Current quantum simulators are primarily qubit-based, making them naturally suitable for simulating 2-level quantum systems. However, many systems in nature are inherently $d$-level, including higher spins, bosons, vibrational modes, and itinerant electrons. To simulate $d$-level systems on qubit-based quantum simulators, an encoding method is required to map the $d$-level system onto a qubit basis. Such mapping may introduce illegitimate states in the Hilbert space which makes the simulation more sophisticated. In this paper, we develop a systematic method to address the illegitimate states. In addition, we compare two different mappings, namely binary and symmetry encoding methods, and compare their performance through variational simulation of the ground state and time evolution of various many-body systems. While binary encoding is very efficient with respect to the number of qubits it cannot easily incorporate the symmetries of the original Hamiltonian in its circuit design. On the other hand, the symmetry encoding facilitates the implementation of symmetries in the circuit design, though it comes with an overhead for the number of qubits. Our analysis shows that the symmetry encoding significantly outperforms the binary encoding, despite requiring extra qubits. Their advantage is indicated by requiring fewer two-qubit gates, converging faster, and being far more resilient to Barren plateaus. We have performed variational ground state simulations of spin-1, spin-3/2, and bosonic systems as well as variational time evolution of spin-1 systems. Our proposal can be implemented on existing quantum simulators and its potential is extendable to a broad class of physical models.
Contextuality, one of the strongest forms of quantum correlations, delineates the quantum world and the classical one. It has been shown recently that some quantum models, in the form of infinite one-dimensional translation-invariant Hamiltonians with nearest- and next-to-nearest-neighbor interactions, have the lowest ground state energy density allowed in quantum physics. However, these models all have local Hilbert space dimension larger than two, making the study of their ground state behavior difficult on current qubit-based variational quantum simulation platforms. In this work, we focus on the cost of simulating the local approximations of ground states of these models using qubit-based parameterized quantum circuits. The local approximations, which are 3-site reduced density matrices with local Hilbert space dimension three, are purified then encoded into permutation-symmetric qubits. We develop a universal set of permutation-symmetry preserving qubit-based gates, using them as an ansatz to simulate parameterized quantum circuits designed for qutrits. These techniques allow us to assess the accuracy of simulating the purified local ground states with respect to a fixed amount of classical and quantum resources. We found that given the same quantum circuit and the number of iterations, more contextual ground states with lower energy density are easier to simulate.
Conformation generation, also known as molecular unfolding (MU), is a crucial step in structure-based drug design, remaining a challenging combinatorial optimization problem. Quantum annealing (QA) has shown great potential for solving certain combinatorial optimization problems over traditional classical methods such as simulated annealing (SA). However, a recent study showed that a 2000-qubit QA hardware was still unable to outperform SA for the MU problem. Here, we propose the use of quantum-inspired algorithm to solve the MU problem, in order to go beyond traditional SA. We introduce a highly-compact phase encoding method which can exponentially reduce the representation space, compared with the previous one-hot encoding method. For benchmarking, we tested this new approach on the public QM9 dataset generated by density functional theory (DFT). The root-mean-square deviation between the conformation determined by our approach and DFT is negligible (less than about 0.5 Angstrom), which underpins the validity of our approach. Furthermore, the median time-to-target metric can be reduced by a factor of five compared to SA. Additionally, we demonstrate a simulation experiment by MindQuantum using quantum approximate optimization algorithm (QAOA) to reach optimal results. These results indicate that quantum-inspired algorithms can be applied to solve practical problems even before quantum hardware become mature.
We introduce MindSpore Quantum, a pioneering hybrid quantum-classical framework with a primary focus on the design and implementation of noisy intermediate-scale quantum (NISQ) algorithms. Leveraging the robust support of MindSpore, an advanced open-source deep learning training/inference framework, MindSpore Quantum exhibits exceptional efficiency in the design and training of variational quantum algorithms on both CPU and GPU platforms, delivering remarkable performance. Furthermore, this framework places a strong emphasis on enhancing the operational efficiency of quantum algorithms when executed on real quantum hardware. This encompasses the development of algorithms for quantum circuit compilation and qubit mapping, crucial components for achieving optimal performance on quantum processors. In addition to the core framework, we introduce QuPack-a meticulously crafted quantum computing acceleration engine. QuPack significantly accelerates the simulation speed of MindSpore Quantum, particularly in variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and tensor network simulations, providing astonishing speed. This combination of cutting-edge technologies empowers researchers and practitioners to explore the frontiers of quantum computing with unprecedented efficiency and performance.
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