Quantum cellular automata for quantum error correction and density classification
arXiv:2309.03608 · doi:10.1103/PhysRevLett.133.150601
Abstract
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells/qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In special, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi-)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum error correction capabilities.
5 pages, 3 figures + supplemental material
References in corpus (39)
- Probing many-body dynamics on a 51-atom quantum simulator
- Trapped-Ion Quantum Computing: Progress and Challenges
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Logical quantum processor based on reconfigurable atom arrays
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
- High-fidelity parallel entangling gates on a neutral atom quantum computer
- Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
- ProjectQ: An Open Source Software Framework for Quantum Computing
- Exponential suppression of bit or phase flip errors with repetitive error correction
- Engineered Dissipation for Quantum Information Science
- A Software Methodology for Compiling Quantum Programs
- Index theory of one dimensional quantum walks and cellular automata
- Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
- A review of Quantum Cellular Automata
- Unitary and non-unitary quantum cellular automata with Rydberg arrays
- Cellular-automaton decoders with provable thresholds for topological codes
- Cellular-automaton decoders for topological quantum memories
- A universally programmable Quantum Cellular Automaton
- Time Asymptotics and Entanglement Generation of Clifford Quantum Cellular Automata
- Local Unitary Quantum Cellular Automata
- Improved error thresholds for measurement-free error correction
- Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
- Measurement-free fault-tolerant quantum error correction in near-term devices
- A quantum cellular automaton for one-dimensional QED
- On fault-tolerance with noisy and slow measurements
- Quantum spin systems on infinite lattices
- Quantum Error Correction with Quantum Autoencoders
- Cellular automaton decoders of topological quantum memories in the fault tolerant setting
- Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
- Free quantum field theory from quantum cellular automata: derivation of Weyl, Dirac and Maxwell quantum cellular automata
- Efficient simulation of quantum error correction under coherent error based on non-unitary free-fermionic formalism
- Small-world complex network generation on a digital quantum processor
- Measurement-free implementations of small-scale surface codes for quantum dot qubits
- Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions
- Signatures of a quantum stabilized fluctuating phase and critical dynamics in a kinetically-constrained open many-body system with two absorbing states
- Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density
- Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata
- High-Threshold Low-Overhead Fault-Tolerant Classical Computation and the Replacement of Measurements with Unitary Quantum Gates