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Dirac-2

Overview

Dirac-2 is a "qudit" entropy quantum computer. It minimizes quadratic Hamiltonian operators over a positive integer domain. It uses the same principles as Dirac-1 and all other EQC devices to perform computations.

Our Qudit Programming model

Our qudit programming model, available on the Dirac-2 quantum computer, is
H(z)=∑jhjzj+∑ijJijzizjH(z)=\sum_jh_jz_j+\sum_{ij}J_{ij}z_iz_j
where the z’s are integer variables which can have the values 0 − 63 and {h, J} are constants. Analogous to the QUBO and Ising model, the programmer’s job is to set the h values (linear terms) and J values (quadratic terms) in order to solve the problem, which has been expressed in integer decision variables. There is an additional built-in constraint as follows:
∑jzj=100\sum_jz_j=100
This constraint is specific to Dirac-2. Subsequent generations of EQC will have the flexibility to specify the sum total and eventually, no restriction. An implication of this constraint is that a model must have a natural constraint, which can have its variables scaled to the range 1-100 or the modeling done in a clever way to fit into the total. Another consequence is that interpretation of the model may lead to non-integer results. Again, this is a step in the development of Dirac and not a long-term restriction.

Data format

To upload a Hamiltonian operator, we encode it in a sparse matrix format as shown below. We use Numpy array notation. The order-2 Hamiltonian supported by Dirac-2 has two parts. The first part is a single-dimension array for the linear terms. The second part is a two-dimension array for the quadratic terms. They will be called `h` and `J`, respectively.
1
h = np.array([-1, -1, -1])
1
J = np.array([[0, -1.5, 0.5], [-1.5, 0, 0], [0.5, 0, 0]])
,
We put these together into one matrix sized NxN+1.
1
H = np.hstack([h, J])
then the JSON will take the following list of dictionary sparse matrix format: {(i,j): value}
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hamiltonian_data = {
  "data": [
    {
      "i": 0,
      "j": 0,
      "val": -1
    },
    {
      "i": 1,
      "j": 0,
      "val": -1
    },
    {
      "i": 2,
      "j": 0,
      "val": -1,
    },
    {
      "i": 0,
      "j": 2,
      "val": -1.5
    },
    {
      "i": 0,
      "j": 3,
      "val": 0.5
    },
    {
      "i": 1,
      "j": 1,
      "val": -1.5
    },
    {
      "i": 2,
      "j": 1,
      "val": 0.5
    }
  ],
  "file_name": "simple_hamiltonian.json", # can be any short string
  "num_variables": 3, # number of rows
  "file_type": "hamiltonian" # defines the data type as hamiltonian
}

Uploading

To upload the matrix encoded above in hamiltonian_data, we use the the qci_client imported previously. The following line
1
response_json = qci.upload_file(qubo_data)
The response contains a file_id for the uploaded file. This id is provided when a job is run, along a few other parameters (see #Running). Note: the same file_id can be used multiple times to run a problem repeatedly. This enables an "upload once, run many times" scheme, which is especially useful for job types in which parameter searches may be involved.

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