Quantum systems require a new way to think about math.

"IISc physicists discovered that Ramanujan’s classic π-formulas arise naturally in modern theories describing critical phenomena and black holes. The connection suggests his early mathematics may have foreshadowed key structures in today’s high-energy physics. Credit: Stock" (ScitechDaily, Ramanujan’s 100-Year-Old Pi Formula That Hides the Secrets of the Universe)

"A new study reveals that Srinivasa Ramanujan’s century-old formulas for calculating pi unexpectedly emerge within modern theories of critical phenomena, turbulence, and black holes."(ScitechDaily, Ramanujan’s 100-Year-Old Pi Formula That Hides the Secrets of the Universe)

100 years ago, Srinivasa Ramanujan introduced a Pi formula that hides a powerful argument. Pi is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used. for defining π, to avoid relying on the definition. Of the length of a curve.” Wikipedia, Pi) We know that Pi has a certain value, and we can use that value in mathematical formulae. To use in calculations to determine the area of the circles. 

Pi is also needed. To calculate the volume of things like balls. The ball can be. Determined as a series of circles or rims. So, where is that information needed? What would you do with formulas that can calculate the distance from the ball surface to the layer? That information is useful in the calculations. That is used. For. Calculating the qubit interaction with the receiver. This information is urgent for quantum networking and quantum computing. 

The new quantum systems require new types of calculations. Or those calculations are not. A very new thing. The needed accuracy. The third-degree and higher polynomial functions are very high. The new mathematical formulas must be created. For the quantum systems that require new types of dimensions. And new variables. To make it possible. To simulate quantum systems. For making a complete simulation, the machine requires all information from the system. And the main problem with quantum systems is this. Everything happens in the 3D universe. 

"Choose a point on the circle (blue). You want to map it to a unique point on the straight yellow line. To do this, draw a dashed line between the green point at the top of the circle and your chosen blue point. Then map the blue point to whichever yellow point this dashed line passes through. You can do this for any given point on the circle. (The green point at the top of the circle gets mapped to a special yellow point at infinity.)" (QauntaMagazine, String Theory Inspires a Brilliant, Baffling New Math Proof)

"Unlike in the previous examples, your dashed line sometimes maps two different points on the elliptic curve (blue) to the same point on the yellow line below. You can’t find a map that avoids this, meaning that the elliptic curve has a more complicated set of solutions than the circle or sphere." (QauntaMagazine, String Theory Inspires a Brilliant, Baffling New Math Proof)

A second problem is this. Everything means something in those systems. Things like solar winds, changes in magnetic fields. And other kinds of things. It can have a big effect on systems. There, a superstring travels through a photon. And that turns a photon into a quantum router that shares photonic information into qubits.

Those calculations are needed for models that the systems use for quantum simulations. The millennium problem P=NP (P versus NP) means that checking calculations should be as fast as solving them. Error detection happens. By. Calculating all calculations backward. The problem is in extremely long calculations. If.  The machine uses. Even. Days to calculate some formula. Using backward calculation is a very long process. So if some stage needs more time to check, there should be a problem. But the fact is this. Nobody proved or disproved that problem universally. 

“The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.”(Wikipedia, P versus NP problem). The idea is that these complex polynomials can be checked by calculating the time. If P=NP. 

Here, "quickly" means an algorithm exists that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the size of the input to the algorithm. The general class of questions that some algorithms can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic polynomial time” (Wikipedia, P versus NP problem)

The new calculation models give new changes. To solve and check a complex polynomial problem. Things. Like, high-class polynomial functions are new tools. For quantum simulations. New. High-power computers can be used to calculate polynomial functions with new accuracy. This thing requires new accuracy for mathematical constants, like Pi. 

https://www.claymath.org/millennium/p-vs-np/

https://www.quantamagazine.org/string-theory-inspires-a-brilliant-baffling-new-math-proof-20251212/

https://en.wikipedia.org/wiki/P_versus_NP_problem

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan