Research ArticleQuantum Mechanics

A quantum annealing architecture with all-to-all connectivity from local interactions

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Science Advances  23 Oct 2015:
Vol. 1, no. 9, e1500838
DOI: 10.1126/sciadv.1500838
  • Fig. 1 Illustration of the fully connected architecture.

    (A) The aim is to encode a system of N logical spins with programmable infinite-range interactions (solid lines). (B) New physical qubit variables are introduced for each of the N(N − 1)/2 interactions, which take the value 1 if two connected logical spins point in the same direction and 0 otherwise. (C) The new physical qubits are noninteracting except for local constraints on plaquettes of four spins. (D) The constraints correspond to closed paths connecting logical spins [for example, the red cross in (D) corresponds to the red lines in (A)]. The number of 0’s in a plaquette can be either 0, 2, or 4. The particular arrangement of new spins shown in (D) allows for a two-dimensional representation of the infinite-range model with local constraints only. An additional row of physical qubits fixed to 1 (yellow) completes the implementation. The solution of the optimization problem can be read out in specific combinations of the physical qubits, for example, as marked in (D).

  • Fig. 2 Time-dependent spectrum.

    (A and B) Energy spectrum of a typical adiabatic sweep with N = 4 logical qubits and an additional random field in the programmable implementation (A) and in a fictitious implementation of the logical qubits (B). Here, t is the time and T is the total time of the sweep. Instantaneous eigenenergies Ei are measured with respect to the ground state, ΔE = EiE0. The constraint strength is C/J = 2, and the elements of the Jij matrix are random numbers uniformly taken from the interval [−J,J]. Although the adiabatic transformation follows different quantum paths, at the end of the sweep an exact correspondence between the lowest levels of the programmable architecture and the original model of classical spins is achieved (dashed lines).

  • Fig. 3 Error tolerance.

    The probability for a spin flip due to decoherence increases with the number of physical qubits (quadratically with N) (red). The information loss per physical qubit decreases with N (blue) and compensates the increased spin flips such that the total error scales linearly (dashed). The number of possible readout sequences (inset) exponentially increases with N.

  • Fig. 4 Higher-order interactions.

    (A) Generalization to three-body interaction terms. (B and C) The translation table (B) from three-body configurations to two-level systems, together with constraints (C), allows for a mapping to a three-dimensional cubic lattice. (D) The physical qubits are aligned in a pyramid-slice configuration. Each side of each cube consists of triples, where one index is identical for all four corners. The constraints, identical to that of the pair interaction case, act on the four spins of each side in a face-centered cubic geometry.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Static error from finite constraint strength
    • Fig. S1. Static error.
    • Energy spectrum during the adiabatic optimization
    • Fig. S2. Success probability.
    • Dynamics
    • Special cases
    • Fig. S3. Special cases.

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