Variable and Expression Classes

Var and Expr classes

PyQBPP provides two main classes for building QUBO/HUBO expressions:

• Var: Represents a binary variable, associated with a display name.
• Expr: Represents an expression consisting of an integer constant and zero or more product terms.

Var objects are created using qbpp.var() and are immutable. Expressions are built from variables using arithmetic operators (+, -, *) and are mutable via compound assignment operators such as +=.

The following program demonstrates variable and expression creation:

import pyqbpp as qbpp

x = qbpp.var("x")
y = qbpp.var("y")
f = 2 * x * y - x + 1
f += 3 * y

print("f =", f)

This program prints:

f = 1 -x +2*x*y +3*y

NOTE PyQBPP uses the C++ QUBO++ library as its backend, which internally distinguishes between Term (a single product term like 2*x*y) and Expr (a sum of terms). In PyQBPP, however, you do not need to be aware of this distinction. Python’s dynamic typing automatically converts between types as needed, so you can simply write expressions naturally.

Coefficient and Energy Types

By default, import pyqbpp uses 32-bit coefficients and 64-bit energy (c32e64), which is the fastest type variant suitable for most problems.

For larger problems or arbitrary precision, you can choose a different type variant by importing a submodule:

import pyqbpp as qbpp              # Default: c32e64 (32-bit coeff, 64-bit energy)
import pyqbpp.cppint as qbpp       # Arbitrary precision (cpp_int) for very large coefficients

The following type variants are available:

Import	Coefficient	Energy	Use case
import pyqbpp	32-bit	64-bit	Default; most common choice
import pyqbpp.c16e32	16-bit	32-bit	Small problems
import pyqbpp.c32e64	32-bit	64-bit	Same as default
import pyqbpp.c64e64	64-bit	64-bit	Large coefficients
import pyqbpp.c64e128	64-bit	128-bit	Large energy range
import pyqbpp.c128e128	128-bit	128-bit	Very large problems
import pyqbpp.cppint	unlimited	unlimited	Arbitrary precision

NOTE The type variant must be chosen at import time and cannot be changed afterward. All variables, expressions, and solvers within a program use the same type.

Example with arbitrary precision

import pyqbpp.cppint as qbpp

x = qbpp.var("x")
f = 123456789012345678901234567890 * x + 987654321098765432109876543210
print("f =", f)

This program produces the following output:

f = 987654321098765432109876543210 +123456789012345678901234567890*x