**FROM THEORY TO APPLICATION: QUANTUM CHEMISTRY’S JOURNEY INTO THE QUANTUM COMPUTING AGE**

The future holds immense promise for quantum technology across various fields, including cryptography and security, optimisation, drug discovery, machine learning, and artificial intelligence. Among them, the branch of chemistry called “Quantum Chemistry” will be one of the frontiers that can experience the fascinating capabilities of quantum computing. Quantum computing itself has a huge potential to tackle complex problems that regular computers, even supercomputers, cannot solve within a reasonable amount of time. Quantum chemistry plays a crucial role in understanding the behavior and properties of materials at atomic and molecular levels which leads to high-performance calculations for predicting and optimising molecular structures, interactions, chemical reaction mechanisms, and so on. Quantum computing and quantum chemistry. How can these two areas correlate with each other? Let’s dive into the topic in more detail!

**FOUNDATIONS OF QUANTUM CHEMISTRY**

The origin of quantum chemistry is traced back to the early 20th century when scientists did a tremendous job, effectively explaining the atomic structure and the nature of the interaction between light and matter. Many bright minds including Max Plank, Albert Einstein, Niels Bohr Max Born, Robert Oppenheimer, Erwin Schrödinger, Werner Heisenberg, and others published some important articles that shaped the birth of Quantum Mechanics which revolutionised our understanding of nature thoroughly along with Einstein’s theory of General Relativity.

Quantum Mechanics says a lot about what happens at atomic and subatomic levels which classical physics fails to explain. Many questions surrounding how electrons behave around the nucleus of an atom or how atoms bond to each other and form molecules finally found their answers through the principles of quantum mechanics, therefore, it is safe to say that chemistry was the one that could experience the wonder of quantum mechanics at first. When scientists applied the principles of quantum mechanics to chemistry to describe the chemical and physical properties of molecules and materials, they created a new field “Quantum Chemistry”.

**SOLVING SCHRÖDINGER’S EQUATION: THE CORE OF QUANTUM CHEMISTRY**

In 1925, Austrian physicist Erwin Schrödinger developed one magical equation named after him - Schrödinger’s equation which encompasses mysteries of sub-microscopic phenomena and arises from the fact of the wave-particle duality of the matter and the uncertainty principle. To explain in brief detail, matter can behave like either particles or waves. For example, electrons can be particles or can be waves; plus, Heisenberg’s uncertainty principle says that we cannot identify their locations if we know the speed and vice versa. Mathematically, it is a linear partial differential equation that governs a wave function of a quantum mechanical system. Since the whole of mathematics is much more complicated than we could imagine, let us leave this behind.

Hψ=Eψ

Schrödinger’s equation

We can write Schrödinger’s equation in many forms depending on what kind of atoms or molecules to study, and the proper calculation enables us to define the behavior of electrons in atoms. Hydrogen is the element with the simplest structure among its pals in the periodic table, having only one proton and one electron. By solving this equation, we can obtain energy states, optimized structures of atoms and molecules, and a wide range of spectroscopic data.

**COMPUTATIONAL CHEMISTRY: BRINGING THEORY AND APPLICATION**

For systems with more than one electron and proton or a system with more than one atom such as molecules, it becomes intriguing to calculate and describe the system accurately, thereby scientists came up with the idea of using the approximation methods that can give us not exact but approximate results of Schrödinger’s equation. The approximation methods can be categorized based on the underlying principles, accuracy, and applicability to different types of molecular systems. The most common methods are Hartree-Fock (HF) method, Density Functional Theory (DFT), Semi-Empirical methods, etc.

However, they are common in one thing for sure: Humans cannot perform these calculations solely by hand. Thanks to the development of computers, chemists equipped with high-performance modern computers and supercomputers to do simulation and optimisation needed for describing the chemical system. There are many computational programs on the market including some famous ones: Gaussian, Orca, Avogadro, and Gromax. With the aid of these programs, many quantum chemistry problems can be solved quickly without not that much human intervention. This act of using computer simulation for solving quantum chemistry problems did form a new branch – Computational chemistry or Computational Quantum Chemistry.

