Reference: Modular Addition Qubricks¶

ModularAdd ¶

ModularAdd(adder_qubrick=None, **kwargs)

Bases: Qubrick

Modular addition: computes dst = (dst + rhs) % M, where M is a positive integer.

dst must store a value less than M.

rhs as type QUInt, QInt, and Qubits must store a value less than M. As type QInt, rhs must also store a value greater than -M. If rhs is of type int, it can store any value.

While this was implemented independently, it ended up similar to the one described in "How to compute a 256-bit elliptic curve private key with only 50 million Toffoli gates" (https://arxiv.org/abs/2306.08585 ⧉).

Parameters:

Name	Type	Description	Default
`adder_qubrick`	`Qubrick or None`	Qubrick to perform internal additions. Defaults to GidneyAdd.	`None`

compute ¶

compute(
    dst: QUInt,
    rhs: QInt | int,
    M: int,
    ctrl: Qubits | None = None,
)

Computes dst = (dst + rhs) % M.

Parameters:

Name	Type	Description	Default
`dst`	`QUInt`	Register to add the number to.	required
`rhs`	`QUInt \| QInt \| int`	The number to add to `dst`.	required
`M`	`int`	The modulo used for modular addition.	required
`ctrl`	`Qubits \| None`	Optional quantum control.	`None`

Note

dst is unsigned, and must store a value less than M.
If rhs is a QInt or QUInt, it must store values less than M.
If rhs is a QInt, it must store a value greater than -M.
If rhs is an int, it may store any value.