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API Reference: Representation Core

representation

╔══════════════════════════════════════════════════════════════════════════════╗ ║ MHRQI - Multi-scale Hierarchical Representation of Quantum Images ║ ║ Core Representation and Encoding ║ ║ ║ ║ Author: Keno S. Jose ║ ║ License: Apache 2.0 ║ ╚══════════════════════════════════════════════════════════════════════════════╝

MHRQI

Main class for Multi-scale Hierarchical Representation of Quantum Images. Encapsulates the quantum circuit, registers, and operations.

Source code in mhrqi/core/representation.py 
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class MHRQI:
    """
    Main class for Multi-scale Hierarchical Representation of Quantum Images.
    Encapsulates the quantum circuit, registers, and operations.
    """

    def __init__(self, depth, bit_depth=8):
        """
        Initialize an MHRQI instance.

        Args:
            depth: Hierarchy depth (log2 of image side)
            bit_depth: Bits for intensity encoding (default 8)
        """
        self.depth = depth
        self.bit_depth = bit_depth
        self.hierarchical_coord_matrix = None
        self.denoise_enabled = False

        self.pos_regs = []
        # Position qubits (2 per level: y and x)
        for k in range(depth):
            self.pos_regs.append(QuantumRegister(1, f"q_y_{k}"))
            self.pos_regs.append(QuantumRegister(1, f"q_x_{k}"))

        self.intensity_reg = QuantumRegister(bit_depth, "intensity")
        self.outcome_reg = QuantumRegister(1, "outcome")
        self.work_reg = QuantumRegister(2, "work")

        self.circuit = QuantumCircuit(
            *self.pos_regs, self.intensity_reg, self.outcome_reg, self.work_reg
        )

        # Place position qubits in uniform superposition
        for reg in self.pos_regs:
            self.circuit.h(reg[0])

    @property
    def qubits_to_measure(self):
        """Returns a list of qubits that should be measured for reconstruction."""
        qubits = []
        for reg in self.pos_regs:
            qubits.append(reg[0])
        qubits.extend(list(self.intensity_reg))
        qubits.extend(list(self.outcome_reg))
        return qubits

    def upload(self, hierarchical_coord_matrix, img):
        """
        Upload intensity values using MHRQI(basis) encoding.

        Args:
            hierarchical_coord_matrix: matrix of position states
            img: normalized image (0-1 range)
        """
        self.hierarchical_coord_matrix = hierarchical_coord_matrix
        controls = [reg[0] for reg in self.pos_regs]
        intensity_qubits = list(self.intensity_reg)
        and_ancilla = self.work_reg[0]

        for vec in hierarchical_coord_matrix:
            ctrl_states = list(vec)
            r, c = utils.compose_rc(vec, 2)  # d=2 for images
            pixel_value = float(img[r, c])
            intensity_int = int(pixel_value * (2**self.bit_depth - 1))
            intensity_bits = format(intensity_int, f"0{self.bit_depth}b")[::-1]

            _prepare_controls_on_states(self.circuit, controls, ctrl_states)

            if len(controls) > 0:
                self.circuit.mcx(controls, and_ancilla)
                for bit_idx, bit_val in enumerate(intensity_bits):
                    if bit_val == "1":
                        self.circuit.cx(and_ancilla, intensity_qubits[bit_idx])
                self.circuit.mcx(controls, and_ancilla)
            else:
                for bit_idx, bit_val in enumerate(intensity_bits):
                    if bit_val == "1":
                        self.circuit.x(intensity_qubits[bit_idx])

            _restore_controls(self.circuit, controls, ctrl_states)
        return self.circuit

    def lazy_upload(self, hierarchical_coord_matrix, image):
        """
        Fast basis upload using direct statevector initialization.

        Args:
            hierarchical_coord_matrix (list): List of hierarchical_coord_vectors for all pixels.
            image (np.ndarray): Normalized image array [0, 1].

        Returns:
            QuantumCircuit: The initialized circuit.
        """
        self.hierarchical_coord_matrix = hierarchical_coord_matrix
        qubit_to_idx = {q: i for i, q in enumerate(self.circuit.qubits)}
        pos_indices = [qubit_to_idx[reg[0]] for reg in self.pos_regs]
        intensity_indices = [qubit_to_idx[q] for q in self.intensity_reg]

        num_qubits = self.circuit.num_qubits
        dim = 2**num_qubits
        state = np.zeros(dim, dtype=complex)

        all_indices = pos_indices + intensity_indices
        is_sequential = all(all_indices[i] == i for i in range(len(all_indices)))

