### Contest Problems

##### 1.Introduction

The rapid evolution of drug discovery is continuously fueled by cutting-edge technologies,
especially in understanding complex molecular interactions pivotal to medical therapies. Among the tools deployed, computational methods have garnered significant attention,
with **machine learning techniques** emerging as a key player in deciphering intricate patterns and optimizing solutions.
**Quantum computing**, when assisted by machine learning techniques, has the potential to redefine drug discovery. It not only presents an opportunity to solve challenges deemed impossible for classical computers but also enhances our ability to predict and understand molecular behaviors with unprecedented accuracy [1].

A critical molecule in the pharmacological landscape is the **hydroxyl cation (·OH)**. This cation is more than just a molecular entity; it's a central axis for numerous drug interactions. Its high reactivity is linked to oxidative stress, resulting in a range of health conditions, from neurodegenerative disorders and cardiovascular diseases to cancers.
Beyond its pathogenic roles, the hydroxyl cation is also integral to the efficacy of many drugs. With the development of quantum computing, we can potentially achieve a deeper understanding of the interactions and effects of molecules like the hydroxyl cation, accelerating breakthroughs in therapeutic developments.

Given its prominence, understanding the quantum mechanics of the hydroxyl cation at an intricate level can significantly impact drug discovery processes. A fundamental starting point is the accurate determination of its ground state energy. This knowledge can serve as a cornerstone, upon which more complex drug-cation interactions can be built. However, the quantum realm is notoriously challenging. With the current limitations in qubit numbers and quantum error rates, comprehensive simulations of larger drug molecules remain a distant goal. This is where the elegance of the hydroxyl cation comes into play. Its relatively smaller size offers a feasible task for current quantum computing capabilities, making it an ideal candidate for a quantum simulation challenge, and more importantly, paving the way towards the future research landscape that large scale is a fundamental need.

##### 2.Objective

The goal of the 2023 Challenge is to calculate the ground state energy of the hydroxyl cation (·OH).

We ask participants to design and implement a working, open-source protocol that can automatically calculate the ground state energy of the **hydroxyl cation (·OH)** from the given
hamiltonian. We allow the participants to freely explore the design space, with some guidelines below. Participants can propose a good qubit mapping strategy by codesigning hardware and software;
Pauli string grouping and other joint measurement strategies can be potentially implemented to reduce the shots on observables to save the cost on quantum resources; AI/ML or scientific-based circuit architecture search framework
could give a good ansatz for better performance; AI/ML or scientific-based error mitigation can also help for better performance. Last but not least, the experience of the optimizer's initial
parameter or initial scaling of the parameter are important topics for this challenge.

##### 3.Data

The data provided for this challenge revolves around the central theme of drug discovery, focusing on the fundamental quantum mechanics of the hydroxyl cation (·OH). As a pivotal entity in numerous drug interactions and physiological processes, an intricate understanding of the hydroxyl cation is crucial. To aid participants in this endeavor, we've curated a specialized dataset tailored to encapsulate the of the hydroxyl cation's hamiltonian. We have provided the the hamiltonian for reference.

##### 4.Data Format

All data is formatted in text. The text file contains the Pauli strings and corresponding coefficiencies of the hydroxyl cation's hamiltonian by Jordan-Wigner mapping [2]. Participants can generate different format of the description of the hydroxyl cation's hamiltonian by prefered tools, but we restricted the fermionic mapping method should be the Jordan-Wigner mapping [2], which should be 12 qubits and 631 pauli strings.

