We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.
Irreversibility and entanglement spectrum statistics in quantum circuits / Shaffer, Daniel; Chamon, Claudio; Hamma, Alioscia; Mucciolo, Eduardo R.. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2014:P12007(2014). [10.1088/1742-5468/2014/12/P12007]
Irreversibility and entanglement spectrum statistics in quantum circuits
Alioscia Hamma;
2014
Abstract
We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.File | Dimensione | Formato | |
---|---|---|---|
Shaffer_2014_J._Stat._Mech._2014_P12007.pdf
accesso aperto
Licenza:
Non specificato
Dimensione
899.79 kB
Formato
Adobe PDF
|
899.79 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.