Quantum hardware characterized by programmable bose-hubbard Hamiltonians
An apparatus includes a first group of superconducting cavities and a second group of superconducting cavities, each of which is configured to receive multiple photons. The apparatus includes couplers, where each coupler couples one superconducting cavity from the first group with one cavity from the second group such that the photons in the coupled superconducting cavities interact. A first superconducting cavity of the first group is connected to a second superconducting cavity of the second group, such that photons of the first and second superconducting cavities are shared by each of the first and second superconducting cavities. The first superconducting cavity is coupled to at least one other superconducting cavity of the first group to which the second superconducting cavities are coupled, and the second superconducting cavity is coupled to at least one other superconducting cavity of the second group to which the first superconducting cavities are coupled.
1. A method of operating a quantum computing device comprising a plurality of superconducting cavities inductively coupled via Josephson junctions, the method comprising:
initializing the quantum computing device to an initial Mott-insulator state with no phase coherence and localized wavefunctions;
causing a quantum phase transition of the quantum computing device from the initial Mott-insulator state to a superfluid state; and
adiabatically guiding the quantum computing device to a ground state encoded by a problem Hamiltonian.
2. The method of claim 1 , further comprising:
causing a quantum phase transition of the quantum computing device from the ground state encoded by the problem Hamiltonian to a final Mott-insulator state; and
reading the state of each superconducting cavity in the quantum computing device in the final Mott-insulator state.
3. The method of claim 2 , wherein reading the state of each superconducting cavity in the quantum computing device comprises determining a photon occupation of each cavity mode.
4. The method of claim 2 , wherein the problem Hamiltonian is characterized as Hp=Σ i h i n i +Σ i U i n i (n i −1)+Σ i,j U i,j n i n j , where n i and n j are particle number operators denoting an occupation number of cavities i and j, respectively, h i and h j are representative of site disorder of cavities i and j, respectively, U i is an on-site interaction of cavity i, and Σ i,j U i,j n i n j is a density-density interaction between cavity i and cavity j.
5. The method of claim 2 , further comprising training the quantum computing device as a Quantum Boltzmann Machine, wherein training the quantum computing device as a Quantum Boltzmann Machine comprises:
training the quantum computing device for probabilistic inference on Markov Random Fields by defining a set of output visible nodes y i , as different photon occupation numbers at a first plurality of superconducting cavities of the quantum computing device and configuring Josephson junctions coupling the first plurality of the superconducting cavities to a second plurality of the superconducting cavities and to reproduce certain probability distribution of outcomes at the output visible nodes y i when the second plurality of superconducting cavities are treated as corresponding to hidden nodes x i in the Markov Random Field.
6. The method of claim 5 , wherein the training is such that: a delocalized energy ground state of a Bose-Hubbard model for each input state has a probability distribution over a computational basis that resembles an output probability distribution function (PDF) of a training example, p({x j }, {y i }).