Quantum Magic in Discrete-Time Quantum Walk
arXiv:2506.17783 · doi:10.1103/7rwg-lhpv
Abstract
Quantum magic, which accounts for the non-stabilizer content of a state, is essential for universal quantum computation beyond classically simulable resources. We investigate the generation and evolution of quantum magic in discrete-time quantum walks (DTQWs) using the Stabilizer Renyi Entropy as a measure of quantum magic. We investigate single- and two-walker quantum walks on a one-dimensional lattice, considering a wide range of initial coin states. Our results reveal that DTQWs can dynamically generate significant magic, with the amount and structure strongly dependent on the initial state of the coin. In the case of a single walker, the relationship between magic and entanglement is found to be nontrivial and complementary at long times. These findings position DTQWs as accessible and controllable platforms for producing quantum magic, offering a new perspective on their role in quantum information processing and reliable quantum computation.
Accepted for publication in Physical Review Research
References in corpus (26)
- Universal computation by quantum walk
- Spatial search by quantum walk
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Exploring Topological Phases With Quantum Walks
- Universal computation by multi-particle quantum walk
- Strongly Correlated Quantum Walks in Optical Lattices
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
- Stabilizer Rényi entropy
- Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
- Ideal negative measurements in quantum walks disprove theories based on classical trajectories
- Stabilizer entropies and nonstabilizerness monotones
- Measuring magic on a quantum processor
- Stabilizer entropies are monotones for magic-state resource theory
- Phase transition in magic with random quantum circuits
- Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
- Magic spreading in random quantum circuits
- Efficient quantum algorithms for stabilizer entropies
- Dynamical Magic Transitions in Monitored Clifford+T Circuits
- Entanglement-magic separation in hybrid quantum circuits
- Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
- Persistence of Topological Phases in Non-Hermitian Quantum Walks
- Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
- The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
- Maximal Magic for Two-qubit States
- Deterministic generation of hybrid entangled states using quantum walks