        if is_sequential:
            for hierarchical_coord_vector in hierarchical_coord_matrix:
                p = 0
                for i, val in enumerate(hierarchical_coord_vector):
                    if val:
                        p |= 1 << i

                r, c = utils.compose_rc(hierarchical_coord_vector, 2)
                pixel_value = float(image[r, c])
                intensity_int = int(pixel_value * (2**self.bit_depth - 1))

                base_idx = p
                intensity_offset = 0
                for bit_idx in range(self.bit_depth):
                    if (intensity_int >> bit_idx) & 1:
                        intensity_offset |= 1 << (len(pos_indices) + bit_idx)
                state[base_idx + intensity_offset] = 1.0
        else:
            warnings.warn("Qubits not sequential, falling back to gate-based upload.", stacklevel=2)
            return self.upload(hierarchical_coord_matrix, image)

        state_norm = np.linalg.norm(state)
        if state_norm > 0:
            state = state / state_norm

        self.circuit.append(SetStatevector(state), self.circuit.qubits)
        return self.circuit

    def simulate(self, shots=None, use_gpu=True, monte_carlo_seed=None):
        """
        Simulate the MHRQI circuit with optional Monte Carlo backend.

        Args:
            shots (int, optional): Number of shots. Returns statevector if None.
                If provided, uses Monte Carlo shot-based sampling.
            use_gpu (bool): Whether to use GPU acceleration (if available).
            monte_carlo_seed (int, optional): Seed for reproducible Monte Carlo sampling.

        Returns:
            MHRQIResult: Simulation results object.
        """
        if shots is None:
            # Statevector simulation (exact)
            backend = Aer.get_backend("statevector_simulator", device="GPU" if use_gpu else "CPU")
            transpiled = transpile(self.circuit, backend)
            raw = backend.run(transpiled).result().get_statevector()
        else:
            # Monte Carlo shot-based simulation
            qc_measure = self.circuit.copy()
            creg = ClassicalRegister(len(self.qubits_to_measure), "c")
            qc_measure.add_register(creg)
            qc_measure.measure(self.qubits_to_measure, creg)

            # Try GPU-accelerated backends first
            if use_gpu:
                try:
                    backend = AerSimulator(
                        method="statevector", device="GPU", cuStateVec_enable=True
                    )
                except Exception:
                    backend = Aer.get_backend("qasm_simulator")
            else:
                backend = Aer.get_backend("qasm_simulator")

            transpiled = transpile(qc_measure, backend)

            # Option 1: Use Qiskit's native sampling (traditional approach)
            try:
                raw = backend.run(transpiled, shots=shots).result().get_counts()
            except Exception as e:
                # Fallback to statevector + Monte Carlo if Qiskit sampling fails
                warnings.warn(f"Qiskit sampling failed ({e}); falling back to Monte Carlo backend.", stacklevel=2)
                statevector_backend = Aer.get_backend("statevector_simulator")
                sv_circuit = self.circuit.copy()
                sv_transpiled = transpile(sv_circuit, statevector_backend)
                statevector = statevector_backend.run(sv_transpiled).result().get_statevector()

                mc_simulator = MonteCarloSimulator(seed=monte_carlo_seed, use_gpu=use_gpu)
                raw = mc_simulator.sample_statevector(statevector, shots, self.qubits_to_measure)

        return MHRQIResult(
            raw, self.hierarchical_coord_matrix, self.bit_depth, self.denoise_enabled
        )

    def apply_denoising(self):
        """
        Apply hierarchical consistency denoising to the circuit.
        """
        _, denoise_qc = apply_denoising(
            self.circuit, self.pos_regs, self.intensity_reg, self.outcome_reg
        )
        self.denoise_enabled = True
        return denoise_qc

    def decode(self, results):
        """
        Decode simulation results into image bins.

        Args:
            results (dict or Statevector): Simulation results.

        Returns:
            dict: Reconstructed image bins.
        """
        # The actual decoding logic is now handled within MHRQIResult
        # This method might be removed or refactored depending on usage
        # For now, it can serve as a placeholder or direct call to MHRQIResult's decode
        mhrqi_result = MHRQIResult(
            results, self.hierarchical_coord_matrix, self.bit_depth, self.denoise_enabled
        )
        return mhrqi_result.decode()

qubits_to_measure property

Returns a list of qubits that should be measured for reconstruction.

__init__(depth, bit_depth=8)

Initialize an MHRQI instance.

Parameters:

Name Type Description Default
depth

Hierarchy depth (log2 of image side)

 required
bit_depth

Bits for intensity encoding (default 8)

 8
Source code in mhrqi/core/representation.py 
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def __init__(self, depth, bit_depth=8):
    """
    Initialize an MHRQI instance.

