Quantum lattice gas algorithmic representation of gauge field theory
arXiv:1609.02225 · doi:10.1117/12.2246702
Abstract
Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles contained in the spacetime. Despite being a lattice based algorithm, Lorentz invariance is preserved down to the grid scale, with the continuum Dirac Hamiltonian generating the local unitary evolution even at that scale: there is nonlinear scaling between the smallest observable time and that time measured in the quantum field theory limit, a kind of time dilation effect that emerges on small scales but has no effect on large scales. The quantum lattice gas algorithm correctly accounts for the anticommutative braiding of indistinguishable fermions---it does not suffer the Fermi-sign problem. It provides a highly convergent numerical simulation for strongly-correlated fermions equal to a covariant path integral, presented here for the case when a Dirac particle's Compton wavelength is large compared to the grid scale of the qubit array.
arXiv commentSPIE Quantum Information Science and Technology, Paper 9996-22 (2016)
References in corpus (14)
- Elementary gates for quantum computation
- Two-Bit Gates are Universal for Quantum Computation
- Quantum simulation of the Dirac equation
- Experimental realization of a quantum algorithm
- Efficient Simulation of Quantum Systems by Quantum Computers
- Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
- A Universal Two--Bit Gate for Quantum Computation
- Quantum simulation of the Klein paradox with trapped ions
- Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata
- Direct observation of zitterbewegung in a Bose-Einstein condensate
- Simulating quantum mechanics on a quantum computer
- Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades
- Quantum lattice-gas models for the many-body Schrodinger equation
- Quantum logic as superbraids of entangled qubit world lines
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- Discretizing quantum field theories for quantum simulation
- A single-particle framework for unitary lattice gauge theory in discrete time
- The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media
- Some Comments on Unitary Qubit Lattice Algorithms for Classical Problems