1,996 research outputs found
Causal Fermions in Discrete Spacetime
In this paper, we consider fermionic systems in discrete spacetime evolving
with a strict notion of causality, meaning they evolve unitarily and with a
bounded propagation speed. First, we show that the evolution of these systems
has a natural decomposition into a product of local unitaries, which also holds
if we include bosons. Next, we show that causal evolution of fermions in
discrete spacetime can also be viewed as the causal evolution of a lattice of
qubits, meaning these systems can be viewed as quantum cellular automata.
Following this, we discuss some examples of causal fermionic models in discrete
spacetime that become interesting physical systems in the continuum limit:
Dirac fermions in one and three spatial dimensions, Dirac fields and briefly
the Thirring model. Finally, we show that the dynamics of causal fermions in
discrete spacetime can be efficiently simulated on a quantum computer.Comment: 16 pages, 1 figur
An algorithm for simulating the Ising model on a type-II quantum computer
Presented here is an algorithm for a type-II quantum computer which simulates
the Ising model in one and two dimensions. It is equivalent to the Metropolis
Monte-Carlo method and takes advantage of quantum superposition for random
number generation. This algorithm does not require the ensemble of states to be
measured at the end of each iteration, as is required for other type-II
algorithms. Only the binary result is measured at each node which means this
algorithm could be implemented using a range of different quantum computing
architectures. The Ising model provides an example of how cellular automata
rules can be formulated to be run on a type-II quantum computer.Comment: 14 pages, 11 figures. Accepted for publication in Computer Physics
Communication
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