Generating topological order: No speedup by dissipation
نویسندگان
چکیده
منابع مشابه
Generating topological order: No speedup by dissipation
We consider the problem of converting a product state to a ground state of a topologically ordered system through a locally generated open-system dynamic. Employing quantum-information tools, we show that such a conversion takes an amount of time proportional to the diameter of the system. Our result applies to typical twodimensional topologically ordered systems as well as, for example, the th...
متن کاملSupplemental Material for : “ Generating topological order : no speedup by dissipation ”
Here we consider the problem of transferring information from a few qubits into the code space C ⊂ (C2)⊗n of a topological code (i.e., the degenerate ground space of a Hamiltonian of the form (1) in the main text, defined on a qubit lattice with local stabilizers Πa having support with diameter bounded by an ‘interaction length’ ξ and a code distance growing with L – see below). An encoder is a...
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We consider the problem of preparing topologically ordered states using unitary and non-unitary circuits, as well as local time-dependent Hamiltonian and Liouvillian evolutions. We prove that for any topological code in D dimensions, the time required to encode logical information into the ground space is at least Ω(d), where d is the code distance. This result is tight for the toric code, givi...
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2014
ISSN: 1098-0121,1550-235X
DOI: 10.1103/physrevb.90.045101