Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation

Abstract

We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient universal quantum computation with the result of the computation encoded in the steady state. Due to the purely dissipative nature of the process, this way of doing quantum computation exhibits some inherent robustness and defies some of the DiVincenzo criteria for quantum computation. We show that there is a natural class of problems that can be solved with such a model - the preparation of ground states of frustration free quantum Hamiltonians. This allows for robust and efficient creation of exotic states that exhibit features like topological quantum order and the creation of PEPS and it proves the existence of novel dissipative phase transitions. In particular the latter can in principle be verified experimentally with present day technology such as with optical lattices.

7 pages

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Cited by in corpus (14)

• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Topology by Dissipation in Atomic Quantum Wires
• Quantum Decoherence
• Dissipation induced Tonks-Girardeau gas in an optical lattice
• Full counting statistics and phase diagram of a dissipative Rydberg gas
• Linear Optics Simulation of Non-Markovian Quantum Dynamics
• Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping
• Mixing times and cutoffs in open quadratic fermionic systems
• Topological transport in the steady state of a quantum particle with dissipation
• Measurement-induced phase transition in teleportation and wormholes
• Protecting subspaces by acting on the outside
• Uniqueness regime for Markov dynamics on quantum lattice spin systems
• An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma
• Molecular machines for quantum error correction