Using model.add_constraint_eq_zero(----, lam=xxxx) with multiple indexed variables and sums

[CPalas]

When developing a QUBO model for quantum optimisation, I am not able to create several constraints such as the one below:

\begin{equation}
\sum_k\sum_{\substack{j \in L \ j \ne i}}x_{i,j,k}+\sum_k\eta_{i,k}=1, \forall i \in L
\end{equation}

node j can be reached only by another node i, or it is the last location served by k.

I managed to create two and three-indexed variables ,such as x(i,j,k), by using for ... in loops, but I am not able to create the constraints.

I imagine I could go for one constraints for each i index, by using the function
model.add_constraint_eq_zero(----, lam=xxxx)

but I do not know how to nest the sums inside the function, to properly write the constraint.

[jtiosue]

Let me show a simple of example of nested sums in constraints. You should be able to simply modify it for your application. Suppose I have Boolean variables x(i,j) and coefficients c(i,j). That is,

import qubovert as qv
import random

n = 10

x = {
    (i, j): qv.boolean_var(f"x({i}, {j})")
    for i in range(n)
    for j in range(n)
}

c = {
    (i, j): random.random()
    for i in range(n)
    for j in range(n)
}

Given this, I want to enforce the constraint

$$\sum_{i,j=1}^n c(i,j) x(i,j) = 2.$$

Let's say I have a PCBO model that I want to add this constraint to. Then we can do this:

model = qv.PCBO() # make whatever PCBO you want

constraint = 0
for i in range(n):
    for j in range(n):
        constraint += c[(i,j)] * x[(i,j)]

constraint -= 2

model.add_constraint_eq_zero(constraint, lam=1) # set the Lagrange multiplier however you want

[CPalas]

Dear Joe, thank you very much for your solution and example, very explicative. Best regards, Claudio Sent from Outlook for Mac From: Joseph T. Iosue ***@***.***> Date: Wednesday, 4 February 2026 at 21:25 To: jtiosue/qubovert ***@***.***> Cc: Claudio Palasciano ***@***.***>, Author ***@***.***> Subject: Re: [jtiosue/qubovert] Using model.add_constraint_eq_zero(----, lam=xxxx) with multiple indexed variables and sums (Issue #51) [https://avatars.githubusercontent.com/u/17017344?s=20&v=4]jtiosue left a comment (jtiosue/qubovert#51)<#51 (comment)> Let me show a simple of example of nested sums in constraints. You should be able to simply modify it for your application. Suppose I have Boolean variables x(i,j) and coefficients c(i,j). That is, import qubovert as qv import random n = 10 x = { (i, j): qv.boolean_var(f"x({i}, {j})") for i in range(n) for j in range(n) } c = { (i, j): random.random() for i in range(n) for j in range(n) } Given this, I want to enforce the constraint $$\sum_{i,j=1}^n c(i,j) x(i,j) = 2.$$ Let's say I have a PCBO model that I want to add this constraint to. Then we can do this: model = qv.PCBO() # make whatever PCBO you want constraint = 0 for i in range(n): for j in range(n): constraint += c[(i,j)] * x[(i,j)] constraint -= 2 model.add_constraint_eq_zero(constraint, lam=1) # set the Lagrange multiplier however you want — Reply to this email directly, view it on GitHub<#51 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AEVTIFN4UDN5DYNWUWD6VAD4KJITDAVCNFSM6AAAAACTAJYKN2VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZTQNBZGQYTKNZSG4>. You are receiving this because you authored the thread.