##### 5. IBM Qiskit Platform, System & Noise Model from Real Quantum Processor Backend

We acknowledge the use of IBM Quantum services for this contest. Qiskit [3] is an open-source quantum computing framework primarily developed by IBM. It offers tools for creating and manipulating quantum programs and running them on prototype quantum devices and simulators. Designed with modularity in mind, Qiskit provides components that cater to all aspects of quantum computing, from foundational elements to more advanced quantum algorithms. In the contemporary realm of quantum computing, noise poses a significant challenge [4]. As such, we urge all participants to consider the inherent noise when designing their quantum algorithms or circuits. Qiskit [3] offers tools that facilitate the simulation of quantum algorithms or circuits as if executed on an actual quantum device, complete with the associated noise. Since not everyone have access on real machine, for fairness, we require all participants training the model on a given noise model which will released on the registration deadline date. Simulating a quantum system, complemented with a noise model, is imperative to gain insights into the potential performance of quantum algorithms on current NISQ (Noisy Intermediate-Scale Quantum) devices [4]. We acknowledge that while participants might be inclined to optimize basis gates at the pulse level to curtail the duration of the quantum circuit and thereby conserve quantum resources [5], characterizing a time-dependent noise model from a real quantum machine poses unsolved obstacles in preparation for this quantum computing for drug discovery challenge. We regretfully must resort to using the standard gate-based noise model for evaluating circuits. However, in the spirit of fairness, we will compute the relative decoherence fidelity and adjust your circuit performance accordingly [6].

The IBM qiskit platform is open for public and easy to access online. However, if you do need support, please contact us.

##### Scoring Criteria

We will employ specific metrics to rigorously evaluate each submitted algorithm.

###### Ground State Energy Estimation Accuracy

The accuracy of estimating the ground state energy is vital. This will be measured using the following formula:

*E _{score} = (1 - | (E_{estimated} - E_{ideal}) / E_{ideal} |) × 100%*

Where,

*E*represents the average result procured from the participant's framework across ten disparate seeds, while

_{estimated}*E*is the objective value ascertained using classical computational methodologies. This precision component garners up to 100 credits.

_{ideal}###### Quantum Resource Consumption

The efficient utilization of quantum resources is paramount. This metric will be broken down into two principal parts:

**Total Number of Shots of Quantum Circuits:**- 3786000 shots (which equates to 631 Pauli strings x default 6000 shots): 15 points
- Under 1800000 shots: 25 points
- For shots falling between 1800000 and 3786000: Points will be awarded based on the formula

*15 + (3786000 - n) / (3786000 - 1800000) × 10*

Here, 'n' represents the total quantum circuit shots used by the participant.

**Circuit Size (Duration):**- 1st rank: 15 points
- Ranks 2 to 5: A decrement of 0.1 point per subsequent rank
- Ranks 6 to 10: A decrement of 0.2 points per subsequent rank
- Rankings beyond 10: A decrement of 0.3 points for each descending rank

###### Technical Reflection & Description

Beyond the quantitative assessment, we emphasize a qualitative evaluation. Participants are mandated to introspect and elucidate their technical methodologies. This should include a clear mention of any innovative pre-processing techniques or strategies employed, as well as any notable consumption of classical resources. This reflective and descriptive component can earn participants up to 10 points. These 10 credits will be discerningly evaluated by a panel of three expert graders, who will consider the depth of self-reflection, technical novelty, logical coherence, among other salient factors.

##### 7.Example Code

We have provided an example algorithm to illustrate how to train the model.

##### 8.Special Thanks

We are appreciate the valuable discussion provided by following people: Zhixin Song (Georgia Institute of Technology, US), Hang Ren (University of California, Bekerley, US), Jinglei Cheng (Purdue University, US).

##### 9.References

[1] Cao, Yudong, Jhonathan Romero, and Alán Aspuru-Guzik. "Potential of quantum computing for drug discovery." IBM Journal of Research and Development 62.6 (2018): 6-1.

[2] Tranter, Andrew, et al. "A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry." Journal of chemical theory and computation 14.11 (2018): 5617-5630.

[3] Aleksandrowicz, Gadi, et al. "Qiskit: An open-source framework for quantum computing." Accessed on: Mar 16 (2019).

[4] Preskill, John. "Quantum computing in the NISQ era and beyond." Quantum 2 (2018): 79.

[5] Earnest, Nathan, Caroline Tornow, and Daniel J. Egger. "Pulse-efficient circuit transpilation for quantum applications on cross-resonance-based hardware." Physical Review Research 3.4 (2021): 043088.

[6] McKinney, Evan, et al. "Parallel Driving for Fast Quantum Computing Under Speed Limits." Proceedings of the 50th Annual International Symposium on Computer Architecture. 2023.