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Science China Physics Mechanics and Astronomy

Resource-optimized VQE implementation: Bridging algorithmic innovation and hardware realities

Li-Wei Yu

Published Apr 15, 2025• 0 citations
Publisher
DOI
10.1007/s11433-025-2651-5

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Quantum-computational chemistry in noisy intermediate-scale quantum era: TenCirChem and its application

Zirui Sheng, Weitang Li, Zhigang Shuai

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.

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Solving the Challenge of Protein Folding with Quantum Computing... Demonstration of a Resource-Efficient Quantum Algorithm

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- A study published in the international journal npj Quantum Information (Nature Portfolio) presents a resource-efficient quantum algorithm framework based on the Variational Quantum Eigensolver (VQE) for peptide and protein folding. - By translating protein folding into a tetrahedral lattice model and combining Conditional Value-at-Risk (CVaR) VQE with a classical evolutionary algorithm, the number of required qubits was drastically reduced. - It successfully folded a 7-amino acid neuropeptide using only 9 qubits on actual IBM 20-qubit quantum hardware, demonstrating its practical potential for next-generation drug discovery in the NISQ (Noisy Intermediate-Scale Quantum) era. [Quantum Biology Society] The protein folding problem, which involves predicting the three-dimensional structure of proteins and peptides from their primary amino acid sequence, plays a central role in various applications such as chemistry, biology, and medicine. However, as the sequence lengthens, the number of possible structures to explore explodes exponentially, making it difficult for classical computers to handle its intrinsic NP-hard complexity. Recently, a new quantum algorithm that can efficiently solve this long-standing challenge even on noisy intermediate-scale quantum (NISQ) computers has been developed, drawing the attention of the academic community. The paper titled "Resource-efficient quantum algorithm for protein folding," published in the international journal npj Quantum Information, presents an innovative computing framework for the discovery of next-generation peptide drugs. The research team of Anton Robert and Ivano Tavernelli from IBM Quantum, IBM Research - Zurich in Switzerland successfully led this groundbreaking study. ■ The Meeting of Lattice Models and Qubit Optimization Until now, attempts to introduce quantum computing to protein folding have required an unattainably high number of qubits that current, near-term quantum hardware cannot handle. To solve this, the research team converted protein folding into a tetrahedral lattice model. This model can efficiently depict the growth of a polymer chain while maintaining chemically plausible bond angles. In particular, they adopted a method of adding penalty terms to the Hamiltonian to prevent unphysical amino acid overlaps (e.g., beads occupying the same lattice site). Through this, they succeeded in drastically reducing the number of qubits required for calculation while suppressing the complexity of the algorithm to the level of O(N⁴). ■ Demonstration of Folding on Actual Quantum Hardware This algorithm maximized efficiency by combining CVaR-VQE, a variation of the Variational Quantum Eigensolver (VQE), with a classical Differential Evolution optimizer. Applying this technique, the researchers simulated the folding of the 10-amino acid Angiotensin peptide using only 22 qubits, successfully finding the most stable energy state (native fold). Furthermore, they successfully demonstrated the folding of a 7-amino acid neuropeptide (APRLRFY) using only 9 qubits on IBM's 20-qubit quantum computer hardware. This study is a groundbreaking achievement proving that the protein folding problem, which previously required massive computing resources, can be successfully solved even in a noisy real quantum processor environment. It is expected to bring tremendous innovation to next-generation /de novo/ drug design and disease treatment research utilizing quantum computing in the future.

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Practical Utility of Hybrid Quantum-Classical Machine Learning: A Rigorous Benchmarking of VQE and QAOA on NISQ-Era Simulators

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Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.

