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Bind

The bind statement (operator ->) is used to rewire the qubits referenced by one or more source variables to one or more destination variables. In accordance with the no-cloning principle, the source variables, which are initialized prior to the bind statement, become uninitialized subsequently. You can use the bind statement to split one quantum object into multiple objects and to join multiple objects into one. You can also use it to reinterpret a numeric object as a qubit array and vice versa.

Syntax

source-var-list -> destination-var-list

source-var-list and destination-var-list are either a single quantum variable or a list of one-or-more comma-separated quantum variables enclosed in { }

def bind(
    source: Union[Input[QVar], List[Input[QVar]]],
    destination: Union[Output[QVar], List[Output[QVar]]],
) -> None:
    pass

Semantics

  • Prior to a bind statement variables in source-var-list must be initialized and variables in destination-var-list must be uninitialized.
  • Following a bind statement variables in source-var-list are uninitialized and variables in destination-var-list are initialized.
  • If more than one variable is listed in destination-var-list, the overall size in bits of each variable must be known. This is required to determine the partition of qubits between them.
    • qnum variables must have a declared or previously inferred size.
    • qbit[] variables must have a declared or previously inferred length.
  • The sum of sizes associated with variables in destination-var-list must agree with the overall number of qubits actually used by variables in source-var-list.
  • Following a bind statement qubits are rewired from the source variable(s) to the respective position in the destination variable(s).

Note that the bind statement is only rewiring qubits across model variables and has no resource footprint (additional gates or auxiliary qubits) on the resulting circuit.

Examples

Example 1: Cast

The following example demonstrates how to use the bind statement to cast a numeric variable to a qubit array and cast back. In it, all bits of some number are flipped. Accessing qubits cannot be performed directly on a qnum variable. Therefore, x is bound to a qbit[] variable to perform the operation and subsequently bound back.

qfunc main(output x: qnum) {
  prepare_int<5>(x);
  qba: qbit[];
  x -> qba;
  repeat (i: qba.len) {
    X(qba[i]);
  }
  qba -> x;
}

from classiq import qfunc, Output, QNum, prepare_int, QArray, bind, repeat, X


@qfunc
def main(x: Output[QNum]) -> None:
    prepare_int(5, x)

    qba = QArray("qba")
    bind(x, qba)
    repeat(qba.len, lambda i: X(qba[i]))
    bind(qba, x)

Example 2: Split and join

The following example demonstrates how to apply an operation on a specific qubit of a numeric variable. In function xor_lsb the LSB (least significant bit) of argument x is the target of a CX operation. This is done by splitting it from x while keeping the rest of the qubits in msbs and subsequently joining x back.

qfunc xor_lsb(x: qnum, xor_bit: qbit) {
  lsb: qnum<1, False, 1>;
  msbs: qbit[x.len - 1];
  x -> {lsb, msbs};
  CX(xor_bit, lsb);
  {lsb, msbs} -> x;
}

qfunc main(output x: qnum) {
  prepare_int<5>(x);
  xor_bit: qbit;
  allocate<1>(xor_bit);
  H(xor_bit);
  xor_lsb(x, xor_bit);
}

from classiq import (
    qfunc,
    Output,
    QBit,
    QNum,
    QArray,
    prepare_int,
    bind,
    CX,
    allocate,
    H,
)


@qfunc
def xor_lsb(x: QNum, xor_bit: QBit):
    lsb = QNum("lsb", 1, False, 1)
    msbs = QArray("msbs", QBit, x.size - 1)
    bind(x, [lsb, msbs])
    CX(xor_bit, lsb)
    bind([lsb, msbs], x)


@qfunc
def main(x: Output[QNum]) -> None:
    prepare_int(5, x)
    xor_bit = QBit("xor_bit")
    allocate(1, xor_bit)
    H(xor_bit)
    xor_lsb(x, xor_bit)

In the overall model, function main calls xor_lsb with the number 5. Its output is the uniform distribution of 5 and 4, correlative to the xor_bit being 0 and 1. Below is the visualization of the resulting quantum program.

xor_lsb.png