A Quantum Multiverse Model

The circuit model of quantum computation is reformulated as a multilayer network theory [3] called a Quantum Multiverse Network (QuMvN). The QuMvN formulation allows us to interpret the quantum wave function as a combination of ergodic Markov Chains where each Markov Chain occupies a different layer in the QuMvN structure. Layers of a QuMvN are separable components of the corresponding wave function. Single qubit measurement is defined as a state transition of the Markov Chain that emits either a $0$ or $1$ making each layer of the QuMvN a Discrete Information Source. A message is equivalent to a possible measurement outcome and the message length is the number of qubits. Therefore, the quantum wave function can be treated as a combination of multiple discrete information sources analogous to what Shannon called a "mixed" information source [18]. We show the QuMvN model has significant advantages in the classical simulation of some quantum circuits by implementing quantum gates as edge transformations on the QuMvNs. We implement a quantum virtual machine capable of simulating quantum circuits using the QuMvN model and use our implementation to classically simulate Shor's Algorithm [19]. We present results from multiple simulations of Shor's Algorithm culminating in a $70$ qubit simulation of Shor's Algorithm on a commodity cloud server with $96$ CPUS and $624$ GB of RAM. Lastly, the source of quantum speedups is discussed in the context of layers in the QuMvN framework and how randomized algorithms can push the quantum supremacy boundary.The circuit model of quantum computation is reformulated as a multilayer network theory [3] called a Quantum Multiverse Network (QuMvN). The QuMvN formulation allows us to interpret the quantum wave function as a combination of ergodic Markov Chains where each Markov Chain occupies a different layer in the QuMvN structure. Layers of a QuMvN are separable components of the corresponding wave function. Single qubit measurement is defined as a state transition of the Markov Chain that emits either a $0$ or $1$ making each layer of the QuMvN a Discrete Information Source. A message is equivalent to a possible measurement outcome and the message length is the number of qubits. Therefore, the quantum wave function can be treated as a combination of multiple discrete information sources analogous to what Shannon called a "mixed" information source [18]. We show the QuMvN model has significant advantages in the classical simulation of some quantum circuits by implementing quantum gates as edge transformations on the QuMvNs. We implement a quantum virtual machine capable of simulating quantum circuits using the QuMvN model and use our implementation to classically simulate Shor's Algorithm [19]. We present results from multiple simulations of Shor's Algorithm culminating in a $70$ qubit simulation of Shor's Algorithm on a commodity cloud server with $96$ CPUS and $624$GB of RAM. Lastly, the source of quantum speedups is discussed in the context of layers in the QuMvN framework and how randomized algorithms can push the quantum supremacy boundary.

arXiv:1909.09863Sep 21, 20190 citations

Quantum Multiverses

James B. Hartle

A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the universe's spacetime geometry and matter content. These consequences follow: (a) The universe generally exhibits different quantum multiverses at different levels and kinds of coarse graining. (b) Quantum multiverses are not a choice or an assumption but are consequences of the theory or not. (c) Quantum multiverses are generic for simple theories (d) Anthropic selection is automatic because observers are physical systems within the universe not somehow outside it. (e) Quantum multiverses can provide different mechanisms for the variation constants in effective theories (like the cosmological constant) enabling anthropic selection. (f) Different levels of coarse grained multiverses provide different routes to calculation as a consequence of decoherence. We support these conclusions by analyzing the quantum multiverses of a variety of quantum cosmological models aimed at the prediction of observable properties of our universe. In particular we show how the example of a multiverse consisting of a vast classical spacetime containing many pocket universes arises automatically as part of a quantum multiverse describing an eternally inflating false vacuum that decays by the quantum nucleation of true vacuum bubbles. In a FAQ we argue that the quantum multiverses of the universe are scientific, real, testable, falsifiable, and similar to those in other areas of science even if they are not directly observable on arbitrarily large scales.A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the universe's spacetime geometry and matter content. These consequences follow: (a) The universe generally exhibits different quantum multiverses at different levels and kinds of coarse graining. (b) Quantum multiverses are not a choice or an assumption but are consequences of the theory or not. (c) Quantum multiverses are generic for simple theories (d) Anthropic selection is automatic because observers are physical systems within the universe not somehow outside it. (e) Quantum multiverses can provide different mechanisms for the variation constants in effective theories (like the cosmological constant) enabling anthropic selection. (f) Different levels of coarse grained multiverses provide different routes to calculation as a consequence of decoherence. We support these conclusions by analyzing the quantum multiverses of a variety of quantum cosmological models aimed at the prediction of observable properties of our universe. In particular we show how the example of a multiverse consisting of a vast classical spacetime containing many pocket universes arises automatically as part of a quantum multiverse describing an eternally inflating false vacuum that decays by the quantum nucleation of true vacuum bubbles. In a FAQ we argue that the quantum multiverses of the universe are scientific, real, testable, falsifiable, and similar to those in other areas of science even if they are not directly observable on arbitrarily large scales.

arXiv:1801.08631WORLD SCIENTIFIC eBooksDec 9, 20205 citations

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making each layer of the QuMvN a Discrete Information Source. A message is equivalent to a possible measurement outcome and the message length is the number of qubits. Therefore, the quantum wave function can be treated as a combination of multiple discrete information sources analogous to what Shannon called a "mixed" information source [18]. We show the QuMvN model has significant advantages in the classical simulation of some quantum circuits by implementing quantum gates as edge transformations on the QuMvNs. We implement a quantum virtual machine capable of simulating quantum circuits using the QuMvN model and use our implementation to classically simulate Shor's Algorithm [19]. We present results from multiple simulations of Shor's Algorithm culminating in a

70

qubit simulation of Shor's Algorithm on a commodity cloud server with

96

CPUS and

624

GB of RAM. Lastly, the source of quantum speedups is discussed in the context of layers in the QuMvN framework and how randomized algorithms can push the quantum supremacy boundary.