NISQ hardware and to identify potential applications for which it can provide unique advantages. However, this discovery marks a significant step forward in the development of quantum computing and its potential to transform various fields of science and technology.

The possibility of quantum computers outperforming classical ones has been a topic of interest for many years. While significant progress has been made in developing programmable quantum simulator platforms, the range of viable applications remains limited due to gate errors and the number of high-quality qubits. However, researchers have developed an approach that places digital noisy intermediatescale quantum (NISQ) hardware as a versatile platform for simulating multi-dimensional condensed matter systems.

This method encodes a high-dimensional lattice in terms of many-body interactions on a reduced dimension model, taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error-mitigation techniques, researchers have measured the topological state dynamics and protected midgap spectra of higher-order topological lattices in up to four dimensions with high accuracy.

The projected resource requirements for this approach scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term. This development is significant, as it opens up new possibilities for simulating complex systems that were previously inaccessible.

Programmable quantum simulators are platforms that allow researchers to simulate complex quantum systems on a quantum computer. These simulators have been developed using various technologies, including superconducting transmon and fluxonium-based processors, trapped ion systems, ultracold atomic lattices, and Rydberg atom arrays.

Recent years have seen tremendous progress in the development of these platforms, with numerous successful demonstrations reported in contexts such as quantum chemistry and quantum many-body dynamics. The hope is that these computational platforms can outperform conventional classical counterparts in a range of useful applications, enabling novel capabilities beyond our current reach.

However, existing studies have focused on highly specific tailored problems, such as random quantum circuit sampling and boson sampling, which limit their broader applicability. Finding applications for which quantum platforms provide unique advantages and pushing the capabilities of near-term NISQ hardware remain pertinent and timely objectives.

The approach developed in this work establishes NISQ hardware as a particularly suitable platform for simulating generic multidimensional condensed matter lattice models. As a demonstration, researchers have utilized their method to realize higher-order topological (HOT) phases in high-dimensional lattices of unprecedented size and complexity.

Unlike previous quantum simulator studies that implemented topological models through synthetic dimensions, this approach realizes HOT lattices in real space in up to four dimensions (a tesseract). Central to the approach is a mapping procedure that encodes single-particle degrees of freedom of a high-dimensional lattice in terms of many-body interactions on a reduced dimension model.

This encoding takes full advantage of the exponentially large Hilbert space of the host quantum system, allowing researchers to simulate complex systems with high accuracy. With circuit optimization and error-mitigation techniques, researchers have measured the topological state dynamics and protected midgap spectra of HOT lattices in up to four dimensions with high accuracy.

Higher-order topological phases (HOTs) are a class of quantum states that exhibit unique properties, such as protected midgap spectra and non-trivial topology. These phases have been the subject of intense research in recent years, as they offer new possibilities for simulating complex systems.

In this work, researchers have realized HOT lattices in real space in up to four dimensions (a tesseract), demonstrating a significant advance over previous studies that implemented topological models through synthetic dimensions. The approach developed here provides a versatile platform for simulating generic multidimensional condensed matter lattice models, opening up new possibilities for research and discovery.

The implications of this work are significant, as it opens up new possibilities for simulating complex systems that were previously inaccessible. By establishing NISQ hardware as a versatile platform for simulating generic multidimensional condensed matter lattice models, researchers have taken an important step towards realizing useful quantum advantage in the longer term.

The projected resource requirements for this approach scale favorably with system size and lattice dimensionality compared to classical computation, suggesting that it may be possible to simulate complex systems that were previously thought to be beyond the reach of NISQ hardware. This development has significant implications for research and discovery, as it opens up new possibilities for simulating complex quantum systems.

The next steps in this work will involve further developing and refining the approach developed here. Researchers will need to continue optimizing circuit designs and error-mitigation techniques to improve the accuracy and efficiency of simulations.

Additionally, researchers will need to explore new applications for NISQ hardware, pushing the capabilities of near-term devices to simulate complex systems that were previously inaccessible. This work has significant implications for research and discovery, as it opens up new possibilities for simulating complex quantum systems.

In conclusion, this work has taken an important step towards realizing useful quantum advantage in the longer term by establishing NISQ hardware as a versatile platform for simulating generic multidimensional condensed matter lattice models. The approach developed here provides a significant advance over previous studies, allowing researchers to simulate complex systems with high accuracy.

The implications of this work are significant, as it opens up new possibilities for research and discovery. By continuing to develop and refine the approach developed here, researchers can push the capabilities of near-term NISQ hardware to simulate complex systems that were previously inaccessible.