## MISSION QUANTUM

#### MISSION QUANTUM

**Note and Trigger Warning: This story like my previous work The Opponent, is completely a different story. It could be understood by those, who know the concept of Physics well-versed and owing to it's intensity, age group of 12 to 14 years people definitely needs parental guidance so that, they could understand the story well and better.**

__MANGLA RESERVOIR, PAKISTAN:__

Near to the Mangla Reservoir of Pakistan around 7:30 PM, terrorists enters inside the camp taking few important Indian scientist as hostages, having killed few Indian Army officers, who guarded them. After seizing Uranium-247 from the young scientists, one of the terrorists orders his men to shoot them and kill.

However, at the nick of time, a DIA agent enters inside their camp, who have the symbol of DIA in the left side of his shirts and on the other hand, holds Mimmi gun. In a violent gun fight, the DIA Agent kills the terrorists and successfully rescued the scientists to the safer side back to India, additionally retrieving the Uranium-247.

Inspired with his self-patriotism and pride for sacrificing his life to the country, a famous scientist Doctor Anil Krish comes to meet the DIA Agent's senior officer Vishnu Varma, who is around 65-years old, with a salt and pepper hairstyle.

"Sir. Have a seat. If you have called me, I myself could have came right?" asked Vishnu Varma.

The 68-year old Anil Krish looks at Varma and replies, "Why to give unnecessary troubles for you sir? That's why I myself have came here." Pausing for a while, Krish asked him: "Ok. May I meet DIA Agent Dhaswin?"

"Sure sir. I will ask my subordinates to bring him" said Varma and he brings Dhaswin to Krish.

Surprised seeing Krish, Dhaswin asked to Varma, "Sir. Who is he?"

"He is Doctor Anil Krish. A renowned scientist from Quantum organization. He wished to meet you. That's why I have brought you here" said Varma. After a while, the scientist is asked by Varma, "Sir. Why do you want to meet Dhaswin? What's the main purpose sir?"

"I have planned for an important mission. For that, I need your help Dhaswin!" Krish slowly said to him, to which Dhaswin asked him: "Mission with me. What's the name of this mission sir?"

__QUANTUM ORGANIZATION, MEHRAULI, NEW DELHI:__

Silent for a while, he replied him: "Mission Quantum." Krish takes the duo to the Quantum Organization at Mehrauli in New Delhi. Dhaswin blinks for a while at Vishnu Varma, who too is confused and asked to Krish, "Quantum. What's meant by that sir? It seems I have learnt it from some books."

Krish explained them: **"It's the physics that explains how everything works: the best description we have of the nature of the particles that make up matter and the forces with which they interact. Quantum physics underlies how atoms work."**

Now, Dhaswin asked the scientist: "Sir. I understand what you say. But, what is the link between Quantum and the mission? I am seriously getting confused."

Seeing to this, the scientist now explains him in further saying about the Schrodinger equation by telling him: "It is a linear partial differential equation that governs the wave function of a quantum mechanical system and showcases the properties and formulas to Dhaswin, explaining him about the concepts.

After one hour of explanation, he now comes to the real motive of this mission saying him: "Have you heard about Hiroshima-Nagasaki Bombings in 1945 Dhaswin?"

After thinking a while, he tells him: "Yes sir. I remember that well. Due to the nuclear bombings, children are still more getting the radiation of cancers in that country."

"The same way is going to happen to our world countries because of: General Wu Xing." Krish said to him.

Varma asked him: "Sir. What's the problem with that? What are they planning?" Reading the research analysis papers that he had brought, Anil Krish tells them: "HA-360."

"You mean?" asked Dhaswin to which, he tells him: **"Hydrogen-Atom 360. Schrodinger equation, the General have done five year periods of research. He have additionally used Newton's Second Law of motion to strengthen this bomb. Using this bomb, they are planning to spread widespread cancers all over the nation."**

**Confused and puzzled, Dhaswin asked to the scientist: "Sir. How could it be possible?"**

**Now, Anil Krish explains him about the Schrodinger equation for the hydrogen atom by telling: "In the radial equation,**

