As a key index for applications of a device, the device's reliability is its ability to survive (function normally over time) under the influence of some environment. In this paper we present a quantum energy-storing device model with a quantum spin chain, whose environment influence is described by the Lindblad master equation. Here the device survives if the spin system stays in the state with nonzero excitations; otherwise, it fails. Because the Lindblad dynamics enforces one-way energy decay and strict irreversibility of the failure state, we can investigate the reliability of the quantum device directly using classical reliability theory. Focusing on the minimal nontrivial case -- a two-site spin-1/2 chain -- we derive closed-form expressions for the reliability and the hazard rate. The dynamics exhibit an overdamped-underdamped crossover controlled by the competition between coherent exchange and dissipation inhomogeneity. The exact analytical formulas are in excellent agreement with numerical simulations. More importantly, we establish an experimentally accessible protocol for assessing reliability based on first-passage time statistics.As a key index for applications of a device, the device's reliability is its ability to survive (function normally over time) under the influence of some environment. In this paper we present a quantum energy-storing device model with a quantum spin chain, whose environment influence is described by the Lindblad master equation. Here the device survives if the spin system stays in the state with nonzero excitations; otherwise, it fails. Because the Lindblad dynamics enforces one-way energy decay and strict irreversibility of the failure state, we can investigate the reliability of the quantum device directly using classical reliability theory. Focusing on the minimal nontrivial case -- a two-site spin-1/2 chain -- we derive closed-form expressions for the reliability and the hazard rate. The dynamics exhibit an overdamped-underdamped crossover controlled by the competition between coherent exchange and dissipation inhomogeneity. The exact analytical formulas are in excellent agreement with numerical simulations. More importantly, we establish an experimentally accessible protocol for assessing reliability based on first-passage time statistics.

quant-pharXiv:2603.11484Physics Letters AMar 13, 20260 citations

Dissipation driven quantum phase transition in a spin chain

Philipp Werner, Matthias Troyer, Klaus Voelker +1 more

APSMar 1, 20040 citations

Large-scale quantum simulations of dissipative spin-1/2 Heisenberg chains

João C. Getelina, Andrew Cox, Muhammad Asaduzzaman +4 more

A quantum many-body system coupled to an environment relaxes to a nonequilibrium steady state that can sustain order with no equilibrium counterpart. Computing such steady states is harder than closed-system dynamics as the density matrix problem squares the Hilbert-space dimension, and no free energy selects the steady state. The dissipative spin-1/2 Heisenberg chain is a benchmark example for nonequilibrium steady state physics; various methods have each calculated its phase diagram but do not agree, and a controlled determination at large system size has remained out of reach. Here we simulate the Lindblad dynamics of chains of up to 50 sites on the superconducting processor ibm_kingston -- 100 simultaneously active qubits at up to 1700 entangling-gate depths -- realizing the dissipation via Stinespring dilation. The system's dissipative evolution is a self-correcting mechanism that effectively erases errors, so hardware noise enters only as a weak competing dissipator. We measure static structure factors and resolve ferromagnetic, antiferromagnetic, spin-density-wave, and paramagnetic steady states, mapping the phase diagram with 117 quantum hardware data points across the $J_x$ -- $J_y$ plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.A quantum many-body system coupled to an environment relaxes to a nonequilibrium steady state that can sustain order with no equilibrium counterpart. Computing such steady states is harder than closed-system dynamics as the density matrix problem squares the Hilbert-space dimension, and no free energy selects the steady state. The dissipative spin-1/2 Heisenberg chain is a benchmark example for nonequilibrium steady state physics; various methods have each calculated its phase diagram but do not agree, and a controlled determination at large system size has remained out of reach. Here we simulate the Lindblad dynamics of chains of up to 50 sites on the superconducting processor ibm_kingston -- 100 simultaneously active qubits at up to 1700 entangling-gate depths -- realizing the dissipation via Stinespring dilation. The system's dissipative evolution is a self-correcting mechanism that effectively erases errors, so hardware noise enters only as a weak competing dissipator. We measure static structure factors and resolve ferromagnetic, antiferromagnetic, spin-density-wave, and paramagnetic steady states, mapping the phase diagram with 117 quantum hardware data points across the $J_x$--$J_y$ plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.

quant-pharXiv:2609.16108Sep 16, 20260 citations

Statistical physics of quantum systems : novel orders and dynamics

Naomichi Hatano

Physical Society of Japan eBooksJan 1, 20058 citations

Quantum Spin Chains with Site Dissipation

Philipp Werner, Matthias Troyer, Subir Sachdev A

We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with the predictions from a dissipative $ϕ^4$ field theory.We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with the predictions from a dissipative $ϕ^4$ field theory.

arXiv:cond-mat/0412529Journal of the Physical Society of JapanJan 1, 200547 citations

Dynamic properties of quantum spin chains

Joachim Stolze, Taras Verkholyak, Oleg Derzhko +1 more

Oct 15, 20076 citations

J_x

J_y

plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.

ϕ^4

field theory.