Quantum simulation more stable than expected

A localization phenomenon increases the accuracy of solving multiple-body quantum problems with quantum computers. These problems are also difficult for conventional computers. This allows digital quantum simulation to be within our reach thanks to the quantum devices available today.

Quantum computers promise to solve some computing problems exponentially faster than any conventional machine. "A particularly promising solution is the solution of multi-body quantum problems using the concept of digital quantum simulation," says Markus Heyl of the Max Planck Institute for Complex Physics in Dresden, Germany. "Such simulations could have a major impact on quantum chemistry, material science, and fundamental physics."

In numerical quantum simulation, the temporal evolution of the targeted multi-body quantum system is performed by a sequence of elementary quantum gates by discretizing temporal evolution, a process called trotterization. "A fundamental challenge, however, is the control of an intrinsic error source, which appears because of this discretization," said Markus Heyl.

With international colleagues, they showed in a recent Progress of science article that quantum localization by constraining temporal evolution through quantum interference strongly limits these errors for local observables.

More robust than expected

"Digital quantum simulation is therefore inherently much more robust than one would expect from known error terminals on multibody body wave function," Heyl explains. This robustness is characterized by a net threshold as a function of the temporal granularity used as measured by the size of the trotter pitch. The threshold separates a regular region with controllable trotter errors, where the system shows a location in the operator's own states space of evolution over time, of a quantum regime chaotic where errors accumulate quickly, rendering the result of quantum simulation unusable.

"Our results show that digital quantum simulation with relatively large Trotter steps can maintain controlled Trotter errors for local observables," says Markus Heyl. "It is thus possible to reduce the number of quantum gate operations necessary to accurately represent the desired time course, thereby mitigating the effects of imperfect individual gate operations." This puts digital quantum simulation for classical multibody quantum problems within the reach of today's quantum devices.