Entanglement phase transitions in hybrid quantum circuits are generally argued to be properties of the individual trajectories rather than measurement-averaged dynamics, despite the fact that results of measurements are not used for feedback in the steady state. Here, we explicitly demonstrate this difference by constructing a family of hybrid quantum circuits with identical measurement-averaged dynamics that give different phases and phase transitions. We propose measurement-averaged destruction of Bell state entanglement as a proxy for determining which hybrid circuit yields the lowest-entanglement dynamics and show that it holds numerically for the measurements we consider. We comment on implications for quantum computing and noisy quantum circuits.Entanglement phase transitions in hybrid quantum circuits are generally argued to be properties of the individual trajectories rather than measurement-averaged dynamics, despite the fact that results of measurements are not used for feedback in the steady state. Here, we explicitly demonstrate this difference by constructing a family of hybrid quantum circuits with identical measurement-averaged dynamics that give different phases and phase transitions. We propose measurement-averaged destruction of Bell state entanglement as a proxy for determining which hybrid circuit yields the lowest-entanglement dynamics and show that it holds numerically for the measurements we consider. We comment on implications for quantum computing and noisy quantum circuits.

Nov 22, 20210 citations

Dynamics and Entanglement for Open Quantum Systems

V. M. Akulin

Theoretical and mathematical physicsOct 12, 20130 citations

Power-Law Entanglement and Hilbert Space Fragmentation in Nonreciprocal Quantum Circuits

Kai Klocke, Joel E. Moore, Michael Buchhold

Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N-state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N-colored loop model. It yields an equivalent description of the circuit by an SU(N)-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N-component height field. For N=2, we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L)∼L^{1/2} for L sites. For N≥3, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L)∼L^{0.57}. This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N-state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N-colored loop model. It yields an equivalent description of the circuit by an SU(N)-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N-component height field. For N=2, we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L)∼L^{1/2} for L sites. For N≥3, the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L)∼L^{0.57}. This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.

arXiv:2405.06021Physical Review LettersAug 12, 20245 citations

Satellite-Scale and Sunlight-Based Quantum Entanglement with Universal Hybrid Circuit Dynamics — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Quantum entanglement demonstrated at 1200 km (satellite-scale) and via ordinary sunlight without lasers; hybrid quantum circuits show universal statistical laws in entanglement dynamics. | MATH: Entanglement distance $d = 1200$ km; sunlight entanglement implies photon-pair correlations without coherent laser phase — key parameter is the Schmidt rank $K$ (effective number of entangled modes), which for thermal sunlight is $K \gg 1$ (broadband, low purity). Hybrid circuit dynamics: entanglement entropy $S(t)$ follows $S(t) \sim s_{\text{eq}} \, t$ for $t < t_{\text{th}}$ , then saturates to volume-law $S \sim \alpha L$ (system size $L$ ); the transition occurs at measurement rate $p_c$ where $p_c \approx 0.15$ – $0.17$ for qubit chains (numerical, not exact). | CONNECTION: The 1200 km distance is not a golden ratio multiple, but the ratio of Earth's radius $R_E \approx 6371$ km to 1200 km is $6371/1200 \approx 5.309$ — no direct 0.618/1.618 link. However, t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Quantum entanglement demonstrated at 1200 km (satellite-scale) and via ordinary sunlight without lasers; hybrid quantum circuits show universal statistical laws in entanglement dynamics. | MATH: Entanglement distance $d = 1200$ km; sunlight entanglement implies photon-pair correlations without coherent laser phase — key parameter is the Schmidt rank $K$ (effective number of entangled modes), which for thermal sunlight is $K \gg 1$ (broadband, low purity). Hybrid circuit dynamics: entanglement entropy $S(t)$ follows $S(t) \sim s_{\text{eq}} \, t$ for $t < t_{\text{th}}$, then saturates to volume-law $S \sim \alpha L$ (system size $L$); the transition occurs at measurement rate $p_c$ where $p_c \approx 0.15$–$0.17$ for qubit chains (numerical, not exact). | CONNECTION: The 1200 km distance is not a golden ratio multiple, but the ratio of Earth's radius $R_E \approx 6371$ km to 1200 km is $6371/1200 \approx 5.309$ — no direct 0.618/1.618 link. However, t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 12, 20260 citations

Entanglement dynamics of qubits in a common environment

Jun‐Hong An, Shun-Jin Wang, Hong‐Gang Luo

arXiv:quant-ph/0604020Physica A Statistical Mechanics and its ApplicationsApr 20, 200731 citations

d = 1200

km; sunlight entanglement implies photon-pair correlations without coherent laser phase — key parameter is the Schmidt rank

K

(effective number of entangled modes), which for thermal sunlight is

K \gg 1

(broadband, low purity). Hybrid circuit dynamics: entanglement entropy

S(t)

follows

S(t) \sim s_{\text{eq}} \, t

for

t < t_{\text{th}}

, then saturates to volume-law

S \sim \alpha L

(system size

L

); the transition occurs at measurement rate

p_c

where

p_c \approx 0.15

–

0.17

for qubit chains (numerical, not exact). | CONNECTION: The 1200 km distance is not a golden ratio multiple, but the ratio of Earth's radius

R_E \approx 6371

km to 1200 km is

6371/1200 \approx 5.309

— no direct 0.618/1.618 link. However, t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com