** **

**ddr(r2dRdr) 2μr2ℏ2(E Ze24πϵ0r)R−l(l 1)R=0,**

**apply the product rule to the first term:**

** **

**r2d2Rdr2 2rdRdr 2μr2ℏ2(E Ze24πϵ0r)R−l(l 1)R=0,**

**and divide by r2:**

** **

**d2Rdr2 2rdRdr (2μℏ2(E Ze24πϵ0r)−l(l 1)r2)R=0.**

**We can't solve this straight away, but for very large r, the highlighted terms are forced to zero because they go reciprocal with r.**

** **

**That leaves us with an asymptotic equation:**

**d2R∞dr2 2μEℏ2R∞=0,**

**which is another ODE with constant coefficients. Solution:**

** **

**R∞=c3exp(i2μEℏ2−−−−√r) c4exp(−i2μEℏ2−−−−√r).**

**It makes sense to use as the zero point of potential energy the energy of a free electron, i.e. in this asymptotic case, E→0 for an electron far away from the nucleus, as it is practically free. Since the presence of the positive charge in the nucleus stabilizes the atom, we must look for solutions where E becomes negative as the electron comes closer to the nucleus. These two conditions are met if we choose c4=0 and use the fact that E<0 to get rid of the imaginary unit.**

** **

**The asymptotic solution is then**

**R∞=c3exp−(−2μEℏ2−−−−−−√r).**

**The detail nearer the nucleus is expanded in a power series:**

**R=R∞∑q=0∞bqrq.**

**This results in a series of powers of r whose coefficients must all be zero to match the RHS of the differential equation. From that, a recursion formula is derived for the bq, and the requirement for the series to converge produces another quantum number, n.**

** **

**This results in the radial solution**

**Rn,l(r)=R∞(r)b0exp(μZe2r2πϵ0ℏ2n),**

**where the coefficient b0 contains the l-dependence.**

**At the same time, the solution of the radial part also fixes the possible energy levels by linking them to the quantum number n."**

Now, he explained him in further by stating: "The radiations are created along with Plutonium into this bomb Dhaswin. If it is combined, the quantum becomes serious and there are high threat for cancer disease in the world nations." Shocked by this, Varma asked him: "Sir. Why do they want to do this?"

"Because America and European countries are dominating and well-developed, Chinese are jealous of it and tries to curb their financial and Economic power by affecting the world countries peace, so that they could gain No. 1 position in everything." The Scientist explains them about everything clearly.

The scientist gives Varma the details about this mission and explains him about the objective of this mission, clearly after sending out Dhaswin. Following this, Varma meets Dhaswin in his DIA Office and shows him the photo of a man. Seeing his photo, he asked him: "Sir. Who is she? What's her name?"

"And this man's name is James Christopher, an arms dealer in Mumbai. She is an art appraiser in Pakistan. I will tell the rest later after, you meet that woman in Gulmarg, North-western border of India" said Vishnu Varma.

__MUMBAI:__

As instructed by Varma, Dhaswin meets James Christopher in Mumbai at Leopold Café around 6:30 PM. Introducing himself to be in the "Mission Quantum" and explaining about the problems told by the Scientist Krish, he asked him to help in the mission.

Confirming this from Krish to be a truth, James explains him about the Uranium-247 and Hydrogen catridges, being purchased by Pakistan oligarch Muhammad Irfan Khan, who is residing in Gulmarg, the North-western India's border.

Henceforth, he heads to Gulmarg and through interrogation and investigation, comes across Zareena, Irfan Khan's estranged wife.

He approaches Zareena Khan in a drawing mall, where she is currently residing. Meeting her, he greets her through Muslim style and tells her, "Greetings madam. I am Irfan Khan's friend Muhammad Abdullah. He sent me to meet you."

Dhaswin said this to test her and as he predicted, she gets angered upon hearing Irfan Khan's name and walks away from that place. However, Dhaswin consoled her and reveals his real-identity as a DIA Agent. After a while, he tells her: "I know that you are an art appraiser and additionally, know you have authenticated a forged Mahmud of Ghazni drawing. And using this situation to his advantage, Irfan purchased the drawing from the forger and is using your authentication to blackmail you and keep you controlled in relationship. Am I right Zareena?"

Zareena nods her head and her eyes is filled with some sorts of fear and tears. Upon learning this from her, Dhaswin contacts Vishnu Varma and have a conference call with Doctor Anil Krish.

