Digitized-Counterdiabatic Quantum Algorithm for Protein Folding

AI: The highlighted parts of the scientific paper discuss the following key points: - The part discusses different strategies and techniques for circuit optimization and error mitigation in quantum algorithms implemented on IBM superconducting chips. It covers topics such as qubit selection, SWAP strategies, native gate compilation, dynamical decoupling, and measurement error mitigation. The aim is to minimize errors and optimize the performance of quantum circuits on specific hardware. - The highlighted part discusses the experimental implementations of the CD-inspired ansatz on various hardware platforms, including trapped-ion systems and superconducting chips. It provides details about the initialization of the system, parameterized rotations, two-body interactions, and circuit optimization. The results of the experiments are presented, including the probability distributions and the protein configurations obtained from the hardware. - The highlighted parts describe various techniques and strategies for optimizing quantum circuits on IBM's quantum chips. Some of the techniques mentioned include sub-graph isomorphism algorithm for selecting the best qubits, SWAP strategies for minimizing the number of SWAP gates, native gate compilation for reducing the depth of the logical circuit, dynamical decoupling techniques for reducing noise during idle time, and measurement error mitigation to compensate for readout errors. These techniques are described and referenced in the paper. - The highlighted part discusses a hybrid classical-quantum digitized-counterdiabatic algorithm for protein folding. It proposes a problem-inspired and hardware-efficient variational quantum circuit as a quantum part of the algorithm. The algorithm is benchmarked using various quantum hardware platforms and achieves high success probabilities with low-depth circuits. The paper presents a novel approach to tackle the complexity of protein folding using quantum computing. - The highlighted part focuses on the performance analysis of the CD-inspired ansatz in various proteins with different numbers of amino acids. It describes the construction of the ansatz, parameterization, and classical optimization using stochastic gradient-descent-based optimizers. It compares the performance of the CD-inspired ansatz with the problem-inspired ansatz (QAOA), showing that the CD-inspired ansatz performs better in terms of success probability and energy convergence. It also discusses the challenges and potential limitations of the CD-inspired ansatz. - The highlighted part discusses the performance comparison of the CD-inspired ansatz with other quantum algorithms, such as QAOA and hardware-efficient ansatz (HEA). It shows that the CD-inspired ansatz outperforms QAOA in terms of energy convergence and approximate ground-state energy. It also discusses the challenges of the CD-inspired ansatz, such as choosing suitable CD terms and difficulties in finding the exact ground state for larger system sizes. Circuit optimization strategies for experimental implementation on real hardware are mentioned. - The highlighted part introduces the CD-inspired ansatz, which is a hybrid digitized-counterdiabatic algorithm proposed to address a problem in quantum adiabatic evolution. It discusses the selection of the ansatz parameterization and its advantages for near-term devices. The performance of the CD-inspired ansatz is analyzed in the context of protein folding problems with different numbers of amino acids using classical optimization routines. - The highlighted part describes the proposal of a hybrid digitized-counterdiabatic quantum algorithm for investigating the protein folding problem. It applies the algorithm to a tetrahedral lattice protein folding problem and achieves excellent performance in terms of convergence and circuit depth. The challenges, such as sensitivity towards initial parameters and the choice of appropriate counterdiabatic (CD) terms, are mentioned. The importance of protein folding in quantum computing and its potential applications in industrial use cases are also highlighted. - The highlighted part proposes a hybrid classical-quantum digitized-counterdiabatic algorithm for tackling the protein folding problem on a tetrahedral lattice. The algorithm utilizes a parameterized quantum circuit (PQC) inspired by counterdiabatic (CD) protocols to generate trial quantum states, and a classical optimization routine for parameter optimization. The authors benchmark the performance of their algorithm against state-of-the-art problem-inspired ansatz and hardware-efficient ansatz and perform experiments on various quantum hardware platforms. The importance of protein folding in understanding enzymes and finding remedies for protein-related diseases is mentioned. - The highlighted part discusses the encoding of qubits to represent amino acid turns in a protein chain, the encoding using two sets of lattice, and the Hamiltonian for the protein folding problem. It also covers the inclusion of qubits to account for interactions between nearest-neighbor beads and the native gate decomposition of the $YZ(\theta)$ gate for different hardware. - The highlighted part discusses the use of different ansatz types in quantum state generation algorithms, including hardware-efficient ansatz and problem-inspired ansatz. It compares their advantages and disadvantages and introduces the concept of a cost function minimized using the ansatz. - The highlighted part specifically discusses the DC-QAOA method and its use of counterdiabatic (CD) terms to improve the performance of QAOA. It introduces the equation for the CD terms obtained using the nested commutator method. It also mentions the proposal of a CD-inspired circuit ansatz that combines the advantages of both problem-inspired and hardware-efficient ansatzes. - The highlighted part discusses the experimental implementations of the proposed CD-inspired ansatz on different available hardware and emulators, specifically on trapped-ions and superconducting systems. It provides details about the challenges and techniques used for circuit optimization and error mitigation in these hardware implementations. It includes results obtained from the experiments for protein systems of different sizes and compares them with the exact ground state configurations. The challenges involved in implementing the CD-inspired ansatz, such as the choice of suitable CD terms and the requirement for additional circuit optimization strategies, are mentioned as well. - The highlighted part describes the implementation of a hybrid digitized-counterdiabatic quantum algorithm for investigating the protein folding problem. It introduces the algorithm and its parameterized quantum circuit with a complexity of O(N^2). The algorithm is applied to a tetrahedral lattice protein folding problem and achieves high performance in terms of convergence and circuit depth. The implementation of the algorithm on different quantum hardware platforms, including trapped ions and superconducting systems, is highlighted along with the challenges and future directions for improving the performance. The significance of digitized-counterdiabatic quantum algorithms for practical quantum advantage and their potential applications in other areas is emphasized. - The highlighted part discusses the selection of a model for protein folding using a 5-local Ising Hamiltonian. It shows that despite the increased locality of the Hamiltonian, the CD-inspired ansatz can still obtain optimal solutions using only 2-local terms in the PQC. This is in contrast to QAOA, which requires 5-local terms. The importance of the CD-inspired ansatz for the protein folding problem is emphasized.