Can quantum computers help to solve questions of general relativity theory?

Question

My question is rather straightforward: Can quantum computers be used to solve problem within general relativity theory?

To put more context. As GR is based on solution of rather complicated systems of differentials equation, often numerical approaches are needed (there is even part of GR called numerical relativity). Since numerical solution of differential equations is based on their conversion to algebraic ones, I can imagine application of linear algebra algorithms like HHL.

Gravity is only force for which we do not have quantum theory which can be renormalized. Hence, there is still quest for building up such theory - loop gravity, string theory etc being candidates. As quantum computers were originally proposed for simulation of quantum systems, it would be possible to use them for that task within quantum gravity theories.

So, I would like therefore ask if any body is aware of papers trying to apply quantum computing within general relativity theory.

Answer 1

Based on comments by Cuhrazatee and my further searching, I figured out that QC can be used in solving problems arising within general relativity. However, as pointed out by Cuhrazatee, differential equations of GR are rather non-linear whereas quantum mechanics, and hence quantum computers, is governed by linear equations. To tackle this difficulty, equations of GR have to be firstly linearized. Fortunately, there are several articles dealing with that and presenting quantum algorithms for solving non-linear differential equations. As these algorithms are general, they can be used also outside GR, e.g. in fluid mechanics (Navier-Stokes equations), plasma physics (somehow related to fluid mechanics) and many other ares.

Here is a brief list of articles dealing with solution of non-linear differential equations:

• Quantum algorithm for nonlinear differential equations
• Efficient quantum algorithm for dissipative nonlinear differential equations
• Improved quantum algorithms for linear and nonlinear differential equations
• Quantum algorithms for nonlinear equations in fluid mechanics

Interestingly, my attention was also brought to an article speculating what would happen if quantum mechanics were non-linear and hence quantum computers allowed to solve non-linear differential equations without necessity of linearization (i.e. natively). Here is a link to question dealing with this (rather speculative) possibility and its consequences for complexity theory.