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# HRSCumulativeMultiplier¶

Bases: Multiplier

A multiplication circuit to store product of two input registers out-of-place.

Circuit uses the approach from [1]. As an example, a multiplier circuit that performs a non-modular multiplication on two 3-qubit sized registers with the default adder is as follows (where Adder denotes the CDKMRippleCarryAdder):

  a_0: ────■─────────────────────────
│
a_1: ────┼─────────■───────────────
│         │
a_2: ────┼─────────┼─────────■─────
┌───┴────┐┌───┴────┐┌───┴────┐
b_0: ┤0       ├┤0       ├┤0       ├
│        ││        ││        │
b_1: ┤1       ├┤1       ├┤1       ├
│        ││        ││        │
b_2: ┤2       ├┤2       ├┤2       ├
│        ││        ││        │
out_0: ┤3       ├┤        ├┤        ├
│        ││        ││        │
out_1: ┤4       ├┤3       ├┤        ├
out_2: ┤5       ├┤4       ├┤3       ├
│        ││        ││        │
out_3: ┤6       ├┤5       ├┤4       ├
│        ││        ││        │
out_4: ┤        ├┤6       ├┤5       ├
│        ││        ││        │
out_5: ┤        ├┤        ├┤6       ├
│        ││        ││        │
aux_0: ┤7       ├┤7       ├┤7       ├
└────────┘└────────┘└────────┘


Multiplication in this circuit is implemented in a classical approach by performing a series of shifted additions using one of the input registers while the qubits from the other input register act as control qubits for the adders.

References:

[1] Häner et al., Optimizing Quantum Circuits for Arithmetic, 2018. arXiv:1805.12445

Parameter
• num_state_qubits (int) – The number of qubits in either input register for state $$|a\rangle$$ or $$|b\rangle$$. The two input registers must have the same number of qubits.

• num_result_qubits (Optional[int]) – The number of result qubits to limit the output to. If number of result qubits is $$n$$, multiplication modulo $$2^n$$ is performed to limit the output to the specified number of qubits. Default value is 2 * num_state_qubits to represent any possible result from the multiplication of the two inputs.

• adder (Optional[QuantumCircuit]) – Half adder circuit to be used for performing multiplication. The CDKMRippleCarryAdder is used as default if no adder is provided.

• name (str) – The name of the circuit object.

Verursacht

NotImplementedError – If num_result_qubits is not default and a custom adder is provided.

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}

clbits

Returns a list of classical bits in the order that the registers were added.

data

Return the circuit data (instructions and context).

Rückgabe

a list-like object containing the CircuitInstructions for each instruction.

Rückgabetyp

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

instances = 153
layout

Return any associated layout information anout the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or PassManager.run() to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

num_ancillas

Return the number of ancilla qubits.

num_clbits

Return number of classical bits.

num_parameters

The number of parameter objects in the circuit.

num_qubits

Return number of qubits.

num_result_qubits

The number of result qubits to limit the output to.

Rückgabe

The number of result qubits.

num_state_qubits

The number of state qubits, i.e. the number of bits in each input register.

Rückgabe

The number of state qubits.

op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

Rückgabe

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

Verursacht

AttributeError – When circuit is not scheduled.

parameters

The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

Examples

The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])


Bear in mind that alphabetical sorting might be unituitive when it comes to numbers. The literal „10“ comes before „2“ in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
└─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])


To respect numerical sorting, a ParameterVector can be used.



>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
..., ParameterVectorElement(x[11])
])

Rückgabe

The sorted Parameter objects in the circuit.

prefix = 'circuit'
qubits

Returns a list of quantum bits in the order that the registers were added.