Universal quantum computation and quantum error correction using discrete holonomies

• Holonomic quantum computation exploits a quantum state's nontrivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through parameter space have been well researched. Discrete holonomies, on the other hand, where the state jumps from point to point in state space, have had little prior investigation. Using a sequence of incomplete projective measurements of the spin operator, we build an explicit approach to universal quantum computation. We show that quantum error correction codes integrate naturally in our scheme, providing a model for measurement-based quantum computation that combines the passive error resilience of holonomic quantum computation and active error correction techniques. In the limit of dense measurements we recover known continuous-path holonomies.

Subject headings

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

NATURVETENSKAP  -- Fysik -- Atom- och molekylfysik och optik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Atom and Molecular Physics and Optics (hsv//eng)

Keyword

Quantum computation

quantum error correction

quantum measurements

geometric phase

spin coherent states

Fysik

Physics

Fysik med inriktning mot atom- molekyl- och kondenserande materiens fysik

Physics with spec. in Atomic, Molecular and Condensed Matter Physics

Publication and Content Type

ref (subject category)

art (subject category)