Some researchers from **IBM** published a study in which they report the discovery of a technique they call ** tangle forging**or

**“correlation forging”**, which allows you to divide a problem into two parts and then put the solutions together to arrive at the solution of the original problem. The advantage of this approach is that you can get better results on current issues or tackle bigger issues.

## Correlation forging: how IBM breaks down problems (and then puts them back together)

A popular programming technique called “divide and conquer” involves splitting a problem into smaller parts, which are processed independently, and the results of which are then reassembled to obtain the result of the initial larger problem. This appears to be, at least in spirit, the approach taken by IBM researchers in creating “correlation forging.”

As explained in a article on the company’s blog, this process involves a **dividing a problem into several stages and into two parts**, such as calculating the ground state of a water particle. The first part is that of**problem analysis** with traditional computers, looking for a way to divide it into two parts. Once this path is found, the solutions to both halves of the problem come **calculated by quantum computer** and then they come **joined on traditional computers**.

This method, seemingly very simple in essence, achieves results similar to, if not better than, those obtained by dealing with the big problem entirely on quantum computers. IBM researchers simulated the ground state of a water molecule, with ten spin orbitals, **on only five qubits** of the 27 available on a Falcon processor. **Normally this would require at least 10 qubits**so the advantage of this technique is clear: it is theoretically possible to find solutions to problems larger than those otherwise treatable with currently available hardware.

It should be noted that **not all problems can be solved this way**: IBM researchers talk about *“weakly entangled halves”*, or “weakly correlated halves”, as a prerequisite for being able to use the Correlation Forge. In other words, the problem itself must lend itself to being “split” in two, as is the case with the water molecule where it is possible to separate the spin-up orbitals from the spin orbitals -down.

## Divide and conquer in quantum: a solution to the problem of today’s quantum computers

The difficulty, and the novelty, of IBM’s research was precisely to demonstrate that the approach *divide and impose* could also apply to quantum problems. There are limits, however: classical computers that participate in the calculations must maintain a list of values representing the correlations between the two halves of the problem, and these lists can have problematic dimensions. There is also **problem of air**, i.e. the calculations that must be made to operate the system without any contribution to the solution, which can be significant; Phone

*air*it grows as the two halves of the problem are linked together. However, unnecessary calculations can be greatly reduced when the halves of the problem are weakly correlated.

The hope of the IBM researchers is therefore that this technique may lead to better results and to larger problems even on current quantum computers, which are severely limited by noise (i.e. by the presence of errors) and by the still low number of qubits. **Blake Johnson**leader of the IBM Quantum platform, states that *“Tangle forging is essentially breaking a circuit *[ovvero una serie di operazioni da eseguire su un computer quantistico, NdR] *bigger in smaller circuits that we can run on smaller hardware. Smaller circuits are not only easier to run, they are also able to tolerate a lot more noise just by being smaller. In general, if you want to extend creating correlations to a broader set of problems, one potential avenue would be to include a step in your process where you look for the best place to cut, where reassembly is cheapest. »*

This is not the first time that such an approach has been successfully attempted: there is already a family of techniques called *“circuit knitting”* in English, or “circuit network” in Italian, which uses a similar approach; the difference is that correlation forging is highly scalable. The evolution of problem-solving techniques is an integral part of the development of quantum computers and is essential to obtain significant future results with these new devices.