There are many versions of the argument supporting this hypothesis, which has become more plausible (or at least more popular) over time as computational power, and our familiarity with computers and virtual worlds within them, has increased.
Modern cosmology suggests that our universe, our galaxy, and our solar system, have billions of years ahead of them, during which our civilization (currently only ~10ky old!), and others, will continue to evolve. It seems reasonable that technology and science will continue to advance, delivering ever more advanced computational platforms. Within these platforms it is likely that quasi-realistic simulations, of our world, or of imagined worlds (e.g., games), will be created, many populated by AI agents or avatars. The number of simulated beings could eventually be much larger than the number of biologically evolved sentient beings. Under these assumptions, it is not implausible that we ourselves are actually simulated beings, and that our world is not base reality.
One could object to using knowledge about our (hypothetically) simulated world to reason about base reality. However, the one universe that we have direct observational contact with seems to permit the construction of virtual worlds with large populations of sentient beings. While our simulation may not be entirely representative of base reality, it nevertheless may offer some clues as to what is going on "outside"!
The simulation idea is very old. It is almost as old as computers themselves. However, general awareness of the argument has increased significantly, particularly in the last decade. It has entered the popular consciousness, transcending its origins in the esoteric musings of a few scientists and science fiction authors.
The concept of a quantum computer is relatively recent -- one can trace the idea back to Richard Feynman's early-1980s Caltech course: Physical Limits to Computation. Although quantum computing has become a buzzy part of the current hype cycle, very few people have any deep understanding of what a quantum computer actually is, and why it is different from a classical computer. A prerequisite for this understanding is a grasp of both the physical and mathematical aspects of quantum mechanics, which very few possess. Individuals who really understand quantum computing tend to have backgrounds in theoretical physics, physics, or perhaps computer science or mathematics.
The possibility of quantum computers requires that we reformulate the Simulation Hypothesis in an important way. If one is willing to posit future computers of gigantic power and complexity, why not quantum computers of arbitrary power? And why not simulations which run on these quantum computers, making use of quantum algorithms? After all, it was Feynman's pioneering observation that certain aspects of the quantum world (our world!) are more efficiently simulated using a quantum computer than a classical (e.g., Turing) machine. (See quantum extension of the Church-Turing thesis.) Hence the original Simulation Hypothesis should be modified to the Quantum Simulation Hypothesis: Do we live in a quantum simulation?
There is an important consequence for those living in a quantum simulation: they exist in a quantum multiverse. That is, in the (simulated) universe, the Many Worlds description of quantum mechanics is realized. (It may also be realized in base reality, but that is another issue...) Within the simulation, macroscopic, semiclassical brains perceive only one branch of the almost infinite number of decoherent branches of the multiverse. But all branches are realized in the execution of the unitary algorithm running on qubits. The power of quantum computing, and the difficulty of its realization, both derive from the requirement that entanglement and superposition be maintained in execution.
Given sufficiently powerful tools, the beings in the simulation could test whether quantum evolution of qubits under their control is unitary, thereby verifying the absence of non-unitary wavefunction collapse, and the existence of other branches (see, e.g., Deutsch 1986).
We can give an anthropic version of the argument as follows.
1. The physical laws and cosmological conditions of our universe seem to permit the construction of large numbers of virtual worlds containing sentient beings.
2. These simulations could run on quantum computers, and in fact if the universe being simulated obeys the laws of quantum physics, the hardware of choice is a quantum computer. (Perhaps the simulation must be run on a quantum computer!)
If one accepts points 1 and 2 as plausible, then: Conditional on the existence of sentient beings who have discovered quantum physics (i.e., us), the world around them is likely to be a simulation running on a quantum computer. Furthermore, these beings exist on a branch of the quantum multiverse realized in the quantum computer, obeying the rules of Many Worlds quantum mechanics. The other branches must be there, realized in the unitary algorithm running on (e.g., base reality) qubits.
See also
Gork revisited 2018
Are You Gork?
Big Ed
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