Krish gives him an instruction saying, "Dhaswin. To meet Irfan, you have only one option. You have to steal the drawings of Ghazni." While, Vishnu Varma traces the location of the drawing to be in the storage facility at the Jammu Airport. Reaching there, Dhaswin kills two men, who were guarding the facility and steals the drawing from the storage. Now, he meets James Christopher in Srinagar of Kashmir.

There, Christopher explained him about the secret underground in Wu Xing's office. For that, he explained him about the concept of Quantum phase estimation algorithm telling, **"It is to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator. More precisely, given a unitary matrix {\displaystyle U}U and a quantum state {\displaystyle |\psi \rangle }|\psi \rangle such that {\displaystyle U|\psi \rangle =e^{2\pi i\theta }|\psi \rangle }{\displaystyle U|\psi \rangle =e^{2\pi i\theta }|\psi \rangle }, the algorithm estimates the value of {\displaystyle \theta }\theta with high probability within additive error {\displaystyle \varepsilon }\varepsilon , using {\displaystyle O(\log(1/\varepsilon ))}O(\log(1/\varepsilon )) qubits (without counting the ones used to encode the eigenvector state) and {\displaystyle O(1/\varepsilon )}{\displaystyle O(1/\varepsilon )} controlled-U operations. The algorithm was initially introduced by Alexei Kitaev in 1995. Phase estimation is frequently used as a subroutine in other quantum algorithms, such as Shor's algorithm and the quantum algorithm for linear systems of equations. **After researching, Wu Xing have worked out the formulas in the computer, with the help of Irfan Khan and have cleverly protected the HA-360 Bombs having prepared a locker for it's safety." James Christopher leaves the place, being alerted that Zareena is arriving to meet Dhaswin.

__ARABIAN SEA, JAMMU AND KASHMIR:__

Zareena introduces Dhaswin to Irfan Khan in the middle of Arabian Sea in Jammu & Kashmir, where he resides in a ship. He learns from him about the meeting with Wu Xing in the upcoming week at Wuhan Laboratory of China, from where they are planning to conduct the widespread attacks. Afterwards, Irfan Khan captures Dhaswin, holding him hostage with the help of his henchmen.

He tells him, "I know for what purpose you have came to meet me Dhaswin. And additionally, I know about your profession." However, Dhaswin tries to manage him by telling, "Basically, I am an arms dealer, planning to sell some of my weapons to you." But, Irfan is blind and refuses to hear his words. At that time, he sees some of his henchman been stabbed by Zareena and she attempts to have Irfan drowned in the sea. However, Dhaswin saves him from being killed by Zareena.

Impressed with this, Irfan Khan strikes a deal with Dhaswin. He tells him, "I am not interested in the deal of Wu Xing. Actually, I wanted to add nuclear powers too in the bomb, that I and Wu Xing had created using Quantum Mechanics. He refused and instead added the Hydrogen, Atomic particles and Plutonium. He doesn't pay heed to my words." Irfan Khan further explains to Dhaswin that, "He know about the password of the underground place, where Wu Xing have hidden the bomb in a safe place."

__THREE DAYS LATER:__

__SPRATLY ISLANDS, CHINA:__

Three days later, Dhaswin and Irfan Khan reaches China. Lying to Irfan Khan that, he is going for Manasarowar Lake in Mount Kailash, he reaches Spratly Islands through the ship. While driving, he recalls about the instructions given by Vishnu Varma. He told to Dhaswin, "Dhaswin. There are some suspicious activities going in this particular islands. Your duty is to go and learn what's happening in this place!"

Reaching the place, Dhaswin uses his binoculars to know what's happening in the place exactly. From the binoculars, he sees the rigorous training given to the Chinese army men. Additionally, he sees few dangerous weaponries being prepared and the hardcore exercises being given by the retired soldiers of the Chinese army. Further, he is shocked upon knowing that, "Nuclear Rocket is being launched there" and it implies to him, "They are ready to fight against the world nation, if they attempt to hold an attack against the country."

Parking the ship nearby, he silently enters into the research room, after beating up two guards unconscious. There, he is shocked to find out that: "Chinese have planned to stage 'Third World War' and have done ten years of research about Quantum mechanics and Physics theories, with which they have prepared several of these missiles and weaponries." He exits from Spratly Islands and meets Irfan Khan, who takes him to Wuhan Laboratory, as the time is already up to see Wu Xing, who sees punctuality as important.

