Quantum Computing
Accurate electronic structure calculations are considered one of the most anticipated applications of quantum computing that will revolutionize theoretical chemistry and other related fields. Using the Google Sycamore quantum processor, Google AI Quantum and collaborators performed a variational quantum eigensolver (VQE) simulation of two intermediate-scale chemistry problems: the binding energy of hydrogen chains (as large as H12) and the isomerization mechanism of diazene (see the Perspective by Yuan). The simulations were performed on up to 12 qubits, involving up to 72 two-qubit gates, and show that it is possible to achieve chemical accuracy when VQE is combined with error mitigation strategies. The key building blocks of the proposed VQE algorithm are potentially scalable to larger systems that cannot be simulated classically.
Science , this issue p. [1084][1]; see also p. [1054][2]
[1]: /lookup/doi/10.1126/science.abb9811
[2]: /lookup/doi/10.1126/science.abd3880
Quantum Computing
Accurate electronic structure calculations are considered one of the most anticipated applications of quantum computing that will revolutionize theoretical chemistry and other related fields. Using the Google Sycamore quantum processor, Google AI Quantum and collaborators performed a variational quantum eigensolver (VQE) simulation of two intermediate-scale chemistry problems: the binding energy of hydrogen chains (as large as H12) and the isomerization mechanism of diazene (see the Perspective by Yuan). The simulations were performed on up to 12 qubits, involving up to 72 two-qubit gates, and show that it is possible to achieve chemical accuracy when VQE is combined with error mitigation strategies. The key building blocks of the proposed VQE algorithm are potentially scalable to larger systems that cannot be simulated classically.
Twelve-qubit quantum computing for chemistry Accurate electronic structure calculations are considered one of the most anticipated applications of quantum computing that will revolutionize theoretical chemistry and other related fields. Using the Google Sycamore quantum processor, Google AI Quantum and collaborators performed a variational quantum eigensolver (VQE) simulation of two intermediate-scale chemistry problems: the binding energy of hydrogen chains (as large as H 12 ) and the isomerization mechanism of diazene (see the Perspective by Yuan). The simulations were performed on up to 12 qubits, involving up to 72 two-qubit gates, and show that it is possible to achieve chemical accuracy when VQE is combined with error mitigation strategies. The key building blocks of the proposed VQE algorithm are potentially scalable to larger systems that cannot be simulated classically. Science , this issue p. 1084 ; see also p. 1054
QUANTUM COMPUTING IN CHEMISTRY. Quantum computing offers transformative potential for quantum chemistry, enabling the exploration of complex molecular simulations with unprecedented accuracy. By leveraging qubits and powerful quantum algorithms like the variational quantum eigensolver (VQE) and quantum phase estimation (QPE), quantum computing provides a novel approach to unraveling the intricacies of electronic structures and properties of molecules. While challenges persist in qubit stability and error mitigation, continuous innovation is fostered by collaborative efforts between the quantum computing and chemistry communities. These collaborations pave the way for groundbreaking advancements in drug discovery and materials science. This research employed quantum computing simulators to investigate the potential energy surface (PES) of the H2 molecule at the CCSD/STO-3G level of theory. These simulators, leveraging qubits and sophisticated algorithms, facilitated the acquisition of detailed information regarding the electronic structure, bonding mechanisms, and spectroscopic properties of the diatomic molecules.
However, accurately simulating molecular interactions constitutes the central, but open question of computer chemistry. This is a core task for efforts in drug development, catalyst design, and materials science. Most classical algorithms perform well on smaller systems, but incumbent exponential scaling penalties are unavoidable as models grow larger and more complex to describe quantum behaviour. An entirely new paradigm for this problem is now introduced by quantum computing: superposition and entanglement resources natively encode quantum states and model their electronic structures. The paper will thus take a high-level view of the leading quantum algorithms, with particular regard to those called Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE), while evaluating their performance on today's Noisy Intermediate Scale Quantum (NISQ) devices. Next will follow discussions on algorithm design and current hardware capabilities, before which open challenges on scalability, error mitigation, and algorithm design will be outlined. Emphasis shall also be placed on the ethics and accessibility issues as well as the timelines with which quantum computing might gain a practical advantage. Linking together the recent advances and limitations, this paper posits how quantum computer implementation may change the face of chemical modelling and scientific discovery.
