Merge pull request #1059 from qiboteam/encodings

Creation of `qibo.models.encodings` and implementation of `unary_encoder`

doc/source/api-reference/qibo.rst

@@ -222,6 +222,20 @@ Adiabatic evolution
     :members:
     :member-order: bysource
 
+
+.. _data-encoders:
+
+Data Encoders
+^^^^^^^^^^^^^
+
+We provide a family of algorithms that encode classical data into quantum circuits.
+
+Unary Encoder
+"""""""""""""
+
+.. autofunction:: qibo.models.encodings.unary_encoder
+
+
 .. _error-mitigation:
 
 Error Mitigation

src/qibo/models/__init__.py

@@ -1,5 +1,6 @@
 from qibo.models import hep, tsp
 from qibo.models.circuit import Circuit
+from qibo.models.encodings import unary_encoder
 from qibo.models.error_mitigation import (
     CDR,
     ZNE,

src/qibo/models/encodings.py

@@ -0,0 +1,94 @@
+"""Module with functions that encode classical data into quantum circuits."""
+
+import math
+
+import numpy as np
+
+from qibo import gates
+from qibo.config import raise_error
+from qibo.models.circuit import Circuit
+
+
+def unary_encoder(data):
+    """Creates circuit that performs the unary encoding of ``data``.
+
+    Given a classical ``data`` array :math:`\\mathbf{x} \\in \\mathbb{R}^{d}` such that
+
+    .. math::
+        \\mathbf{x} = (x_{1}, x_{2}, \\dots, x_{d}) \\, ,
+
+    this function generate the circuit that prepares the following quantum state
+    :math:`\\ket{\\psi} \\in \\mathcal{H}`:
+
+    .. math::
+        \\ket{\\psi} = \\frac{1}{\\|\\mathbf{x}\\|_{\\textup{HS}}} \\,
+            \\sum_{k=1}^{d} \\, x_{k} \\, \\ket{k} \\, ,
+
+    with :math:`\\mathcal{H} \\cong \\mathbb{C}^{d}` being a :math:`d`-qubit Hilbert space,
+    and :math:`\\|\\cdot\\|_{\\textup{HS}}` being the Hilbert-Schmidt norm.
+    Here, :math:`\\ket{k}` is a unary representation of the number :math:`1` through
+    :math:`d`.
+
+    Args:
+        data (ndarray, optional): :math:`1`-dimensional array of data to be loaded.
+
+    Returns:
+        :class:`qibo.models.circuit.Circuit`: circuit that loads ``data`` in unary representation.
+
+    References:
+        1. S. Johri *et al.*, *Nearest Centroid Classification on a Trapped Ion Quantum Computer*.
+        `arXiv:2012.04145v2 [quant-ph] <https://arxiv.org/abs/2012.04145>`_.
+    """
+    if len(data.shape) != 1:
+        raise_error(
+            TypeError,
+            f"``data`` must be a 1-dimensional array, but it has dimensions {data.shape}.",
+        )
+    elif not math.log2(data.shape[0]).is_integer():
+        raise_error(
+            ValueError, f"len(data) must be a power of 2, but it is {len(data)}."
+        )
+
+    nqubits = len(data)
+    j_max = int(nqubits / 2)
+
+    circuit, _ = _generate_rbs_pairs(nqubits)
+
+    # calculating phases and setting circuit parameters
+    r_array = np.zeros(nqubits - 1, dtype=float)
+    phases = np.zeros(nqubits - 1, dtype=float)
+    for j in range(1, j_max + 1):
+        r_array[j_max + j - 2] = math.sqrt(data[2 * j - 1] ** 2 + data[2 * j - 2] ** 2)
+        theta = math.acos(data[2 * j - 2] / r_array[j_max + j - 2])
+        if data[2 * j - 1] < 0.0:
+            theta = 2 * math.pi - theta
+        phases[j_max + j - 2] = theta
+
+    for j in range(j_max - 1, 0, -1):
+        r_array[j - 1] = math.sqrt(r_array[2 * j] ** 2 + r_array[2 * j - 1] ** 2)
+        phases[j - 1] = math.acos(r_array[2 * j - 1] / r_array[j - 1])
+
+    circuit.set_parameters(phases)
+
+    return circuit
+
+
+def _generate_rbs_pairs(nqubits):
+    """Generating list of indexes representing the RBS connections
+    and creating circuit with all RBS initialised with 0.0 phase."""
+    pairs_rbs = [[(0, int(nqubits / 2))]]
+    indexes = list(np.array(pairs_rbs).flatten())
+    for depth in range(2, int(math.log2(nqubits)) + 1):
+        pairs_rbs_per_depth = [
+            [(index, index + int(nqubits / 2**depth)) for index in indexes]
+        ]
+        pairs_rbs += pairs_rbs_per_depth
+        indexes = list(np.array(pairs_rbs_per_depth).flatten())
+
+    circuit = Circuit(nqubits)
+    circuit.add(gates.X(0))
+    for row in pairs_rbs:
+        for pair in row:
+            circuit.add(gates.RBS(*pair, 0.0, trainable=True))
+
+    return circuit, pairs_rbs

tests/test_models_encodings.py

@@ -0,0 +1,33 @@
+"""Tests for qibo.models.encodings"""
+import numpy as np
+import pytest
+
+from qibo.models.encodings import unary_encoder
+
+
+@pytest.mark.parametrize("nqubits", [2, 4, 8])
+def test_unary_encoder(backend, nqubits):
+    sampler = np.random.default_rng(1)
+
+    with pytest.raises(TypeError):
+        data = sampler.random((nqubits, nqubits))
+        data = backend.cast(data, dtype=data.dtype)
+        unary_encoder(data)
+    with pytest.raises(ValueError):
+        data = sampler.random(nqubits + 1)
+        data = backend.cast(data, dtype=data.dtype)
+        unary_encoder(data)
+
+    # sampling random data in interval [-1, 1]
+    sampler = np.random.default_rng(1)
+    data = 2 * sampler.random(nqubits) - 1
+    data = backend.cast(data, dtype=data.dtype)
+
+    circuit = unary_encoder(data)
+    state = backend.execute_circuit(circuit).state()
+    indexes = np.flatnonzero(state)
+    state = np.sort(state[indexes])
+
+    backend.assert_allclose(
+        state, np.sort(data) / backend.calculate_norm(data, order=2)
+    )