Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
Magic transition in monitored free fermion dynamics
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
We investigate magic and its connection to entanglement in 1+1 dimensional random free fermion circuits, with a focus on hybrid free fermion dynamics that can exhibit an entanglement phase transition. To quantify magic, we use the Stabilizer R\'enyi Entropy (SRE), which we compute numerically via a perfect sampling algorithm. We show that although the SRE remains extensive as the system transitions from a critical phase to an area-law (disentangled) phase, the structure of magic itself undergoes a delocalization phase transition. This transition is characterized using the bipartite stabilizer mutual information, which exhibits the same scaling behavior as entanglement entropy: logarithmic scaling in the critical phase and a finite constant in the area-law phase. Additionally, we explore the dynamics of SRE. While the total SRE becomes extensive in $O(1)$ time, we find that in the critical phase, the relaxation time to the steady-state value is parameterically longer than that in generic random circuits. The relaxation follows a universal form, with a relaxation time that grows linearly with the system size, providing further evidence for the critical nature of the phase.
fields
quant-ph 6representative citing papers
A sampling method combining fast Walsh-Hadamard transform and Clifford-preconditioned Monte Carlo reduces Pauli-string sampling cost from O(2^N) to O(N) with sample count independent of N for stabilizer Rényi entropies and nullity.
In U(1)-symmetric 1D random circuits the stabilizer Rényi entropy gap closes diffusively as 1/t, with the same scaling seen in an energy-conserving Ising chain.
A tunable mixing parameter p in random quantum circuits controls the transition from classically simulable to expressive quantum reservoir dynamics via entanglement and nonstabilizer content.
citing papers explorer
-
Unitary Designs from Doped Matchgate Circuits
Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
-
Exponentially Accelerated Sampling of Pauli Strings for Nonstabilizerness
A sampling method combining fast Walsh-Hadamard transform and Clifford-preconditioned Monte Carlo reduces Pauli-string sampling cost from O(2^N) to O(N) with sample count independent of N for stabilizer Rényi entropies and nullity.
-
Diffusive Dynamics of Nonstabilizerness
In U(1)-symmetric 1D random circuits the stabilizer Rényi entropy gap closes diffusively as 1/t, with the same scaling seen in an energy-conserving Ising chain.
-
Optimal quantum reservoir learning in proximity to universality
A tunable mixing parameter p in random quantum circuits controls the transition from classically simulable to expressive quantum reservoir dynamics via entanglement and nonstabilizer content.
- Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions
- Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics