HRSCumulativeMultiplier#

class qiskit.circuit.library.HRSCumulativeMultiplier(num_state_qubits, num_result_qubits=None, adder=None, name='HRSCumulativeMultiplier')[source]#

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: ────■─────────────────────────
           β”‚
  a_1: ────┼─────────■───────────────
           β”‚         β”‚
  a_2: ────┼─────────┼─────────■─────
       β”Œβ”€β”€β”€β”΄β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”΄β”€β”€β”€β”€β”β”Œβ”€β”€β”€β”΄β”€β”€β”€β”€β”
  b_0: ─0       β”œβ”€0       β”œβ”€0       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
  b_1: ─1       β”œβ”€1       β”œβ”€1       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
  b_2: ─2       β”œβ”€2       β”œβ”€2       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
out_0: ─3       β”œβ”€        β”œβ”€        β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
out_1: ─4       β”œβ”€3       β”œβ”€        β”œ
       β”‚  Adder β”‚β”‚  Adder β”‚β”‚  Adder β”‚
out_2: ─5       β”œβ”€4       β”œβ”€3       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
out_3: ─6       β”œβ”€5       β”œβ”€4       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
out_4: ─        β”œβ”€6       β”œβ”€5       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
out_5: ─        β”œβ”€        β”œβ”€6       β”œ
       β”‚        β”‚β”‚        β”‚β”‚        β”‚
aux_0: ─7       β”œβ”€7       β”œβ”€7       β”œ
       β””β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”˜β””β”€β”€β”€β”€β”€β”€β”€β”€β”˜

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] HΓ€ner et al., Optimizing Quantum Circuits for Arithmetic, 2018. arXiv:1805.12445

Paramètres:
  • 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 (int | None) – 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 (QuantumCircuit | None) – 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.

Lève:

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).

Renvoie:

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

Type renvoyΓ©:

QuantumCircuitData

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

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'#
instances = 127#
layout#

Return any associated layout information about 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.

metadata#

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.

Renvoie:

The number of result qubits.

num_state_qubits#

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

Renvoie:

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.

Renvoie:

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

Lève:

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.

Exemples

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 unintuitive 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()
   β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”
q: ─ U(angle_1,angle_2,angle_10) β”œ
   β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜
>>> 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])
])
Renvoie:

The sorted Parameter objects in the circuit.

prefix = 'circuit'#
qubits#

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