•Apr 9, 2026•0 citations
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.
- A study published in the international journal npj Quantum Information (Nature Portfolio) presents a resource-efficient quantum algorithm framework based on the Variational Quantum Eigensolver (VQE) for peptide and protein folding. - By translating protein folding into a tetrahedral lattice model and combining Conditional Value-at-Risk (CVaR) VQE with a classical evolutionary algorithm, the number of required qubits was drastically reduced. - It successfully folded a 7-amino acid neuropeptide using only 9 qubits on actual IBM 20-qubit quantum hardware, demonstrating its practical potential for next-generation drug discovery in the NISQ (Noisy Intermediate-Scale Quantum) era. [Quantum Biology Society] The protein folding problem, which involves predicting the three-dimensional structure of proteins and peptides from their primary amino acid sequence, plays a central role in various applications such as chemistry, biology, and medicine. However, as the sequence lengthens, the number of possible structures to explore explodes exponentially, making it difficult for classical computers to handle its intrinsic NP-hard complexity. Recently, a new quantum algorithm that can efficiently solve this long-standing challenge even on noisy intermediate-scale quantum (NISQ) computers has been developed, drawing the attention of the academic community. The paper titled "Resource-efficient quantum algorithm for protein folding," published in the international journal npj Quantum Information, presents an innovative computing framework for the discovery of next-generation peptide drugs. The research team of Anton Robert and Ivano Tavernelli from IBM Quantum, IBM Research - Zurich in Switzerland successfully led this groundbreaking study. ■ The Meeting of Lattice Models and Qubit Optimization Until now, attempts to introduce quantum computing to protein folding have required an unattainably high number of qubits that current, near-term quantum hardware cannot handle. To solve this, the research team converted protein folding into a tetrahedral lattice model. This model can efficiently depict the growth of a polymer chain while maintaining chemically plausible bond angles. In particular, they adopted a method of adding penalty terms to the Hamiltonian to prevent unphysical amino acid overlaps (e.g., beads occupying the same lattice site). Through this, they succeeded in drastically reducing the number of qubits required for calculation while suppressing the complexity of the algorithm to the level of O(N⁴). ■ Demonstration of Folding on Actual Quantum Hardware This algorithm maximized efficiency by combining CVaR-VQE, a variation of the Variational Quantum Eigensolver (VQE), with a classical Differential Evolution optimizer. Applying this technique, the researchers simulated the folding of the 10-amino acid Angiotensin peptide using only 22 qubits, successfully finding the most stable energy state (native fold). Furthermore, they successfully demonstrated the folding of a 7-amino acid neuropeptide (APRLRFY) using only 9 qubits on IBM's 20-qubit quantum computer hardware. This study is a groundbreaking achievement proving that the protein folding problem, which previously required massive computing resources, can be successfully solved even in a noisy real quantum processor environment. It is expected to bring tremendous innovation to next-generation /de novo/ drug design and disease treatment research utilizing quantum computing in the future.
Abstract The emergence of noisy intermediate-scale quantum (NISQ) devices has fueled the development of hybrid quantum-classical algorithms for machine learning (ML), promising potential advantages over classical methods. However, the practical efficacy of these algorithms remains uncertain due to challenges like noise susceptibility, trainability issues, and a lack of rigorous benchmarking. This study presents a comprehensive empirical evaluation of two flagship hybrid algorithms the Variational Quantum Eigensolver (VQE) for classification and the Quantum Approximate Optimization Algorithm (QAOA) for combinatorial optimization against state-of-the-art classical baselines under equivalent resource constraints. Through extensive simulations incorporating realistic noise models, we demonstrate that while these quantum approaches achieve competitive performance (e.g., 91.2% accuracy for VQE on a binary classification task), they consistently underperformed optimized classical models like Support Vector Machines (94.8% accuracy) and require orders of magnitude more computational time. Furthermore, we provide empirical validation of critical barriers to scalability, including the barren plateau phenomenon and significant performance degradation under noise, even with advanced error mitigation. Our results indicate that for the tasks studied, current NISQ era algorithms do not yet provide a tangible quantum advantage. This work contributes a rigorous benchmarking framework and a critical, realistic assessment of the field, suggesting that future progress hinges on fundamental algorithmic innovations and hardware improvements rather than incremental refinements of existing paradigms.