Fixes #975 : Implement QFT in lightning.qubit and benchmark

[gzquse]

Dear Thomas,

Solution from my side

• add support for the Quantum Fourier Transform (QFT) gate in the OpToMemberFuncPtr.hpp file

Add the Struct: Add a new specialization of the GateOpToMemberFuncPtr template for the QFT gate.
Implement member

/**
* @brief Pointer to apply the Quantum Fourier Transform (QFT) operation.
*/
template <class PrecisionT, class ParamT, class GateImplementation>
struct GateOpToMemberFuncPtr<PrecisionT, ParamT, GateImplementation,
                             GateOperation::QFT> {
    using Type = void (GateImplementation::*)(std::complex<PrecisionT> *);
    constexpr static Type value = &GateImplementation::template applyQFT<PrecisionT>;
};

• update the list of supported gates to include the QFT gate in the lightning_qubit.py

_operations = frozenset(
    {
        "Identity",
        "QubitUnitary",
        "MultiControlledX",
        "DiagonalQubitUnitary",
        "PauliX",
        "PauliY",
        "PauliZ",
        "MultiRZ",
        "GlobalPhase",
        "Hadamard",
        "S",
        "Adjoint(S)",
        "T",
        "Adjoint(T)",
        "SX",
        "Adjoint(SX)",
        "CNOT",
        "SWAP",
        "ISWAP",
        "PSWAP",
        "Adjoint(ISWAP)",
        "SISWAP",
        "Adjoint(SISWAP)",
        "SQISW",
        "CSWAP",
        "Toffoli",
        "CY",
        "CZ",
        "PhaseShift",
        "ControlledPhaseShift",
        "RX",
        "RY",
        "RZ",
        "Rot",
        "CRX",
        "CRY",
        "CRZ",
        "C(PauliX)",
        "C(PauliY)",
        "C(PauliZ)",
        "C(Hadamard)",
        "C(S)",
        "C(T)",
        "C(PhaseShift)",
        "C(RX)",
        "C(RY)",
        "C(RZ)",
        "C(Rot)",
        "C(SWAP)",
        "C(IsingXX)",
        "C(IsingXY)",
        "C(IsingYY)",
        "C(IsingZZ)",
        "C(SingleExcitation)",
        "C(SingleExcitationMinus)",
        "C(SingleExcitationPlus)",
        "C(DoubleExcitation)",
        "C(DoubleExcitationMinus)",
        "C(DoubleExcitationPlus)",
        "C(MultiRZ)",
        "C(GlobalPhase)",
        "C(QubitUnitary)",
        "CRot",
        "IsingXX",
        "IsingYY",
        "IsingZZ",
        "IsingXY",
        "SingleExcitation",
        "SingleExcitationPlus",
        "SingleExcitationMinus",
        "DoubleExcitation",
        "DoubleExcitationPlus",
        "DoubleExcitationMinus",
        "QubitCarry",
        "QubitSum",
        "OrbitalRotation",
        "ECR",
        "BlockEncode",
        "C(BlockEncode)",
        "QFT",  # Add this line to include QFT
    }
)

• add C++ tests for the QFT gate in the Test_GateImplementations_Nonparam.cpp file

Use PENNYLANE_RUN_TEST Macro, implement test function, and add test case
QFT(∣000⟩)= ​1/sqrt(8) * (∣000⟩+∣001⟩+∣010⟩+∣011⟩+∣100⟩+∣101⟩+∣110⟩+∣111⟩)
so each amplitude is approximately 0.353553

template <typename PrecisionT, class GateImplementation> void testApplyQFT() {
    using ComplexT = std::complex<PrecisionT>;
    const std::size_t num_qubits = 3;

    auto st = createZeroState<ComplexT>(num_qubits);
    GateImplementation::applyQFT(st.data(), num_qubits, {0, 1, 2}, false);

    // Expected result of QFT(|000>) for a 3-qubit system
    std::vector<ComplexT> expected_result = {
        ComplexT{0.353553, 0.0}, ComplexT{0.353553, 0.0}, ComplexT{0.353553, 0.0},
        ComplexT{0.353553, 0.0}, ComplexT{0.353553, 0.0}, ComplexT{0.353553, 0.0},
        ComplexT{0.353553, 0.0}, ComplexT{0.353553, 0.0}
    };

    CHECK(st == approx(expected_result).margin(1e-7));
}
PENNYLANE_RUN_TEST(QFT);

• implement QFT

template <class PrecisionT>
    [[nodiscard]] static auto applyQFT(
        std::complex<PrecisionT> *arr, std::size_t num_qubits,
        const std::vector<std::size_t> &wires, bool inverse = false) {
        auto local_wires = wires;
        for (std::size_t i = 0; i < local_wires.size(); ++i) {
            applyHadamard(arr, num_qubits, {local_wires[i]}, inverse);
            for (std::size_t j = i + 1; j < local_wires.size(); ++j) {
                PrecisionT angle = M_PI / (1U << (j - i));
                if (inverse) {
                    angle = -angle;
                }
                applyControlledPhaseShift(arr, num_qubits, {local_wires[j], local_wires[i]}, inverse, angle);
            }
        }
        std::reverse(local_wires.begin(), local_wires.end());
    }

• add pytest qft

@pytest.mark.parametrize("num_qubits", [2, 3, 4])
def test_qft_gate(num_qubits):
    dev = qml.device("lightning.qubit", wires=num_qubits)
    @qml.qnode(dev)
    def circuit():
        qml.QFT(wires=range(num_qubits))
        return qml.state()
    output_state = circuit()
    expected_matrix = qml.QFT.compute_matrix(num_qubits)
    initial_state = np.zeros((2**num_qubits,), dtype=np.complex128)
    initial_state[0] = 1
    expected_state = expected_matrix @ initial_state
    assert output_state.shape == expected_state.shape, "State dimensions mismatch"
    assert np.allclose(output_state, expected_state, atol=1e-6), "QFT state does not match expected state"

---

Fixes #975

[tomlqc]

@gzquse I just triggered the CI

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[gzquse]

review required

[tomlqc]

Thanks @gzquse
Please link the PR to the issue and give the PR a name that describes the feature.
I was wondering about the benchmark script and results. Have I missed them?

