In quantum mechanics, the Heisenberg uncertainty principle prevents an external observer from measuring both the position and speed (referred to as momentum) of a particle at the same time.
They can only know with a high degree of certainty either one or the other – unlike what happens at large scales where both are known. To identify a given particle's characteristics, physicists introduced the notion of quasi-distribution of position and momentum. This approach was an attempt to reconcile quantum-scale interpretation of what is happening in particles with the standard approach used to understand motion at normal scale, a field dubbed classical mechanics.
In a new study published in EPJ ST, Dr J.S. Ben-Benjamin and colleagues from Texas A and M University, USA, reverse this approach; starting with quantum mechanical rules, they explore how to derive an infinite number of quasi-distributions, to emulate the classical mechanics approach. This approach is also applicable to a number of other variables found in quantum-scale particles, including particle spin.
For example, such quasi-distributions of position and momentum can be used to calculate the quantum version of the characteristics of a gas, referred to as the second virial coefficient, and extend it to derive an infinite number of these quasi-distributions, so as to check whether it matches the traditional expression of this physical entity as a joint distribution of position and momentum in classical mechanics.
This approach is so robust that it can be used to replace quasi-distributions of position and momentum with time and frequency distributions. This, the authors note, works for both well-determined scenarios where time and frequency quasi-distributions are known, and for random cases where the average of time and average of frequency are used instead.
University of Innsbruck
Quantum simulation more stable than expected
Quantum computers promise to solve certain computational problems exponentially faster than any classical machine. "A particularly promising application is the solution of quantum many-body problems utilizing the concept of digital quantum simulation", says Markus Heyl from Max Planck Institute for the Physics of Complex in Dresden, Germany. "Such simulations could have a major impact on quantum chemistry, materials science and fundamental physics."
Within digital quantum simulation the time evolution of the targeted quantum many-body system is realized by a sequence of elementary quantum gates by discretizing time evolution, called Trotterization.
"A fundamental challenge, however, is the control of an intrinsic error source, which appears due to this discretization", says Markus Heyl. Together with Peter Zoller from the Department of Experimental Physics at the University of Innsbruck and the Institute of Quantum Optics and Quantum Communication at the Austrian Academy of Sciences and Philipp Hauke from the Kirchhoff Institute for Physics and the Institute for Theoretical Physics at the University of Heidelberg they show in a recent paper in Science Advances that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables.
More robust than expected
"Digital quantum simulation is thus intrinsically much more robust than what one might expect from known error bounds on the global many-body wave function", Heyl summarizes. This robustness is characterized by a sharp threshold as a function of the utilized time granularity measured by the so-called Trotter step size.
"The threshold separates a regular region with controllable Trotter errors, where the system exhibits localization in the space of eigenstates of the time-evolution operator, from a quantum chaotic regime where errors accumulate quickly rendering the outcome of the quantum simulation unusable.
"Our findings show that digital quantum simulation with comparatively large Trotter steps can retain controlled Trotter errors for local observables", says Markus Heyl.
"It is thus possible to reduce the number of quantum gate operations required to represent the desired time evolution faithfully, thereby mitigating the effects of imperfect individual gate operations." This brings digital quantum simulation for classically challenging quantum many-body problems within reach for current day quantum devices.
