Quantum computers are devices that use (sub)atomic particles to store and process information, instead of the comparatively clumsy and gigantic transistors used by modern classical computers. Recently there have been reaaally intruiging developments in cosmology that have come from re-imagining the laws of physics as a kind of algorithm. In fact it turns out to be very natural to think about our entire universe simply as a set of rules for how a collection of bits in space can share and transform information. This is deeply connected to the notion of duality, whereby two descriptions of nature that look totally different can be proven to encode exactly the same information. This is a bit like the way a piece of code can be written into different programming languages which look nothing alike, while producing an identical structure in bytecode. If two descriptions are dual to each other, there is no really meaningful way in which they are distinct.

 

In a recent paper I developed a quantum computational algorithm for simulating the behavior of a holographic wormhole. The idea of a holographic wormhole comes from The Holographic Principle, which is the idea that everything about our 3-dimensional universe can be encoded onto a 2-dimensional surface that forms the boundary of our universe. This is an exact duality, so for every state that can appear and every action that can happen in a volume of space, there is a corresponding state and action that occurs on its boundary. This is much like the way in which a 3D hologram works by projecting the 3D information from a 2D surface.

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In this paper I designed algorithms for constructing holographic wormholes in a 1-dimensional toy universe called the Ising model. These algorithms were tested using a quantum circuit simulator that I wrote in python and the results were checked against known analytical calculations. Below are some plots from the paper showing the spatial distribution of correlations across the wormhole (x-axis) as a function of the wormhole's temperature (y-axis), for a few different model parameters. Due to the enormous resources required in order for classical computers to simulate quantum computers, my study was limited to a simulation on only 8 qubits. However the algorithms can be scaled arbitrarily. These wormholes have the special property that an observer who only has access to one side of it will observe the wormhole to be totally random. This is because every degree of freedom on one side of the wormhole is 100% correlated with a piece on the other side. The correlations across a boundary therefore increase linearly until the boundary crosses the wormhole, at which point it decreases linearly, as shown in the plots.

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