November 30, 2022

Fast-Forwarding Quantum Evolution: Physical Features Boost the Efficiency of Quantum Simulations

Two current documents settle long-standing questions about algorithms on future quantum computers.
Current theoretical advancements have settled two enduring concerns about the viability of mimicing quantum systems on future quantum computer systems, getting rid of challenges from complexity analyses to allow more sophisticated algorithms. Included in two publications, the work by a quantum group at Los Alamos National Laboratory shows that physical homes of quantum systems enable faster simulation methods.

” Algorithms based upon this work will be needed for the first major demonstration of quantum simulations on quantum computers,” stated Rolando Somma, a quantum theorist at Los Alamos and coauthor on the 2 papers.
Low-energy quantum states key to much faster quantum simulation
The paper “Hamiltonian simulation in the low-energy subspace” demonstrates that the complexity of a quantum simulation algorithm depends on the appropriate energy scale and not the full variety of energies of the system, as previously thought. Some quantum systems can have states of unbounded energies, hence simulations would prove intractable even on big quantum computers.
This new research study discovered that, if a quantum system explores the low-energy states only, it might be simulated with low complexity on a quantum computer system without errors crashing the simulation.
” Our work supplies a course to an organized study of quantum simulations at low energies, which will be needed to push quantum simulations closer to truth,” stated Burak Sahinoglu, a theoretical physicist at Los Alamos and lead author on the paper, published in the journal Quantum Information, a Nature partner journal.
” We show that at every action of the algorithm, you never escape to the huge energies,” said Somma. “Theres a way of writing your quantum algorithm so that after each action youre still within your low-energy subspace.”
The authors stated their research uses to a large class of quantum systems and will be useful in simulating quantum field theories, which describe physical phenomena within their low-energy states.
Fast-forwarding of quantum systems bypasses the time-energy unpredictability concept
The other paper, “Fast-forwarding quantum development,” a cooperation with Caltechs Shouzhen Gu– a former Los Alamos quantum computing summer school student– is released in Quantum. It reveals 3 quantum systems in which a quantum simulation algorithm can run faster– and in many cases tremendously quicker– than the limits recommended by the time-energy uncertainty principle.
” In quantum mechanics, the best precision that can be attained when measuring a systems energy scales, in general, with the inverse of the duration of the measurement,” said Somma.
” However, this principle does not apply to all quantum systems, specifically those that have particular physical functions,” stated Sahinoglu.
The authors revealed that when this principle is bypassed, such quantum systems can also be simulated really efficiently, or fast-forwarded, on quantum computer systems.
Referrals:
” Hamiltonian simulation in the low-energy subspace” by Burak Sahinoglu and Rolando D. Somma, 27 July 2021, npj Quantum Information.DOI: 10.1038/ s41534-021-00451-w.
” Fast-forwarding quantum evolution” by Shouzhen Gu, Rolando D. Somma and Burak Sahinoglu, 15 November 2021, Quantum.DOI: 10.22331/ q-2021-11-15-577.
Financing: DOE SC HEP, ASCR, National Quantum Information Science Research Centers, Quantum Science.

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