A two-dimensional dissipative quantum cellular automaton achieves passive quantum error correction with a nonzero noise threshold and supports fault-tolerant universal computation.
Reversible quantum cellular automata
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions this allows us to give an explicit characterization of all local rules generating such automata. The same local rules also generate the global time step for automata with periodic boundary conditions. Our main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitary operations in a generalized Margolus partitioning scheme. This implies that, in contrast to the classical case, the inverse of a nearest neighbor quantum cellular automaton is again a nearest neighbor automaton. We present several construction methods for quantum cellular automata, based on unitaries commuting with their translates, on the quantization of (arbitrary) reversible classical cellular automata, on quantum circuits, and on Clifford transformations with respect to a description of the single cells by finite Weyl systems. Moreover, we indicate how quantum random walks can be considered as special cases of cellular automata, namely by restricting a quantum lattice gas automaton with local particle number conservation to the single particle sector.
verdicts
UNVERDICTED 6representative citing papers
Exact Fibonacci many-body scars engineered via soliton skeleton and invisible decorations in Rule-54 QCA, with finite translation orbits producing low-entanglement Floquet states.
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.
The authors define the QA-KS(φ) gate family embedding Toffoli with Hadamard sandwich and CP kickback, provide its exact 8x8 unitary, and demonstrate orthogonality to CCX on q0=1 inputs while agreeing on q0=0.
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
Proposes continuous matrix product operators for QFT with closed-form matrix-function expressions from continuum limits of MPOs that preserve area-law entanglement and enable new continuous unitaries beyond quantum cellular automata.
citing papers explorer
-
Mobility edges in pseudo-unitary quasiperiodic quantum walks
A pseudo-unitary quasiperiodic quantum walk model exhibits a novel mobility edge sharply dividing metallic and insulating phases plus a second transition unique to discrete time, with PT-symmetry breaking quantified by spectral winding number.