The advancements in classical computational components such as CPUs and GPUs have had a reverberating impact on the democratization of computational power available, with the field of computational chemistry reaping significant benefits from the propulsion of the limits of systems studied. The accurate prediction of chemical properties and reaction dynamics through computational simulation is now a centerpiece of modern chemical research, significantly accelerating discoveries research areas of materials science and drug development, as well as industrially relevant processes such as the emission of aldehydes from soft foams, flame retardants and pyrolysis and the carbonylation of epoxides. These achievements of computational chemistry still are overshadowed in the face of fundamental bottlenecks where classical methods remain constrained by the exponential scaling when treating large and/or strongly correlated quantum many-body systems. This innate computational complexity often constitutes chemically accurate calculations based on first principles impractical, or plain impossible, for systems beyond modest sizes. Quantum computing offers a potential pathway around these limitations, originally formally formulated by David Deutsch as a tool for simulating quantum systems, with the first quantum algorithms indicating speed-ups compared to classical counterparts arising from Peter Shor and Lov Grover for the prime factorization of an integer number and unstructured search respectively. Relying on fundamental theorems by Claude Shannon, it has been demonstrated that through the use of error-correcting codes fault-tolerant quantum computers are able to safeguard information against noise and decoherence, strongly indicating towards exponential speedups in solving central computational chemistry problems, such as determining ground state energies or reaction pathways of chemical systems. Substantial strides in experimental quantum computing over the past decade, including proof-of-principle demonstrations of quantum error correction, mean to bring full-scale fault-tolerant quantum computing within the grasp of humanity. The breakthroughs needed to attain scalable, error-corrected quantum computation with capabilities exceeding those of classical methods in real-world scenarios is likely still some years away. While striving to address the engineering challenges standing in the way of achieving fault tolerant quantum computing, substantial effort has been focused toward developing and benchmarking hybrid algorithms tailored for the Noisy Intermediate- Scale Quantum (NISQ) devices, available now to researchers. These hybrid quantum-classical algorithms, with the most notable being the Variational Quantum Eigensolver (VQE), allow the probing of quantum computing’s utility in computational chemistry even in the face of significant hardware noise and limited coherence times. The work presented in this thesis introduces several key additions the VQE framework, geared especially towards to NISQ hardware, where the mindful use of available resources is imperative. First, the implementation of the Conjugate Model Search optimizer is described, an optimization method that integrates simple models that are surrogate to the original function, combined with conjugate gradient optimization to navigate effectively parameter landscapes typical of variational algorithms, prone to noise. Second, this thesis contains the proposal and extensive study of a hyperparameter tuning procedure employing genetic algorithms, allowing for comprehensive simulation benchmarks that augment the robustness and efficiency of VQE implementations with respect to convergence time through real wall-time models of quantum processors. Continuing, a bridge is presented between quantum simulation and quantum chemistry, through qubit-to-fermion mappings of existing quantum gates, further enabling the direct and accurate modeling of chemical systems on trapped atom quantum hardware with the added arsenal provided by techniques designed for qubit architectures. Additionally, experimental data contained in this thesis include detailed benchmarking data collected from state-of-the-art trapped ion quantum processors available at the Johannes Gutenberg Universität Mainz, demonstrating the actual viability and performance of various methodologies for extracting results. Lastly, the state of VQE is examined, as it served as a springboard for a plethora of advancements in the development of quantum computing hardware, as well as the direction the field of simulation of computational quantum chemistry via quantum devices is headed towards in the coming years.
