Feature: Add Hadamard Test #158
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blolt
commented
Jan 12, 2025
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| ======= | ||
| The Hadamard test is a quantum circuit that allows estimation of the real and imaginary parts of the expected value of a unitary operator. It is a fundamental subroutine used in many quantum algorithms, including quantum phase estimation where it helps extract eigenvalue information through controlled operations. The test works by applying a controlled-unitary operation between an auxiliary qubit and the system of interest, with the measurement statistics of the auxiliary qubit encoding information about the unitary's expectation value. | ||
| >>>>>>> Stashed changes |
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Noticed that these were not merged, miss by myself. Can update this in a following revision, pending comments from reviewers.
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yes, please address this also
mbeach-aws
requested changes
Jan 23, 2025
| "source": [ | ||
| "## Run on a local simulator\n", | ||
| "\n", | ||
| "Braket provides a method, `hadamard_test_circuit`, for estimating both the expected values of both the real and imaginary parts of a given unitary operator. Furthermore, methods for the extended Hadamard test are also provided (TODO: write the extended Hadamard test). We will first go through an example of the basic Hadamard test." |
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could you address or remove this TODO ?
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Great catch. I decided it made sense to address this in a follow-up issue, so I will remove the TODO.
| "0 & -1\n", | ||
| "\\end{bmatrix}\n", | ||
| "$$\n", | ||
| "Though braket has built-in support for the Pauli-Z gate, we will use the `unitary` method to apply the gate to the qubit. Consider playing around with different matrices to test your understanding of the algorithm." |
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| "Though braket has built-in support for the Pauli-Z gate, we will use the `unitary` method to apply the gate to the qubit. Consider playing around with different matrices to test your understanding of the algorithm." | |
| "Though Braket has built-in support for the Pauli-Z gate, we will use the `unitary` method to apply the gate to the qubit. Consider playing around with different matrices to test your understanding of the algorithm." |
| "$$\n", | ||
| "\\dfrac{|0\\rangle |\\psi\\rangle + |1\\rangle U |\\psi\\rangle}{\\sqrt{2}} .\n", | ||
| "$$ \n", | ||
| "Then, a Hadamard gate is applied to the first qubit once more, giving state,\n", |
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| "Then, a Hadamard gate is applied to the first qubit once more, giving state,\n", | |
| "Then, a Hadamard gate is applied to the first qubit once more, giving the state,\n", |
| "source": [ | ||
| "## Description\n", | ||
| "\n", | ||
| "Given a unitary operator $U$ and qubits $|0\\rangle|\\psi\\rangle$, the Hadamard test is used to estimate the expected value of $U$ on $|\\psi\\rangle$, i.e. $\\langle \\psi | U |\\psi \\rangle$. The algorithm is relatively straightforward, so we will walk through it step by step. First, we apply a Hadamard gate to $|0\\rangle$, putting the system into the state,\n", |
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| "Given a unitary operator $U$ and qubits $|0\\rangle|\\psi\\rangle$, the Hadamard test is used to estimate the expected value of $U$ on $|\\psi\\rangle$, i.e. $\\langle \\psi | U |\\psi \\rangle$. The algorithm is relatively straightforward, so we will walk through it step by step. First, we apply a Hadamard gate to $|0\\rangle$, putting the system into the state,\n", | |
| "Given a unitary operator $U$ and qubits $|0\\rangle|\\psi\\rangle$, the Hadamard test is used to estimate the expected value of $U$ on $|\\psi\\rangle$, i.e. $\\langle \\psi | U |\\psi \\rangle$. We will walk through the algorithm step by step. First, we apply a Hadamard gate to $|0\\rangle$, putting the system into the state,\n", |
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| "controlled_unitary = Circuit().unitary([0], np.array([[1, 0], [0, -1]]), \"U\")\n", | ||
| "print(controlled_unitary)" |
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I'd recommend defining the matrix in the line above for readability:
pauli_z = np.array([[1, 0], [0, -1]])
controlled_unitary = Circuit().unitary([0], pauli_z, "U")
print(controlled_unitary)
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| "counts = task.result().measurement_counts\n", | ||
| "p_zero = counts.get('0', 0) / 1000\n", |
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same here, we could use measurement_probabilities instead
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| "# controlled_unitary = Circuit().z(0)\n", | ||
| "# ht_circuit = hadamard_test_circuit(controlled_unitary)\n", |
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I can uncomment this and run on Garnet before we merge the PR if you want.
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| ======= | ||
| The Hadamard test is a quantum circuit that allows estimation of the real and imaginary parts of the expected value of a unitary operator. It is a fundamental subroutine used in many quantum algorithms, including quantum phase estimation where it helps extract eigenvalue information through controlled operations. The test works by applying a controlled-unitary operation between an auxiliary qubit and the system of interest, with the measurement statistics of the auxiliary qubit encoding information about the unitary's expectation value. | ||
| >>>>>>> Stashed changes |
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yes, please address this also
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| circ.h(0) | ||
| if component == 'imaginary': | ||
| circ.s(0).adjoint() | ||
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| # Add control qubit to the unitary circuit | ||
| for inst in controlled_unitary.instructions: | ||
| targets = [q + 1 for q in inst.target] | ||
| controlled_inst = Instruction( | ||
| operator=inst.operator, | ||
| target=targets, | ||
| control=0 | ||
| ) | ||
| circ.add_instruction(controlled_inst) | ||
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||
| circ.h(0) |
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could we generalize this to work on an ancilla qubit(s) q0 instead of hard-coded 0?
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| device = LocalSimulator() | ||
| task = device.run(test_circuit, shots=10000) |
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We could mock the results rather than running a true simulation during unit tests. Especially since the probabilistic nature of shots=10_000 and atol=0.1.
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This PR addresses issue #72.
Description of changes: This PR adds the Hadamard test to the library's implemented algorithms, with an optional flag that can be toggled for estimating either the real or imaginary part of the controlled unitary. An extension could be implementing the modified hadamard test, which could possibly make use of Amplitude amplification (Issue #100).
Testing done: Unit tests and notebook created.
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