On the structure of Clifford quantum cellular automata
arXiv:0804.4447 · doi:10.1063/1.3005565
Abstract
We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin. In the one dimensional case we also find that every uniquely determined and translationally invariant stabilizer state can be prepared from a product state by a single Clifford cellular automaton timestep, thereby characterizing these class of stabilizer states, and we show that all 1D Clifford quantum cellular automata are generated by a few elementary operations. We also show that the correspondence between translationally invariant stabilizer states and translationally invariant Clifford operations holds for periodic boundary conditions.
28 pages, 2 figures, LaTeX
References in corpus (2)
Cited by in corpus (37)
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- A review of Quantum Cellular Automata
- A computationally universal phase of quantum matter
- Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
- Nontrivial Quantum Cellular Automata in Higher Dimensions
- Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata
- Clifford Quantum Cellular Automata: Trivial group in 2D and Witt group in 3D
- Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
- Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
- Crystalline Quantum Circuits
- Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
- Entanglement Generation of Clifford Quantum Cellular Automata
- Zero-temperature entanglement membranes in quantum circuits
- Scrambling in quantum cellular automata
- Does causal dynamics imply local interactions?
- Exactly solvable many-body dynamics from space-time duality
- Operator dynamics and entanglement in space-time dual Hadamard lattices
- Quantum cellular automata without particles
- Integrable spin chains and the Clifford group
- Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries
- Absence of localization in two-dimensional Clifford circuits
- Invertible subalgebras
- Homological invariants of Pauli stabilizer codes
- Bounds on the Speedup in Quantum signalling
- Classification of measurement-based quantum wire in stabilizer PEPS
- Quantum computation by teleportation and symmetry
- Measurement-based quantum computation from Clifford quantum cellular automata
- Exotic equilibration dynamics on a 1-D quantum CNOT gate lattice
- Entangled quantum cellular automata, physical complexity, and Goldilocks rules
- Kicked-Ising Quantum Battery
- The fractal structure of cellular automata on Abelian groups
- The Equivalence of Schrödinger and Heisenberg Pictures in Quantum Cellular Automata
- An overview of Quantum Cellular Automata
- Non-trivial Lyapunov spectrum from fractal quantum cellular automata
- Quantum Algorithm of Evolutionary Analysis of 1D Cellular Automata
- On the bosonic behavior of mean-field fluctuations in atomic ensembles
- Remarks on the structure of Clifford quantum cellular automata