## Overview:

The goal of this challenge is to come up with a 25*25 circuit or equivalent to be solved with reasonable accuracy using Qiskit. Some sample problem statements are provided. There is flexibility in terms of circuit sizes and problem statements, but they have to be agreed upon by the organizers (see details below). This challenge is not just about getting the best accuracy for the problem statement, it is also about *finding a circuit that is deep enough and being able to solve them with reasonable fidelity*. We will evaluate the strength of the solution based on the quantum tools/techniques used in Qiskit with respect to the spirit of the challenge i.e. the capability to evaluate deep circuits.

## Details:

### Circuit sizes:

We define a x*y circuit as follows:

x is the number of qubits in the circuit.

y is two-qubit gate depth where the circuit contains at least one qubit involved in y two-qubit gates.

The participant team can also propose a circuit of a different dimension and argue (at a high level) that it’s equivalent/harder than 25*25.

### Problem statement:

Any problem statement for which the circuit size criteria is satisfied will be permitted.

## Stages of the competition:

- The participant team to submit a 25×25 circuit (or equivalent described above) with respect to a problem statement. The team also submits a solution based on a simulator execution for this circuit (or a smaller one with around 15 qubits) to validate the correctness of this circuit and to provide a base solution.
- There is a sample problem statement provided. We will upload one or two more problem statements by the end of February. The participants are also allowed to choose their own problem statement of interest that fits the circuit-size criteria.
- The organizers will validate the submission. Once validated, the team will be provided access to a premium 27 qubit IBM machines through the IIT Madras Quantum Innovation Center’s provider for the duration of the competition.
- The premium access will be limited in terms of hours. So, the best practice is to test any hypothesis and a smaller version of the circuit in simulators and open hardware before going on to use the premium hardware. (There’s also an option to get additional premium access by yourselves through pay-as-you-go access from IBM cloud if that’s affordable).
- Once initial progress has been made, the teams will get mentorship on their work from experts in IIT Madras and IBM.
- Intermediate checkpoint on April 12th: The top few teams at this stage will have an opportunity to showcase their work in this competition in the grand industry event to happen at IIT Madras with dignitaries from IIT Madras and IBM including Jay Gambetta, VP at IBM Quantum, in the audience.
- The competition will conclude at the end of May with a final evaluation.

## Note:

The participants should be citizens of India.

###### 1 a. Protein Folding

You are given a peptide chain with a given sequence of amino acids. Consider that the amino acids are categorized into two types: **H** and **P** (**H **= hydrophobic, **P** = Polar). For example, a chain could be of the form **HPHPHPP**, etc. Amino acids of the type H have strong interactions and tend to stick together. You are given a 3-dimensional lattice where the chain will reside. The objective of the problem is to find the final structure of the folded chain such that the system’s overall energy is minimum. The energy of the system could be considered as the negative of the sum of the interactions.

For example, consider a chain **HPPHPH**. We have three **H** amino acids. The energy could be written as

Here, c_ij is the interaction strength between the amino acids with indices i and j , and both belonging to the type **H**. d_ij is a quadratic function and reflects the distance between the amino acids i and j. The interaction is stronger when the amino acids are closer, and for our problem, we could consider the function to be a scalar multiple of the Euclidean distance.

The lattice where the peptide chain resides could be considered as a 3D cubic lattice. Every amino acid resides on a discrete point in the lattice. You could consider two different cases,

(a) two amino acids can reside on a same point in the lattice and

(b) no two amino acids can reside on the same point in the lattice.

The continuity of the chain must be maintained, even in the final folded structure.

Write a formulation of the above problem that can be implemented using a gate-based Quantum algorithm. Find the lowest energy state or the final folded structure of the peptide chain from the results of the implementation.

## 1 b. Protein Folding

Problem: Given a “n” amino acid peptide, (user input: length of the peptide, string containing

the peptide sequence) find the lowest minimum energy state of the protein on a 3D cubic lattice.

Consider the amino acids as beads and start by fixing the bead1 at the starting point of the

lattice. Now the bead2 can take any position on the lattice but adjacent to bead1 as all beads

are connected. This condition remains the same for all the beads. You will be getting different

combinations of bead positions on the lattice. For each of the combinations of beads, calculate

the interaction energy using MJ potential (bead pair interaction energy table – consisting of

interaction energy between 2 adjacent beads, provided below). Then try to minimize the energy

and represent the least energy combination over the lattice that determines your folded state of

the protein. Ensure that 2 beads never overlap.

User Input:

Case-1: 7, APRLRFY

Case-2: 10, GYDPETGTWG

MJ Matrix

## 2. AML and Fraud Detection

Problem Statement:

AML and Fraud detection use case for QML

Training data set:

Test data set:

## Submit your solution HERE

## Deadline to submit the circuit and a first cut simulator solution – **March 22 nd 2023**

Have questions/doubts? Join the Quantum Grand Challenge 2023 google group – Link here!