Unitary Gate¶

Given a \(2^{n}\times2^{n}\) unitary matrix, the unitary-gate function constructs an equivalent unitary gate which acts on \(n\) qubits accordingly. For \(n>2\), the synthesis process implementation is based on [1].

Syntax¶

Function: UnitaryGate

Parameters:

data: DataArray

{
  "function": "UnitaryGate",
  "function_params": {
    "data": [
      [1, 0, 0, 0],
      [0, 1, 0, 0],
      [0, 0, "-1j", 0],
      [0, 0, 0, "1j"]
    ]
  }
}

Example¶

The following example shows a \(2\)-qubit unitary gate generated from a series of arbitrary \(2\)-rotations in the formed \(4\) dimensional space. The SDK code includes the construction of the matrix using NumPy functions, while the textual model is created by feeding the explicit numerical values.

Textual ModelSDK

{
    "logic_flow": [
        {
            "function": "UnitaryGate",
            "function_params": {
                "data": [
                    [
                        "(-0.437588928003977-0.22742705999986979j)",
                        "(0.5162471759231342+0.5412974930115615j)",
                        "(-0.0257562186040025-0.09612351644098814j)",
                        "(0.11352149651283158+0.41771820225920475j)"
                    ],
                    [
                        "(-0.4657883653698742-0.4426774493996494j)",
                        "(-0.3564263367893152-0.37953725275954014j)",
                        "(-2.7383934913210134e-17+0.447213595499958j)",
                        "(0.24082111067114909+0.2408211106711492j)"
                    ],
                    [
                        "(0.276003031585611-0.227055039284318j)",
                        "(0.24522446154306524-0.17374499218631134j)",
                        "(0.8720020339202011+0j)",
                        "(0.08819092511956897+0.11739161131796567j)"
                    ],
                    [
                        "(0.08990251208306779-0.4561322296873242j)",
                        "(0.1573622060431408+0.23305019820160192j)",
                        "(-0.08618198713953264+0.14927158042291808j)",
                        "(0.38451638587720915-0.7261015617334183j)"
                    ]
                ]
            }
        }
    ]
}

import numpy as np
from classiq import ModelDesigner
from classiq.builtin_functions import UnitaryGate

num_gate_qubits = 2
thetas = [np.pi / 3, np.pi / 7, np.arccos(3 / 5), 0.2, np.pi / 4, np.pi / 2]
phis = [np.pi / 4, np.pi / 3, np.pi / 2, np.pi / 5, np.pi / 4, np.pi / 3]
pairs = [[0, 3], [3, 2], [1, 2], [0, 1], [1, 3], [0, 1]]
gate_matrix = np.identity(2**num_gate_qubits, dtype=complex)
for theta, phi, index in zip(thetas, phis, pairs):
    data_next = np.identity(2**num_gate_qubits, dtype=complex)
    data_next[index[0], index[0]] = 0
    data_next[index[1], index[1]] = 0
    data_next[np.ix_(index, index)] = [
        [
            np.exp(-1j * phi) * np.cos(theta / 2),
            -np.exp(-1j * phi) * np.sin(theta / 2),
        ],
        [np.sin(theta / 2), np.cos(theta / 2)],
    ]
    gate_matrix = np.dot(gate_matrix, data_next)
gate_matrix = gate_matrix.tolist()

model_designer = ModelDesigner()
unitary_gate_params = UnitaryGate(data=gate_matrix)
model_designer.UnitaryGate(unitary_gate_params)

circuit = model_designer.synthesize()
circuit.show_interactive()

The figure below shows the constituents of the gate.

Mcx example

References¶

[1] R. Iten et al, Quantum Circuits for Isometries ,Phys. Rev. A 93 (2016). https://link.aps.org/doi/10.1103/PhysRevA.93.032318