Quantum computing is emerging as a transformative approach in bioinformatics and quantum chemistry, addressing fundamental computational limitations of classical methods in molecular science. Many biological and chemical systems are inherently governed by quantum mechanics, making accurate simulation with classical algorithms computationally expensive or infeasible. This review examines how quantum computing, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era, is advancing molecular modeling, reaction dynamics, and bioinformatics applications. Key quantum algorithms, including the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE), demonstrate increasing capability in approximating molecular energies and simulating quantum systems. In parallel, applications in bioinformatics—such as protein folding, genomic search, and combinatorial optimization—highlight the potential of quantum computing to address complex biological problems. Quantum machine learning further extends these capabilities by integrating quantum algorithms with data-driven modeling. However, current progress is constrained by NISQ-era limitations, including noise, limited qubit counts, and scalability challenges. These constraints highlight the need for hybrid quantum–classical approaches and improved error mitigation strategies. Overall, quantum computing represents a complementary computational paradigm that can enhance classical methods in bioinformatics and chemistry. Continued advances in quantum algorithms, hardware, and hybrid modeling frameworks are expected to expand its role in molecular science and computational biology.
Quantum computing has emerged as a transformative approach for tackling complex problems in quantum chemistry, particularly in simulating multielectron systems and electron-phonon interactions. However, the current noisy intermediate-scale quantum (NISQ) devices face significant challenges in implementing practical quantum algorithms due to error accumulation caused by increased circuit depth, qubit counts, and gate operations. To address these challenges, we present TenCirChem, an open-source Python package specifically designed for implementing variational quantum algorithms in quantum computational chemistry. TenCirChem demonstrates exceptional performance in simulating unitary coupled-cluster circuits through its innovative use of compact representations for quantum states and excitation operators. This package supports noisy circuit simulation and provides advanced algorithms for variational quantum dynamics, enabling researchers to explore complex chemical phenomena. Its capabilities are exemplified in various applications, including the calculation of potential energy curves and the investigation of quantum gate error impacts on molecular systems. Moreover, TenCirChem’s seamless integration with real quantum hardware makes it a versatile tool for both simulation and experimentation. A key innovation developed within the TenCirChem framework is the Clifford-based Hamiltonian engineering approach for molecules (CHEM). This algorithm addresses the critical challenge of achieving chemical accuracy with shallow quantum circuits, a fundamental requirement for practical applications on NISQ devices. CHEM employs a sophisticated Clifford-based Hamiltonian transformation that operates within the variational quantum eigensolver (VQE) framework using hardware-efficient ansatz. The method ensures four crucial advantages: (1) generation of initial circuit parameters corresponding to Hartree-Fock energy, (2) maximization of initial energy gradients with respect to circuit parameters, (3) minimal classical processing overhead without additional quantum resource requirements, and (4) compatibility with any circuit topology. Through quantum hardware emulator demonstrations, CHEM has achieved chemical accuracy for systems up to 12 qubits with fewer than 30 two-qubit gates, representing a significant advancement in practical quantum computational chemistry. To enhance the efficiency of variational quantum algorithms, we developed the sequential optimization with approximate parabola (SOAP) method, specifically designed for parameter optimization in unitary coupled-cluster ansatz. SOAP addresses the critical bottleneck of measurement requirements in VQE by implementing an innovative optimization strategy that approximates the energy landscape as quadratic functions. This approach minimizes the number of energy evaluations while incorporating parameter correlations through the integration of average directions from previous iterations. Benchmark studies demonstrate SOAP’s superior performance, showing faster convergence and enhanced noise robustness compared to traditional optimization methods. The method’s scalability has been validated through numerical simulations of up to 20 qubits, and its practical efficacy has been confirmed through experiments on superconducting quantum computers. For simulating electron-phonon systems, we introduce a variational basis state encoding algorithm that significantly reduces resource requirements compared to conventional unary and binary encoding schemes. Our approach achieves smaller scaling than traditional methods for qubits and gates for systems obeying the area law of entanglement entropy, this remarkable reduction in resource requirements comes at the cost of a constant amount of additional measurements. The algorithm’s effectiveness has been validated through both numerical simulations and quantum hardware experiments, demonstrating that using just one or two qubits per phonon mode can produce quantitatively accurate results across various coupling regimes. The integration of these innovations within the TenCirChem library represents a significant advancement in quantum computational chemistry. The software package provides researchers with a comprehensive toolkit for developing, testing, and implementing quantum algorithms, while the novel methods address fundamental challenges in circuit depth, parameter optimization, and resource efficiency. These developments collectively enhance the practicality of quantum computing for addressing real-world chemical problems in the NISQ era, offering improved accuracy, efficiency, and noise robustness.