Meeting the Chinese gangsters and Chinese General Wu Xing, Dhaswin secretly makes a call to Varma, Krish and Christopher. When Wu Xing tells about the time to leak out the HA-360 Bombs, Varma instructs Dhaswin to shoot down everyone in the lab, including the security guards and few Defence securities. Dhaswin gets up with his Desert Eagle Gun and keeps it in the head of Irfan Khan telling, "I am sorry Irfan Khan. I have actually used you for my mission Quantum. Thank you for exposing these people."

"Who are you da?" asked Wu Xing, in Chinese language and Irfan translates it to him. For that, he tells, "I am DIA agent Dhaswin Krishna da."

Everyone are shocked. He shoots Irfan to death and in the ensuing gunfight, the Chinese gangsters are brutally killed and finally, Dhaswin kills Wu Xing. He then reaches the underground, where he enters the password as told by Irfan Khan and enters into the laboratory to retrieve the bombs.

However, there's another problem in the place, where the bomb is protected. He is confused with the triangle-free graphs, appearing in the mirror, which he attempts to break off and take the bomb.

Dhaswin asks about this to Christopher who tells him: **"The triangle finding problem is the problem of determining whether a graph is triangle-free or not. When the graph does contain a triangle, algorithms are often required to output three vertices which form a triangle in the graph. It is possible to test whether a graph with m edges is triangle-free in time O(m1.41).[1] Another approach is to find the trace of A3, where A is the adjacency matrix of the graph. The trace is zero if and only if the graph is triangle-free. For dense graphs, it is more efficient to use this simple algorithm which relies on matrix multiplication, since it gets the time complexity down to O(n2.373), where n is the number of vertices. As Imrich, Klavžar & Mulder (1999) showed, triangle-free graph recognition is equivalent in complexity to median graph recognition; however, the current best algorithms for median graph recognition use triangle detection as a subroutine rather than vice versa. The decision tree complexity or query complexity of the problem, where the queries are to an oracle which stores the adjacency matrix of a graph, is Θ(n2). However, for quantum algorithms, the best known lower bound is Ω(n), but the best known algorithm is O(n5/4)."**

Using the concepts explained by Christopher, Dhaswin successfully retrieves the bombs by drawing the algorithm formula, which matches the code. Following this, he retrieves the HA-360. Further, he disables and hacks the launch pad, that is used for the attacks, thus preventing Third World War.

__THREE DAYS LATER:__

__MUMBAI:__

Three days later, Dhaswin returns back to Mumbai and meets James Christopher. He have Zareena as a hostage and tells, "I am planning to kill her Dhaswin. Since, she knows too much about our mission." However, he asked him to release her telling him: "Eventhough she knew too much about this mission, she can't do anything. So, let her go off." As a henceforth, James released her and she bids farewell to Dhaswin, having thanked him for killing Irfan Khan.

While, Dhaswin informed to Krish and Varma saying, "Sir. Mission Quantum is success." While going with Christopher, he tells Dhaswin about Quantum Complexity Theory, Quantum Technology and Quantum Field theory. Hearing this, Dhaswin laughed and tells him: "Hey. The mission is already over. Stop it and just admire the beauty of this place man. Stupid fellow!"

__EPILOGUE:__

__CONCEPTS USED FOR THE STORY:__

**Before working on this story, I deeply researched about Quantum Mechanics, Second Law of Newton's motion, Quantum Algorithm and various other physics concepts. To understand this story, one must have a clear knowledge about Quantum Mechanics and Classical Physics.**

__INSPIRATIONS:__

**Director Christopher Nolan sir's science-fiction thriller films such as Prestige, Inception, Interstellar and Tenet served as an inspiration and role-model for me to sketch and write this story, that's really challenging to me. And several other Science fiction short-stories and novels also became a source of inspirations for me. In most of my works, I influence the themes of Nolan sir's mortifs of Memories, grief, human morality, philosophical ideas and so many of his thought provoking works like Reality, dreams, existential, ethical and epistemological themes....Other Source of inspirations are James Cameron and a few English authors...**

** **