Quantum computers fuel materials development Google processor runs largest, scalable variational quantum algorithm

Researchers at the University of Bristol, quantum startup Phasecraft and Google Quantum AI have revealed properties of electronic systems that could be used to develop more efficient batteries and solar panels. properties using a scalable algorithm on a quantum computer" [1], published in the journal Nature Communications.

Ryan Babbush, head of Quantum AI quantum algorithms at Google, said, "We are excited about this experiment designed and executed by Phasecraft, which performs one of the largest digital fermion simulations to date, and one of the largest variational algorithms to date, on Google's quantum computing hardware. "

01Fermi-Hubbard model for more efficient error mitigation techniques

The research team used quantum computers to determine the low-energy properties of strongly correlated electronic systems that cannot be solved by classical computers. To do so, they developed the first truly scalable algorithm for observing the ground state properties of the Fermi-Haberd model on a quantum computer: the Fermi-Haberd model is a way to discover important insights into the electronic and magnetic properties of materials.

Modeling this form of quantum system has important practical implications, including the design of new materials that can be used to develop more efficient solar panels and batteries and even high-temperature superconductors. However, doing so is still beyond the capabilities of the world's most powerful supercomputers. The Fermi-Haberd model is widely considered to be an excellent benchmark for recent quantum computers because it is the simplest system of materials that includes non-trivial correlations beyond those captured by classical methods. The approximation generates the lowest energy (basis) state of the Fermi-Haberd model enabling the user to compute the key physical properties of the model [2].

In the past, researchers have only succeeded in solving small, highly simplified Fermi-Hubbard instances on quantum computers. This study shows that more ambitious results are possible. Using a new, efficient algorithm and better error mitigation techniques, they have successfully conducted an experiment that is four times larger than anything previously recorded and consists of ten times more quantum gates.

02Validating the variational algorithm on a Google superconducting quantum processor

In this work, the team demonstrated that a much smaller number of ansatz layers can still reproduce the qualitative properties of the Fermi-Hubbard model on quantum hardware.

Specifically, the scientists used superconducting quantum processors to apply the variational quantum algorithm (VQE) to Fermi-Haberd instances on 1 × 8 and 2 × 4 lattices and observe expected ground-state physical properties such as metal-insulator jumps (MIT), Friedel oscillations, decay correlations and antiferromagnetic order. These results rely on a series of symmetry-based error mitigation techniques: these techniques greatly improve the accuracy of estimating observables on noise-containing intermediate-scale (NISQ) quantum devices, thus opening the way to useful applications in the near future.

Implementation of efficient Hamiltonian variational ansatz. a) Jordan-Wigner code maps one spin sector of a 2 × 4 lattice to a line; the mapping is repeated for the other spin sector. b), c) Implementation of horizontal terms combined with fermionic exchange (red); then the first set of vertical terms (blue); then another layer of fermionic exchange; then a second set of vertical terms. (d) Quantum circuit structure.

Quantum bit layout implementing two Fermi-Hubbard instances. (a) 1×8 instance, (b) 2×4 instance

Experimental results of the BayesMGD algorithm in the VQE framework and the final energy error associated with the VQE ground state. a) VQE progression for 1 × 8 and 2 × 4 Fermi-Hubbard instances, measured by the error between the energy at parameter θk and the VQE ground state energy Emin (main plot log scale, inset linear scale). b) Final error in the measured energy after error mitigation on the final state error.

03An important breakthrough: the largest scale and first scalable quantum algorithm

"The Fermi-Hubbard example in this experiment represents a key step in the use of quantum computers to solve realistic material systems," said Ashley Montanaro, professor of quantum computing at the University of Bristol and co-founder of Phasecraft: "We have successfully developed the the first truly scalable algorithm, which is particularly exciting because it shows that we will be able to extend our approach to take advantage of more powerful quantum computers as hardware is improved."

Phasecraft brings together many of the world's leading quantum scientists and engineers and partners, and is the world's leading developer of quantum hardware. "We are excited to see this experiment designed and executed by Phasecraft, which performs one of the largest digital fermion simulations to date and one of the largest variational algorithms to date on Google's quantum computing hardware." Ryan Babbush, head of quantum algorithms at Google AI, said [3], "The scalability of their approach stems from the latest techniques in error mitigation and algorithm compilation on recent quantum hardware."