Phase diagram of a dissipative quantum system

Dephasing and decay are the intrinsic dissipative processes prevalent in any open quantum system and the dominant mechanisms for the loss of coherence and entanglement. This inadvertent effect not only can be overcome but can even be capitalized on in a dissipative quantum simulation by means of tailored couplings between the quantum system and the environment. In this context it has been demonstrated that universal quantum computation can be performed using purely dissipative elements, and furthermore, the efficient preparation of highly entangled states is possible. In this article, we are interested in nonequilibrium phase transitions appearing in purely dissipative systems and the exploration of quantum phases in terms of a dissipative quantum simulation. To elucidate these concepts, we scrutinize exemplarily two paradigmatic models: the transverse-field Ising model and the considerably more complex ${\mathbb{Z}}_{2}$ lattice gauge theory. We show that the nonequilibrium phase diagrams parallel the quantum phase diagrams of the Hamiltonian ``blueprint'' theories.Dephasing and decay are the intrinsic dissipative processes prevalent in any open quantum system and the dominant mechanisms for the loss of coherence and entanglement. This inadvertent effect not only can be overcome but can even be capitalized on in a dissipative quantum simulation by means of tailored couplings between the quantum system and the environment. In this context it has been demonstrated that universal quantum computation can be performed using purely dissipative elements, and furthermore, the efficient preparation of highly entangled states is possible. In this article, we are interested in nonequilibrium phase transitions appearing in purely dissipative systems and the exploration of quantum phases in terms of a dissipative quantum simulation. To elucidate these concepts, we scrutinize exemplarily two paradigmatic models: the transverse-field Ising model and the considerably more complex ${\mathbb{Z}}_{2}$ lattice gauge theory. We show that the nonequilibrium phase diagrams parallel the quantum phase diagrams of the Hamiltonian ``blueprint'' theories.

arXiv:1408.4616Physical Review AJul 29, 201544 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

Magnetic flux induce dissipation effect on the quantum phase diagram of mesoscopic SQUID array

Sujit Sarkar

We present the quantum phase diagram of mesoscopic SQUID array. We predict different quan- tum phases and the phase boundaries along with several special points. We present the results of magnetic flux induced dissipation on these points and also on the phase boundaries. The Josephson couplings at these points are dependant on the system parameter in a more complicated fashion and differ from the Ambegaokar and Baratoff relation. We derive the analytical relation between the dissipation strength and Luttinger liquid parameter of the system. We observe some interesting behaviour at the half-integer magnetic flux quantum and also the importance of co-tunneling effect.We present the quantum phase diagram of mesoscopic SQUID array. We predict different quan- tum phases and the phase boundaries along with several special points. We present the results of magnetic flux induced dissipation on these points and also on the phase boundaries. The Josephson couplings at these points are dependant on the system parameter in a more complicated fashion and differ from the Ambegaokar and Baratoff relation. We derive the analytical relation between the dissipation strength and Luttinger liquid parameter of the system. We observe some interesting behaviour at the half-integer magnetic flux quantum and also the importance of co-tunneling effect.

arXiv:1108.4498Aug 23, 20110 citations

Dissipative quantum phase transitions

Philipp Werner

Jan 1, 20053 citations

Dissipative Quantum Systems

WORLD SCIENTIFIC eBooksOct 1, 200813 citations

{\mathbb{Z}}_{2}

lattice gauge theory. We show that the nonequilibrium phase diagrams parallel the quantum phase diagrams of the Hamiltonian ``blueprint'' theories.

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.