pyqpanda_alg.QLuoShu.ConModMul

Module Contents

Functions

ConModMul(a, N, qvec1, qvec2, auxadd)

Constant Modulo Multiplication.

pyqpanda_alg.QLuoShu.ConModMul.ConModMul(a, N, qvec1, qvec2, auxadd)

Constant Modulo Multiplication.

Parameters:

\(a\): int

the integer to be added

\(N\) : int

the modulo

qvec1 & qvec2 : qlist

the qubits list

auxadd : qubit

an auxiliary qubit

Return:

circuit: pq.QCircuit

The circuit can compute \(a*x \mod N\) with a constant integer \(a\) and a constant modulo \(N\), where the \(qvec1\) register holds an integer \(x\) and the \(|qvec2 \rangle\) register is an auxiliary register with the same size as that of the register \(|qvec1 \rangle\). By the circuit of constant QFT modulo addition-multiplication and the swap operation, we have that \(|x \rangle|0 \rangle \rightarrow |ax \mod N \rangle|0 \rangle\). The result of modulo multiplication is deposited in the register \(|qvec1 \rangle\). The circuit needs \(2n+1\) qubits with \(n=\lceil \log_{2}N \rceil\). The inverse of the circuit can compute \(x/a \mod N\).

Example:

If \(a =2,x=8,N=11\), putting x held in \(|qvec1 \rangle\). By the circuit, the result \(|0101 \rangle\) will be held in the \(|qvec1 \rangle\).

from pyqpanda import *
import math
from pyqpanda_alg.QLuoShu import ConModMul

if __name__ == "__main__":
    N = 11
    a = 2
    x = 8
    n = math.ceil(math.log(N, 2))
    qvm = init_quantum_machine(QMachineType.CPU)
    prog = QProg()

    qvec1 = qvm.qAlloc_many(n)
    qvec2 = qvm.qAlloc_many(n)
    auxadd = qvm.qAlloc_many(1)

    prog << bind_nonnegative_data(x, qvec1) \
         << ConModMul.ConModMul(a, N, qvec1, qvec2, auxadd)

    result = prob_run_dict(prog, qvec1, 1)

    for key in result:
        print(key + ":" + str(result[key]))
        c = int(key, 2)
    print("%d*%d mod %d=%d" % (x, a, N, c))

0101:1.0000000000000226
8*2 mod 11=5

Note that: if \(N\) is a power of 2, we need to let \(n=\lceil \log_{2}N \rceil+1\) in the Example.

Here, we give the circuit graph of the example in the above with 9 qubits in the following:

q_0:  |0>──■─── ───────■────── ───────■────── ───────■────── ───────■────── ─■─ ───────■────── ───────■────── >
           │           │              │              │              │        │         │              │       >
q_1:  |0>──┼─── ───────┼────── ───────┼────── ───────┼────── ───────┼────── ─┼─ ───────┼────── ───────┼────── >
           │           │              │              │              │        │         │              │       >
q_2:  |0>──┼─── ───────┼────── ───────┼────── ───────┼────── ───────┼────── ─┼─ ───────┼────── ───────┼────── >
           │┌─┐        │              │              │              │        │         │              │       >
q_3:  |0>──┼┤X├ ───────┼────── ───────┼────── ───────┼────── ───────┼────── ─┼─ ───────┼────── ───────┼────── >
           │└─┘        │              │              │              │        │         │              │       >
q_4:  |0>──┼─── ───────┼────── ───────┼────── ───────┼────── ───────■────── ─┼─ ───────┼────── ───────┼────── >
           │           │              │              │              │        │         │              │       >
q_5:  |0>──┼─── ───────┼────── ───────┼────── ───────■────── ───────┼────── ─┼─ ───────┼────── ───────■────── >
           │           │              │              │              │        │         │              │       >
q_6:  |0>──┼─── ───────┼────── ───────■────── ───────┼────── ───────┼────── ─┼─ ───────■────── ───────┼────── >
           │           │              │              │              │       ┌┴┐ ┌──────┴─────┐ ┌──────┴─────┐ >
q_7:  |0>──┼─── ───────■────── ───────┼────── ───────┼────── ───────┼────── ┤H├ ┤CR(1.570796)├ ┤CR(0.785398)├ >
          ┌┴┐   ┌──────┴─────┐ ┌──────┴─────┐ ┌──────┴─────┐ ┌──────┴─────┐ └─┘ └────────────┘ └────────────┘ >
q_8:  |0>─┤H├── ┤CR(1.570796)├ ┤CR(0.785398)├ ┤CR(0.392699)├ ┤CR(0.196350)├ ─── ────────────── ────────────── >
          └─┘   └────────────┘ └────────────┘ └────────────┘ └────────────┘                                   >