Joonsuk Huh is a tenured Associate Professor in the Department of Chemistry at Sungkyunkwan University (SKKU), South Korea, with adjunct appointments at the SKKU Advanced Institute of Nanotechnology and the Institute of Quantum Biophysics. (JH has a new position at Yonsei University starting in March 2025.) His research primarily focuses on quantum computing and its applications in chemistry, physics, and combinatorics. Joonsuk earned his bachelor’s degree in chemistry from Pohang University of Science and Technology (POSTECH) and a master’s degree in computational science and engineering from the Technical University of Munich, Germany. He completed his Ph.D. in Physics at Goethe University Frankfurt in 2011. Following his Ph.D., he worked as a postdoctoral fellow at Harvard University, USA, contributing to pioneering research linking molecular vibronic spectra with quantum optical sampling, i.e., Gaussian Boson Sampling. Since joining SKKU in 2017, Joonsuk has led the quantum computing and theoretical chemistry laboratory (QCTC Lab.). His research includes developing quantum algorithms for molecular modeling, computational chemistry, and other mathematical applications. He has published around 40 research papers in quantum computing (80 research papers in total), showcasing his significant contributions to advancing this field. Joonsuk's collaborations with academic and industrial partners, including a visiting scientist role at Xanadu Quantum Technologies, highlight his active engagement in pushing the boundaries of quantum computing technologies. Through his research, publications, and teaching, Joonsuk continues to contribute to the growing field of quantum computing, focusing on solving complex problems in chemistry, physics, and biology.Hyuk-Yong Kwon is a Staff Research Scientist at Quantum Intelligence Corp. (QIC), Republic of Korea, where he leads the quantum computing research team. He received his bachelor’s degree in chemistry from Colgate University (NY, USA) and completed his Ph.D. in Chemistry at North Carolina State University in 2022. Prior to joining QIC, Hyuk-Yong conducted postdoctoral research at the Center for Catalytic Hydrocarbon Functionalizations, Institute for Basic Science (Republic of Korea). His current research focuses on developing quantum computing algorithms and tools for computational chemistry and drug discovery applications. Hyuk-Yong has established strategic research collaborations with leading quantum computing companies, including IBM, Classiq, Oxford Quantum Circuits (OQC), and QuEra Computing. Victor S. Batista is the John Gamble Kirkwood Professor of Chemistry at Yale University, USA where he has been a faculty member since 2001. He earned his B.Sc. in Chemistry from the University of Buenos Aires in 1989 and his Ph.D. in Theoretical Chemistry from Boston University in 1996. Following postdoctoral research at the University of California, Berkeley, and the University of Toronto, he joined Yale's Department of Chemistry. Professor Batista's research focuses on theoretical and computational chemistry, particularly in developing semiclassical and quantum dynamics methods to study photoinduced reactions and catalytic processes. He has published over 425 articles in peer-reviewed journals, contributing significantly to the understanding of photosynthetic systems and quantum control of chemical dynamics. As the director of the NSF Center for Quantum Dynamics on Modular Quantum Devices, Professor Batista leads efforts to develop new paradigms for quantum simulations of complex chemical systems using programmable Kerr-cat platforms. The center aims to demonstrate the unique capabilities of bosonic modular devices in simulating chemical dynamics and correlated many-body systems. Throughout his career, Professor Batista has received numerous accolades. He is a Fellow of the Royal Society of Chemistry and an elected member of the Connecticut Academy of Science and Engineering. His recent publications include work on quantum machine learning applications in drug discovery and the development of quantum algorithms for simulating non-Markovian dynamics in chemical systems.

• Part I: The Basics1. Introduction2. Background knowledge3. Energy distribution of quantum statePart II: Quantum algorithms for FTQC4. Quantum Phase EstimationPart III: Quantum algorithms for early FTQC5. Heisenberg-limited Quantum Phase Estimation6. Bayesian Quantum Phase Estimation7. Quantum Imaginary Time Evolution8. Quantum Filtered Search9. Quantum Krylov Subspace Diagonalization10. Quantum Filter Diagonalization11. Quantum Lanczos algorithm12. Resonant Transition13. Dissipative Quantum algorithm14. qDRIFT algorithm15. Quantum Amplitude Amplification Eigensolver with State LearningPart IV: Quantum algorithms for NISQ16. Iterative Quantum Phase Estimation17. Variational Quantum Eigensolver18. Variational Quantum Deflation19. Quantum Dynamics20. Qubit-Oscillator Hybrid Quantum Simulators for Molecular Quantum DynamicsPart V: Perspective21. The Future of Quantum Algorithms