    Args:
        depth: Hierarchy depth (log2 of image side)
        bit_depth: Bits for intensity encoding (default 8)
    """
    self.depth = depth
    self.bit_depth = bit_depth
    self.hierarchical_coord_matrix = None
    self.denoise_enabled = False

    self.pos_regs = []
    # Position qubits (2 per level: y and x)
    for k in range(depth):
        self.pos_regs.append(QuantumRegister(1, f"q_y_{k}"))
        self.pos_regs.append(QuantumRegister(1, f"q_x_{k}"))

    self.intensity_reg = QuantumRegister(bit_depth, "intensity")
    self.outcome_reg = QuantumRegister(1, "outcome")
    self.work_reg = QuantumRegister(2, "work")

    self.circuit = QuantumCircuit(
        *self.pos_regs, self.intensity_reg, self.outcome_reg, self.work_reg
    )

    # Place position qubits in uniform superposition
    for reg in self.pos_regs:
        self.circuit.h(reg[0])

apply_denoising()

Apply hierarchical consistency denoising to the circuit.

Source code in mhrqi/core/representation.py 
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def apply_denoising(self):
    """
    Apply hierarchical consistency denoising to the circuit.
    """
    _, denoise_qc = apply_denoising(
        self.circuit, self.pos_regs, self.intensity_reg, self.outcome_reg
    )
    self.denoise_enabled = True
    return denoise_qc

decode(results)

Decode simulation results into image bins.

Parameters:

Name Type Description Default
results dict or Statevector

Simulation results.

 required

Returns:

Name Type Description
dict

Reconstructed image bins.
Source code in mhrqi/core/representation.py 
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def decode(self, results):
    """
    Decode simulation results into image bins.

    Args:
        results (dict or Statevector): Simulation results.

    Returns:
        dict: Reconstructed image bins.
    """
    # The actual decoding logic is now handled within MHRQIResult
    # This method might be removed or refactored depending on usage
    # For now, it can serve as a placeholder or direct call to MHRQIResult's decode
    mhrqi_result = MHRQIResult(
        results, self.hierarchical_coord_matrix, self.bit_depth, self.denoise_enabled
    )
    return mhrqi_result.decode()

lazy_upload(hierarchical_coord_matrix, image)

Fast basis upload using direct statevector initialization.

Parameters:

Name Type Description Default
hierarchical_coord_matrix list

List of hierarchical_coord_vectors for all pixels.

 required
image ndarray

Normalized image array [0, 1].

 required

Returns:

Name Type Description
QuantumCircuit

The initialized circuit.
Source code in mhrqi/core/representation.py 
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def lazy_upload(self, hierarchical_coord_matrix, image):
    """
    Fast basis upload using direct statevector initialization.

    Args:
        hierarchical_coord_matrix (list): List of hierarchical_coord_vectors for all pixels.
        image (np.ndarray): Normalized image array [0, 1].

    Returns:
        QuantumCircuit: The initialized circuit.
    """
    self.hierarchical_coord_matrix = hierarchical_coord_matrix
    qubit_to_idx = {q: i for i, q in enumerate(self.circuit.qubits)}
    pos_indices = [qubit_to_idx[reg[0]] for reg in self.pos_regs]
    intensity_indices = [qubit_to_idx[q] for q in self.intensity_reg]

    num_qubits = self.circuit.num_qubits
    dim = 2**num_qubits
    state = np.zeros(dim, dtype=complex)

    all_indices = pos_indices + intensity_indices
    is_sequential = all(all_indices[i] == i for i in range(len(all_indices)))

    if is_sequential:
        for hierarchical_coord_vector in hierarchical_coord_matrix:
            p = 0
            for i, val in enumerate(hierarchical_coord_vector):
                if val:
                    p |= 1 << i

            r, c = utils.compose_rc(hierarchical_coord_vector, 2)
            pixel_value = float(image[r, c])
            intensity_int = int(pixel_value * (2**self.bit_depth - 1))

            base_idx = p
            intensity_offset = 0
            for bit_idx in range(self.bit_depth):
                if (intensity_int >> bit_idx) & 1:
                    intensity_offset |= 1 << (len(pos_indices) + bit_idx)
            state[base_idx + intensity_offset] = 1.0
    else:
        warnings.warn("Qubits not sequential, falling back to gate-based upload.", stacklevel=2)
        return self.upload(hierarchical_coord_matrix, image)

    state_norm = np.linalg.norm(state)
    if state_norm > 0:
        state = state / state_norm

    self.circuit.append(SetStatevector(state), self.circuit.qubits)
    return self.circuit

simulate(shots=None, use_gpu=True, monte_carlo_seed=None)

Simulate the MHRQI circuit with optional Monte Carlo backend.

