The Computational universe: Quantum gravity from quantum computation

Abstract

A theory of quantum gravity based on quantum computation is proposed. In this theory, fundamental processes are described in terms of quantum information processing: the geometry of space-time is a construct, derived from the underlying quantum computation. Explicit mechanisms are provided for the back-reaction of the metric to computational 'matter,' black-hole evaporation, holography, and quantum cosmology. 1 Quantum computation can be thought of as a universal theory for discrete quantum mechanics: quantum computers are discrete systems that evolve by local interactions [1], and every discrete quantum system that evolves by local interactions, including lattice gauge theories, can be simulated efficiently on a quantum computer [2]. The quantization of gravity remains one of the primary challenges to physics [3-4]. If, at bottom, quantum gravity is a discrete, local quantum theory [5], then quantum gravity, too, should be describable as a quantum computation. This paper proposes a method of unifying quantum mechanics and gravity based on quantum computation. The basic idea of the 'computational universe' research program proposed here is that what happens to quantum information is fundamental: all other aspects of the universe, including the metric structure of spacetime and the behavior of quantum fields, are derived from the underlying quantum computation. To paraphrase Wheeler, 'it from qubit' [6-7]. The key technique in the program for deriving gravity from quantum computation is to take a quantum computation's causal structure, its 'wiring diagram,' and to embed it in a space-time manifold. The metric for the manifold is then derived from the causal and logical structure of the computation. Since the form of the embedding has no influence on the results of the underlying quantum computation, the resulting theory coupling gravity to quantum computation is automatically generally covariant. That is, embedding a quantum computation in space-time and deriving the metric from the computation automatically gives a finite, fully covariant quantum theory of gravity. The theory proposed here differs from conventional approaches to quantum gravity such as string theory [8], canonical quantization [9], loop quantum gravity [10-11], and Euclidean quantum gravity [12] in that it does not set out to quantize gravity directly. The only thing that is quantum here is information: gravity arises out of the underlying quantum computation. In this theory, the metric is derived from the behavior of quantum bits; because those qubits exhibit quantum fluctuations, so does the metric. The closest existing approach to the one taken here is perhaps …