(I might still have to reverse the bit order for permutation expectation value calculation, or exchange the inverse quantum Fourier transform for the non-inverse, but the hard work of updating the Qrack API and plugin, to trivialize these tasks, is done.)
Inspired (loosely) by Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit, the work presented in that article naturally leads us to question, "If an early FLRW universe could be modeled as a quantum computer program successively entangling more qubits in a growing Hubble sphere volume, then what is the particular ideal circuit definition of the evolution of a universe, in terms of specific gates?"
If we think of the (trans-Planckian) initially unentangled qubits being added to the "circuit" as separable and uniformly random in initial state, an obvious guess is that this initial state constitutes a random matrix product state in phasespace, which time-evolution of the system maps ultimately to a pure state end result in configurationspace. If our Hilbert space basis is discrete, with a finite maximum entropy, this process is simply an inverse FFT, or "QFT," "quantum Fourier transform."
Each additional "layer" of the QFT, composing a full QFT of progressively 1 more qubit at a time at each layer, constitutes 1 exponential "fold" or doubling of the size of the longest harmonic degree of freedom that determines the scale factor. As the space expands, the first qubits to cross the trans-Planckian boundary are stretched most, and therefore remain the longest. We assume that many separate gravitons constitute this wave function, stochastically, but unitary evolution keeps the overall total probability of all stochastic states in the system equal to 1, such that we can simulate the stochastic system as a single pure state. (Admittedly, we assume these modes are the quasi-monopole graviton waves of the author's, Strano's, hobbyist quantum gravity work, but the applicability of this simple of a simulation is likely far broader, independent of resemblance to that particular hypothesis.)
This would likely be more accurate if "annealed" continuously, rather than proceeding in discrete steps, but I wanted to demonstrate that we can hook up OpenRelativity to "graph" the results of this very simple simulation with vm6502q/qrack, to some degree of "resolution." I have used my non-canonical interpretation of interior Schwarzschild metric, as a demonstration, but the quantum mechanics of FLRW would be basically or exactly the same, if we accept the other parts of the premise.
(I might still have to reverse the bit order for permutation expectation value calculation, or exchange the inverse quantum Fourier transform for the non-inverse, but the hard work of updating the Qrack API and plugin, to trivialize these tasks, is done.)
Inspired (loosely) by Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit, the work presented in that article naturally leads us to question, "If an early FLRW universe could be modeled as a quantum computer program successively entangling more qubits in a growing Hubble sphere volume, then what is the particular ideal circuit definition of the evolution of a universe, in terms of specific gates?"
If we think of the (trans-Planckian) initially unentangled qubits being added to the "circuit" as separable and uniformly random in initial state, an obvious guess is that this initial state constitutes a random matrix product state in phase space, which time-evolution of the system maps ultimately to a pure state end result in configuration space. If our Hilbert space basis is discrete, with a finite maximum entropy, this process is simply an inverse FFT, or "QFT," "quantum Fourier transform."
Each additional "layer" of the QFT, composing a full QFT of progressively 1 more qubit at a time at each layer, constitutes 1 exponential "fold" or doubling of the size of the longest harmonic degree of freedom that determines the scale factor. As the space expands, the first qubits to cross the trans-Planckian boundary are stretched most, and therefore remain the longest. We assume that many separate gravitons constitute this wave function, stochastically, but unitary evolution keeps the overall total probability of all stochastic states in the system equal to 1, such that we can simulate the stochastic system as a single pure state. (Admittedly, we assume these modes are the quasi-monopole graviton waves of the author's, Strano's, hobbyist quantum gravity work, but the applicability of this simple of a simulation is likely far broader, independent of resemblance to that particular hypothesis.)
This would likely be more accurate if "annealed" continuously, rather than proceeding in discrete steps, but I wanted to demonstrate that we can hook up OpenRelativity to "graph" the results of this very simple simulation with vm6502q/qrack, to some degree of "resolution." I have used my non-canonical interpretation of interior Schwarzschild metric, as a demonstration, but the quantum mechanics of FLRW would be basically or exactly the same, if we accept the other parts of the premise.