qml.estimator.templates.UnaryIterationQPE

class UnaryIterationQPE(walk_op, num_iterations, adj_qft_op=None, wires=None)

Bases: ResourceOperator

Resource class for Quantum Phase Estimation (QPE) using the unary iteration technique.

This form of QPE, as described in arXiv.2011.03494, requires the unitary operator to be a quantum walk operator constructed from Select and Prepare subroutines. In this approach, unary iteration is used to construct successive powers of the walk operator, which reduces T and Toffoli gate counts in their decomposition at the cost of increasing the number of auxiliary qubits required.

For a detailed explanation of unary iteration, see here. Note that users can also provide a custom adjoint Quantum Fourier Transform (QFT) implementation, which can be used to further optimize the resource requirements.

Parameters:

• walk_op (ResourceOperator) – the quantum walk operator to apply the phase estimation protocol on

• num_iterations (int) – The total number of times the quantum walk operator is applied in order to reach a target precision in the eigenvalue estimate.

• adj_qft_op (ResourceOperator | None) – An optional argument to set the subroutine used to perform the adjoint QFT operation.

• wires (WiresLike | None) – the wires the operation acts on

Resources:

The resources are obtained from Figure 2. in Section III of arXiv.2011.03494.

Raises:

• ValueError – num_iterations must be an integer greater than zero

• TypeError – walk_op must be an instance of Qubitization or QubitizeTHC

See also

Related PennyLane operation QuantumPhaseEstimation and explanation of Unary Iteration.

Example

The resources for this operation are computed as follows:

>>> import pennylane.estimator as qre
>>> thc_ham = qre.THCHamiltonian(num_orbitals=20, tensor_rank=40)
>>> num_iter, walk_op = (11, qre.QubitizeTHC(thc_ham))
>>> res = qre.estimate(qre.UnaryIterationQPE(walk_op, num_iter))
>>> print(res)
--- Resources: ---
 Total wires: 402
   algorithmic wires: 101
   allocated wires: 301
     zero state: 301
     any state: 0
 Total gates : 5.821E+5
   'Toffoli': 3.546E+4,
   'T': 792,
   'CNOT': 4.262E+5,
   'X': 1.833E+4,
   'Z': 475,
   'S': 880,
   'Hadamard': 9.995E+4

Attributes

resource_keys
resource_params	Returns a dictionary containing the minimal information needed to compute the resources.

resource_keys = {'adj_qft_cmpr_op', 'cmpr_walk_op', 'num_iterations'}

resource_params

Returns a dictionary containing the minimal information needed to compute the resources.

Returns:

A dictionary containing the resource parameters:

• cmpr_walk_op (CompressedResourceOp): A compressed resource operator corresponding to the quantum walk operator to apply the phase estimation protocol on.

• num_iterations (int): The total number of times the quantum walk operator is applied in order to reach a target precision in the eigenvalue estimate.

• adj_qft_cmpr_op (CompressedResourceOp | None): An optional compressed resource operator corresponding to the adjoint QFT routine. If None, the default QFT will be used.

Return type:

dict

Methods

resource_decomp(cmpr_walk_op, num_iterations)	Returns the resources for Quantum Phase Estimation implemented using unary iteration.
resource_rep(cmpr_walk_op, num_iterations[, ...])	Returns a compressed representation containing only the parameters of the Operator that are needed to compute the resources.
tracking_name(cmpr_walk_op, num_iterations)	Returns the tracking name built with the operator's parameters.

classmethod resource_decomp(cmpr_walk_op, num_iterations, adj_qft_cmpr_op=None)

Returns the resources for Quantum Phase Estimation implemented using unary iteration.

Parameters:

• cmpr_walk_op (CompressedResourceOp) – A compressed resource operator corresponding to the quantum walk operator to apply the phase estimation protocol on.

• num_iterations (int) – The total number of times the quantum walk operator is applied in order to reach a target precision in the eigenvalue estimate.

• adj_qft_cmpr_op (CompressedResourceOp | None) – An optional compressed resource operator corresponding to the adjoint QFT routine. If None, the default QFT will be used.

Resources:

The resources are obtained from Figure 2. in Section III of arXiv.2011.03494.

Returns:

A list of GateCount objects, where each object represents a specific quantum gate and the number of times it appears in the decomposition.

Return type:

list[GateCount]

classmethod resource_rep(cmpr_walk_op, num_iterations, adj_qft_cmpr_op=None)

Returns a compressed representation containing only the parameters of the Operator that are needed to compute the resources.

Parameters:

• cmpr_walk_op (CompressedResourceOp) – A compressed resource operator corresponding to the quantum walk operator to apply the phase estimation protocol on.

• num_iterations (int) – The total number of times the quantum walk operator is applied in order to reach a target precision in the eigenvalue estimate.

• adj_qft_cmpr_op (CompressedResourceOp | None) – An optional compressed resource operator corresponding to the adjoint QFT routine. If None, the default QFT will be used.

Returns:

the operator in a compressed representation

Return type:

CompressedResourceOp

static tracking_name(cmpr_walk_op, num_iterations, adj_qft_cmpr_op=None)

Returns the tracking name built with the operator’s parameters.

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