Joonsuk Huh is a tenured Associate Professor in the Department of Chemistry at Sungkyunkwan University (SKKU), South Korea, with adjunct appointments at the SKKU Advanced Institute of Nanotechnology and the Institute of Quantum Biophysics. (JH has a new position at Yonsei University starting in March 2025.) His research primarily focuses on quantum computing and its applications in chemistry, physics, and combinatorics. Joonsuk earned his bachelor’s degree in chemistry from Pohang University of Science and Technology (POSTECH) and a master’s degree in computational science and engineering from the Technical University of Munich, Germany. He completed his Ph.D. in Physics at Goethe University Frankfurt in 2011. Following his Ph.D., he worked as a postdoctoral fellow at Harvard University, USA, contributing to pioneering research linking molecular vibronic spectra with quantum optical sampling, i.e., Gaussian Boson Sampling. Since joining SKKU in 2017, Joonsuk has led the quantum computing and theoretical chemistry laboratory (QCTC Lab.). His research includes developing quantum algorithms for molecular modeling, computational chemistry, and other mathematical applications. He has published around 40 research papers in quantum computing (80 research papers in total), showcasing his significant contributions to advancing this field. Joonsuk's collaborations with academic and industrial partners, including a visiting scientist role at Xanadu Quantum Technologies, highlight his active engagement in pushing the boundaries of quantum computing technologies. Through his research, publications, and teaching, Joonsuk continues to contribute to the growing field of quantum computing, focusing on solving complex problems in chemistry, physics, and biology.Hyuk-Yong Kwon is a Staff Research Scientist at Quantum Intelligence Corp. (QIC), Republic of Korea, where he leads the quantum computing research team. He received his bachelor’s degree in chemistry from Colgate University (NY, USA) and completed his Ph.D. in Chemistry at North Carolina State University in 2022. Prior to joining QIC, Hyuk-Yong conducted postdoctoral research at the Center for Catalytic Hydrocarbon Functionalizations, Institute for Basic Science (Republic of Korea). His current research focuses on developing quantum computing algorithms and tools for computational chemistry and drug discovery applications. Hyuk-Yong has established strategic research collaborations with leading quantum computing companies, including IBM, Classiq, Oxford Quantum Circuits (OQC), and QuEra Computing. Victor S. Batista is the John Gamble Kirkwood Professor of Chemistry at Yale University, USA where he has been a faculty member since 2001. He earned his B.Sc. in Chemistry from the University of Buenos Aires in 1989 and his Ph.D. in Theoretical Chemistry from Boston University in 1996. Following postdoctoral research at the University of California, Berkeley, and the University of Toronto, he joined Yale's Department of Chemistry. Professor Batista's research focuses on theoretical and computational chemistry, particularly in developing semiclassical and quantum dynamics methods to study photoinduced reactions and catalytic processes. He has published over 425 articles in peer-reviewed journals, contributing significantly to the understanding of photosynthetic systems and quantum control of chemical dynamics. As the director of the NSF Center for Quantum Dynamics on Modular Quantum Devices, Professor Batista leads efforts to develop new paradigms for quantum simulations of complex chemical systems using programmable Kerr-cat platforms. The center aims to demonstrate the unique capabilities of bosonic modular devices in simulating chemical dynamics and correlated many-body systems. Throughout his career, Professor Batista has received numerous accolades. He is a Fellow of the Royal Society of Chemistry and an elected member of the Connecticut Academy of Science and Engineering. His recent publications include work on quantum machine learning applications in drug discovery and the development of quantum algorithms for simulating non-Markovian dynamics in chemical systems.

• Part I: The Basics1. Introduction2. Background knowledge3. Energy distribution of quantum statePart II: Quantum algorithms for FTQC4. Quantum Phase EstimationPart III: Quantum algorithms for early FTQC5. Heisenberg-limited Quantum Phase Estimation6. Bayesian Quantum Phase Estimation7. Quantum Imaginary Time Evolution8. Quantum Filtered Search9. Quantum Krylov Subspace Diagonalization10. Quantum Filter Diagonalization11. Quantum Lanczos algorithm12. Resonant Transition13. Dissipative Quantum algorithm14. qDRIFT algorithm15. Quantum Amplitude Amplification Eigensolver with State LearningPart IV: Quantum algorithms for NISQ16. Iterative Quantum Phase Estimation17. Variational Quantum Eigensolver18. Variational Quantum Deflation19. Quantum Dynamics20. Qubit-Oscillator Hybrid Quantum Simulators for Molecular Quantum DynamicsPart V: Perspective21. The Future of Quantum Algorithms