Computational chemistry is utilized mainly in designing and predicting structures of molecules for drug discovery, preparation of new advanced materials, and effective chemical reactions. Furthermore, the computational tools are also useful for interpreting and analyzing spectroscopic data which enhances the efficiency of laboratory experiments. On the other hand, for some research, especially in medicine and biotechnology, it is unlikely to do laboratory experiments due to cost, complexity, or ethical reasons. One of the most recent impacts of computational chemistry study was identifying structures of SARS-CoV-2 protein which were impossible to obtain by experiments. If you are curious, here is a list of some applications for computational chemistry:

Drug design

Consumer packaged goods

Organic electronics

Catalysis design

Surface chemistry

Metals, alloys, and ceramics design

Polymer design

Pharmaceutical formulation

Solving quantum chemistry problems requires quite complicated maths and sophisticated tools like supercomputers or high-performance computing (HPC) clusters. Research groups often used to perform calculations on supercomputers – the fastest computers in the world. However, more organisations are running simulations on HPC clusters mainly because they can run multiple tasks simultaneously consisting of multiple high-speed computers connected; also, combined with artificial intelligence and cloud technology, HPC clusters can open new doors for future high-level research projects in many sectors providing much faster simulation while having an affordable cost for companies and research centers to gain access.

*Hewlett Packard Enterprise Frontier or OLCF-5. Source: Wikipedia*

In 2022, the fastest supercomputer in the world – the Frontier broke the record with a peak performance of 1.1 exaflops (quintillions of calculations per second). However, the maximum possible power will be around 5 exaflops due to the physical constraints. This proves the fact that the accuracy of the results obtained with supercomputers is still limited since the computational complexity grows exponentially with the system size.

**ADVANCING QUANTUM CHEMISTRY WITH QUANTUM COMPUTING**

The famous physicist Richard Feynman once said, “If you want to make a simulation of nature, you’d better make it quantum mechanical”. While the majority of the research projects are still dependent on supercomputers and HPC clusters, some technological giants are pioneering in the quantum technology sector to turn Feynman’s insight into reality. In 2023, IBM released a roadmap towards quantum technology development they are planning for the near future. Their ambitious roadmap tells us about unlocking the full power of quantum computing with quantum-centric supercomputers including 1000’s of logical qubits. From the previous article, we have already become aware of what is quantum computer.

As the working principles of quantum computers are based on the concepts of quantum superposition, interference, and entanglement, they can store and process large amounts of data in the form of qubits using less energy and a smaller amount of space than a classical supercomputer. This will bring us to the assumption that it is possible to put all the steps required to solve the infamous Schrödinger’s equation in qubits and process the data. Yes, it is possible! We can represent them in the quantum circuit form and use them together with an estimater primitive and optimiser, then plug all of them into a Variational Quantum Eigenvalue (VQE) solver– a quantum computing algorithm for calculating mathematical equations like Schrödinger’s equation. Then, we get approximate results, but more precise than conventional computing methods, for example, just using the Hartree-Fock method.

Of course, there are still many challenges in both hardware and software. Most quantum computers are noisy and costly to build. There are generally three types of obstacles scientists and engineers need to find solutions:

Qubit Scaling: To make a real-world impact, quantum computers need to be operated on more qubits. In 2023, IBM unveiled the first quantum computer with more than 1000 qubits.

Environmental Sensitivity: Since qubits are extremely sensitive to minor environmental disturbances like thermal fluctuations or stray electromagnetic radiation, professionals are working on creating more stable qubits.

Error Correction: Even the minimum error can affect the calculations, so there must be something called “Quantum Error Correction Codes”.

In addition, we also should be aware of other challenges in the specific case of quantum chemistry simulation. Some research groups are optimistic about the future of quantum computing in chemistry stressing that quantum computing is moving beyond its early stage and seeking commercial applications in chemical and biomedical sciences. Increasing numbers of scientific papers are being published, having an emphasis on enhancing current quantum computing algorithms and hardware. To exemplify, one study published in Nature reveals that a novel VQE algorithm, FMO/VQE, indicated a significant advance in scalability over a conventional one while maintaining accuracy with fever qubits, significantly reducing the computational resources required for the simulations of complex molecular systems.

**CONCLUSION**

Even though there are a lot of remaining challenges, it is evolving rapidly at an exponential rate with the number of qubits and quantum volume doubling almost every year. Thus, it will be not so long before humans face another extraordinary new technological era of the future. The convergence of supercomputers, artificial intelligence, and quantum computers will lead us to the boundless possibilities. Perhaps, a few years from now, we will be discussing how “Super quantum computers”- A combination of quantum computers and supercomputers- shaping the next frontier of scientific exploration.

In the span of a mere century, humanity has witnessed remarkable technological advancements that shaped modern life. We currently stand in the transitional period to delve into the new era defined by the advent of artificial intelligence and quantum technology. It is also a time for us to see and wait or act toward navigating technological development to shape a future that is both promising and prosperous for all.

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