Tensor Networks provide efficient quantum circuits

The findings, published today in Nature Communications, describe how the team have demonstrated that a type of mathematical tool called tensor networks can be used to simulate quantum systems on Google’s Rainbow device – a quantum device that shares its architecture with the Sycamore chip used by Google in 2019 to demonstrate quantum supremacy.

Quantum computers offer the opportunity to explore problems that are thought be unfeasible on classical computers. One potential application is the ability to simulate chemical reactions and material properties that could revolutionize drug discovery or search for new battery materials.

Current quantum computers, so called noisy intermediate scale quantum (NISQ) computers do not have the computational resources needed to directly simulate large quantum systems. However, these devices give researchers the ability to test the future applications of quantum computers.

Corresponding author and UCL PhD candidate from the EPSRC Centre for Doctoral Training in Delivering Quantum Technologies, James Dborin, said: “Finding challenging but feasible problems that can be implemented on current devices is crucial. As well as demonstrating the progress that has been made, these serve to highlight required improvements. Ideally, these problems would be solved more efficiently when suitably powerful quantum computers are developed, as compared to current classical computers.”

The team describe that problems that best display these properties can be found in condensed matter systems – the matter that surrounds us in everyday life. Problems in this area can be scaled to fit current machines while retaining scientific and technological relevance.

Tensor networks provide the best classical approach to simulating condensed matter systems, but more importantly the researchers show that tensor network methods can be directly translated to quantum circuits.

In the study, the team provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve the states that describe simple one-dimensional quantum condensed matter systems. The team report that their circuits are considerably simpler than previous proposals.

All the code used to generate the results is available to download. The next step for the researchers is developing their algorithms to simulate two- or three-dimensional quantum systems.

Professor Andrew Green from UCL’s London Centre for Nanotechnology said: “This work shows the utility of tensor networks in constructing efficient quantum circuits, with the potential for quantum advantage in the next generation of quantum computers.”

Dborin said: “Our algorithms operate directly in the thermodynamic limit - avoiding difficulties of finite-size scaling near criticality. We demonstrate that approximations to the groundstate can be optimised on current devices to good accuracy even at the quantum critical point, and present a significant simplification over previous proposals of the cost-function that can faithfully track dynamics when implemented on the Rainbow device.”

This research received funding from the UK Engineering and Physical Sciences Research Council (EPSRC). This research is an outcome of the EPSRC Prosperity Partnership in Quantum Simulation, led by UCL and Google.

Links:

• Read the article in full at Nature Communications
• Find out more about Tensor Network with the International Quantum Tensor Network
• Visit Professor Andrew Green’s academic profile
• Find out more about UCL’s EPSRC CDT in Delivering Quantum Technologies