[gzquse]

Hi @tomlqc ,

You are right. I have some issues using a local apple chip to do the benchmark and I also tried to use our uni HPC to do the experiment but seems the CMake is not the same.

May I ask if it is possible to get a test environment from Pennylane's HPC? Therefore, I can test it a bit further.

[gzquse]

Benchmark Jupyter notebook for reference

import pennylane as qml
from pennylane import numpy as np
import time

dev = qml.device("default.qubit", wires=10)

def benchmark_qft(num_qubits):
    results = {"num_qubits": [], "QubitUnitary_time": [], "qml_QFT_time": []}
    
    for n in range(1, num_qubits + 1):
        @qml.qnode(dev)
        def qft_with_qubit_unitary():
            qft_matrix = qml.QFT.compute_matrix(n)
            qml.QubitUnitary(qft_matrix, wires=range(n))
            return qml.state()
        
        @qml.qnode(dev)
        def qft_with_qml_gate():
            qml.QFT(wires=range(n))
            return qml.state()
       
        start_time = time.time()
        qft_with_qubit_unitary()
        unitary_time = time.time() - start_time

        start_time = time.time()
        qft_with_qml_gate()
        qml_gate_time = time.time() - start_time

        results["num_qubits"].append(n)
        results["QubitUnitary_time"].append(unitary_time)
        results["qml_QFT_time"].append(qml_gate_time)

    return results

num_qubits = 10  # Adjust based on desired range
benchmark_results = benchmark_qft(num_qubits)

print(benchmark_results)

import pandas as pd
results_df = pd.DataFrame(benchmark_results)

results_df.to_csv("qft_benchmark_results.csv", index=False)
print("Benchmark results saved to qft_benchmark_results.csv.")

[tomlqc]

Hi @gzquse,
You don't need to scale up to a very large number of qubits. Using your local laptop for this is perfectly fine. Please just show the results that you were able to generate. For this create some plots and share them with you analysis in this PR.
To share files or larger chunks of code, as e.g. the jupyter notebook, prefer using https://gist.github.com/, it will be rendered nicely.
Please also check again my previous message about link and title.
Thanks

[tomlqc]

Just a note before we start the actual review. Please use default.qubit in this pytest to check the validity of the new implementation.

[tomlqc]

Does the latest change test your implementation against default.qubit? This is what I meant.
You may want to take a look at the other tests in this file.

[gzquse]

yes

[gzquse]

Benchmark QFT result

[gzquse]

Hi @tomlqc ,
Could you help me manually to link the issue?

Fix issue #975 : Implement QFT in lightning.qubit and benchmark

Thanks

[gzquse]

Gist

script

[tomlqc]

Could you help me manually to link the issue?

https://www.google.com/search?q=how+to+link+github+pr+to+issue
Doesn't it work with using a keyword in the description?

[tomlqc]

Benchmark QFT result

Is your laptop already struggling with >10 qubits?

[gzquse]

Hi @tomlqc,
As expected, I fired up 10 rounds and 14 qubits benchmark scripts, which burn 99% of the memory of my MacOs.
a 14-qubit QFT matrix is 2^14×2^14 > 4 GB in memory.
https://docs.google.com/spreadsheets/d/1Jj-uHv-e42XTPd2RgM6tSz6J7sOS5o1w8RbNINUED24/edit?usp=sharing

[gzquse]

Could you help me manually to link the issue?

https://www.google.com/search?q=how+to+link+github+pr+to+issue Doesn't it work with using a keyword in the description?

I assume the original pr was under the forked branch. So the "Fix" does not work?

[tomlqc]

Thanks @gzquse for the update

a 14-qubit QFT matrix is 2^14×2^14 > 4 GB in memory

• Is the data in the Google sheet of the same kind as in the "Benchmark QFT result" plot but just a different representation?
• Does that mean that you would be able to extend the plot to 13 or even 14 qubit? If so, please update this plot.

[tomlqc]

So the "Fix" does not work?

I added the line to the description (not the title) and it worked fine.

[gzquse]

So the "Fix" does not work?

I added the line to the description (not the title) and it worked fine.

Thanks for pointing out

[gzquse]

Thanks @gzquse for the update

a 14-qubit QFT matrix is 2^14×2^14 > 4 GB in memory

• Is the data in the Google sheet of the same kind as in the "Benchmark QFT result" plot but just a different representation?
• Does that mean that you would be able to extend the plot to 13 or even 14 qubit? If so, please update this plot.

Hi,

• Yes, it is the same representation.
• I just put the 14-qubit benchmark on the right. In the 12-qubit plot on the left, you can see that I set the y-axis to a log scale. Up to 12 qubits, the two methods are relatively close in performance, alternating in speed. However, after 13 qubits, the new method shows a significant advantage in running time. I expect a similar trend on HPC systems.

[tomlqc]

Thanks @gzquse