Parameters:

Name Type Description Default
shots int

Number of shots. Returns statevector if None. If provided, uses Monte Carlo shot-based sampling.

 None
use_gpu bool

Whether to use GPU acceleration (if available).

 True
monte_carlo_seed int

Seed for reproducible Monte Carlo sampling.

 None

Returns:

Name Type Description
MHRQIResult

Simulation results object.
Source code in mhrqi/core/representation.py 
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def simulate(self, shots=None, use_gpu=True, monte_carlo_seed=None):
    """
    Simulate the MHRQI circuit with optional Monte Carlo backend.

    Args:
        shots (int, optional): Number of shots. Returns statevector if None.
            If provided, uses Monte Carlo shot-based sampling.
        use_gpu (bool): Whether to use GPU acceleration (if available).
        monte_carlo_seed (int, optional): Seed for reproducible Monte Carlo sampling.

    Returns:
        MHRQIResult: Simulation results object.
    """
    if shots is None:
        # Statevector simulation (exact)
        backend = Aer.get_backend("statevector_simulator", device="GPU" if use_gpu else "CPU")
        transpiled = transpile(self.circuit, backend)
        raw = backend.run(transpiled).result().get_statevector()
    else:
        # Monte Carlo shot-based simulation
        qc_measure = self.circuit.copy()
        creg = ClassicalRegister(len(self.qubits_to_measure), "c")
        qc_measure.add_register(creg)
        qc_measure.measure(self.qubits_to_measure, creg)

        # Try GPU-accelerated backends first
        if use_gpu:
            try:
                backend = AerSimulator(
                    method="statevector", device="GPU", cuStateVec_enable=True
                )
            except Exception:
                backend = Aer.get_backend("qasm_simulator")
        else:
            backend = Aer.get_backend("qasm_simulator")

        transpiled = transpile(qc_measure, backend)

        # Option 1: Use Qiskit's native sampling (traditional approach)
        try:
            raw = backend.run(transpiled, shots=shots).result().get_counts()
        except Exception as e:
            # Fallback to statevector + Monte Carlo if Qiskit sampling fails
            warnings.warn(f"Qiskit sampling failed ({e}); falling back to Monte Carlo backend.", stacklevel=2)
            statevector_backend = Aer.get_backend("statevector_simulator")
            sv_circuit = self.circuit.copy()
            sv_transpiled = transpile(sv_circuit, statevector_backend)
            statevector = statevector_backend.run(sv_transpiled).result().get_statevector()

            mc_simulator = MonteCarloSimulator(seed=monte_carlo_seed, use_gpu=use_gpu)
            raw = mc_simulator.sample_statevector(statevector, shots, self.qubits_to_measure)

    return MHRQIResult(
        raw, self.hierarchical_coord_matrix, self.bit_depth, self.denoise_enabled
    )

upload(hierarchical_coord_matrix, img)

Upload intensity values using MHRQI(basis) encoding.

Parameters:

Name Type Description Default
hierarchical_coord_matrix

matrix of position states

 required
img

normalized image (0-1 range)

 required
Source code in mhrqi/core/representation.py 
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def upload(self, hierarchical_coord_matrix, img):
    """
    Upload intensity values using MHRQI(basis) encoding.

    Args:
        hierarchical_coord_matrix: matrix of position states
        img: normalized image (0-1 range)
    """
    self.hierarchical_coord_matrix = hierarchical_coord_matrix
    controls = [reg[0] for reg in self.pos_regs]
    intensity_qubits = list(self.intensity_reg)
    and_ancilla = self.work_reg[0]

    for vec in hierarchical_coord_matrix:
        ctrl_states = list(vec)
        r, c = utils.compose_rc(vec, 2)  # d=2 for images
        pixel_value = float(img[r, c])
        intensity_int = int(pixel_value * (2**self.bit_depth - 1))
        intensity_bits = format(intensity_int, f"0{self.bit_depth}b")[::-1]

        _prepare_controls_on_states(self.circuit, controls, ctrl_states)

        if len(controls) > 0:
            self.circuit.mcx(controls, and_ancilla)
            for bit_idx, bit_val in enumerate(intensity_bits):
                if bit_val == "1":
                    self.circuit.cx(and_ancilla, intensity_qubits[bit_idx])
            self.circuit.mcx(controls, and_ancilla)
        else:
            for bit_idx, bit_val in enumerate(intensity_bits):
                if bit_val == "1":
                    self.circuit.x(intensity_qubits[bit_idx])

        _restore_controls(self.circuit, controls, ctrl_states)
    return self.circuit