#36 – Quantum Simulation Theory: the limitations of simulating a quantum reality

In episode 36 of the quantum consciousness series, Justin Riddle describes the popular simulation hypothesis and discusses the implication of running the simulation using quantum computers. First off, Justin makes the argument that the foundation of the simulation hypothesis is strictly based in a digital computer framework. If the world is deterministic and digitizable, then it could in principle be simulated. But, if the world is quantum mechanical – with superposition, measurement, and entanglement – then the world might be non-deterministic or require simulation of the entire universe to capture all the necessary information to make the simulation perfect. Luckily, quantum computer scientists have been working on the concept of simulation for decades. Universal quantum simulation is the theory that if you set up a quantum computer to have the same inputs and the same quantum circuit, then you will get the same probability distribution on different quantum computers. However, when you measure that output, then you get a random digital output drawn from that probability distribution. This means that you can simulate the wave function but measurement fundamentally disrupts the simulation and creates divergence. If you were attempting to simulate a quantum system, then you simulation would start to diverge with each subsequent measurement and by the time you are multiple measurements into the future, reality might be unrecognizably different from the simulation. This massively reduced the controllability and the conclusion is reached that a quantum simulation that fully approximates the world is not sustainable for any substantial amount of time. Second is the problem of scaling. In a digital computer, you can write code that derives a more complicated world from some simple principles. However, in a quantum system, the informational complexity of the system explodes exponentially at every evolution of the wave function. Scientists running quantum simulations of molecular interactions for example are looking to create quantum computers with comparable complexity to those chemical systems in order to simulate them. This is a challenge for the simulation hypothesis because the creator of the simulation would need to have a computer as big as the universe itself in order to run the simulation – there does not appear to be any effective compression techniques for quantum computers. Third, the no-cloning theorem of quantum mechanics states that each wave function is uniquely identifiable and cannot be copied in principle. While the probability distribution of a quantum system can be approximated by other quantum computers, the array of entanglement relationships of a quantum system to the world at large cannot be simulated. This means that any quantum simulation will not be a perfect replication in principle, which could lead to an uncanny valley where the simulation is missing something and appears fake despite attempts to enhance the realism. With all of these metaphysical arguments in mind, there is still a persistent phenomenology of feeling like you are in a simulation. For example, high doses of psychedelic drugs can induce the dissociative feeling that everything around you is fake and this is the first moment of your life. If you were a quantum computer living within a physical brain, then the experience of accessing the data of your brain might be akin to the feeling of living in a simulation. Here you are in the moment collapsing the wave function and entering unique moments of time, but the data you are accessing in your brain contains the narrative construct of your life and knowledge. Hence, a removal of typical “neural access” might create the perception of living in a simulation. Lots to think about in this one! Hope you enjoy