Joonsuk Huh is a tenured Associate Professor in the Department of Chemistry at Sungkyunkwan University (SKKU), South Korea, with adjunct appointments at the SKKU Advanced Institute of Nanotechnology and the Institute of Quantum Biophysics. (JH has a new position at Yonsei University starting in March 2025.) His research primarily focuses on quantum computing and its applications in chemistry, physics, and combinatorics. Joonsuk earned his bachelor’s degree in chemistry from Pohang University of Science and Technology (POSTECH) and a master’s degree in computational science and engineering from the Technical University of Munich, Germany. He completed his Ph.D. in Physics at Goethe University Frankfurt in 2011. Following his Ph.D., he worked as a postdoctoral fellow at Harvard University, USA, contributing to pioneering research linking molecular vibronic spectra with quantum optical sampling, i.e., Gaussian Boson Sampling. Since joining SKKU in 2017, Joonsuk has led the quantum computing and theoretical chemistry laboratory (QCTC Lab.). His research includes developing quantum algorithms for molecular modeling, computational chemistry, and other mathematical applications. He has published around 40 research papers in quantum computing (80 research papers in total), showcasing his significant contributions to advancing this field. Joonsuk's collaborations with academic and industrial partners, including a visiting scientist role at Xanadu Quantum Technologies, highlight his active engagement in pushing the boundaries of quantum computing technologies. Through his research, publications, and teaching, Joonsuk continues to contribute to the growing field of quantum computing, focusing on solving complex problems in chemistry, physics, and biology.Hyuk-Yong Kwon is a Staff Research Scientist at Quantum Intelligence Corp. (QIC), Republic of Korea, where he leads the quantum computing research team. He received his bachelor’s degree in chemistry from Colgate University (NY, USA) and completed his Ph.D. in Chemistry at North Carolina State University in 2022. Prior to joining QIC, Hyuk-Yong conducted postdoctoral research at the Center for Catalytic Hydrocarbon Functionalizations, Institute for Basic Science (Republic of Korea). His current research focuses on developing quantum computing algorithms and tools for computational chemistry and drug discovery applications. Hyuk-Yong has established strategic research collaborations with leading quantum computing companies, including IBM, Classiq, Oxford Quantum Circuits (OQC), and QuEra Computing. Victor S. Batista is the John Gamble Kirkwood Professor of Chemistry at Yale University, USA where he has been a faculty member since 2001. He earned his B.Sc. in Chemistry from the University of Buenos Aires in 1989 and his Ph.D. in Theoretical Chemistry from Boston University in 1996. Following postdoctoral research at the University of California, Berkeley, and the University of Toronto, he joined Yale's Department of Chemistry. Professor Batista's research focuses on theoretical and computational chemistry, particularly in developing semiclassical and quantum dynamics methods to study photoinduced reactions and catalytic processes. He has published over 425 articles in peer-reviewed journals, contributing significantly to the understanding of photosynthetic systems and quantum control of chemical dynamics. As the director of the NSF Center for Quantum Dynamics on Modular Quantum Devices, Professor Batista leads efforts to develop new paradigms for quantum simulations of complex chemical systems using programmable Kerr-cat platforms. The center aims to demonstrate the unique capabilities of bosonic modular devices in simulating chemical dynamics and correlated many-body systems. Throughout his career, Professor Batista has received numerous accolades. He is a Fellow of the Royal Society of Chemistry and an elected member of the Connecticut Academy of Science and Engineering. His recent publications include work on quantum machine learning applications in drug discovery and the development of quantum algorithms for simulating non-Markovian dynamics in chemical systems.

• Part I: The Basics1. Introduction2. Background knowledge3. Energy distribution of quantum statePart II: Quantum algorithms for FTQC4. Quantum Phase EstimationPart III: Quantum algorithms for early FTQC5. Heisenberg-limited Quantum Phase Estimation6. Bayesian Quantum Phase Estimation7. Quantum Imaginary Time Evolution8. Quantum Filtered Search9. Quantum Krylov Subspace Diagonalization10. Quantum Filter Diagonalization11. Quantum Lanczos algorithm12. Resonant Transition13. Dissipative Quantum algorithm14. qDRIFT algorithm15. Quantum Amplitude Amplification Eigensolver with State LearningPart IV: Quantum algorithms for NISQ16. Iterative Quantum Phase Estimation17. Variational Quantum Eigensolver18. Variational Quantum Deflation19. Quantum Dynamics20. Qubit-Oscillator Hybrid Quantum Simulators for Molecular Quantum DynamicsPart V: Perspective21. The Future of Quantum Algorithms