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Determining the energy gap in a quantum many-body system is critical to understanding its behavior and is important in quantum chemistry and condensed matter physics. The challenge of determining the energy gap requires identifying both the excited and ground states of a system. In this work, we consider preparing the prior distribution and circuits for the eigenspectrum of time-independent Hamiltonians, which can benefit both classical and quantum algorithms for solving eigenvalue problems. The proposed algorithm unfolds in three strategic steps: Hamiltonian transformation, parameter representation, and classical clustering. These steps are underpinned by two key insights: the use of quantum circuits to approximate the ground state of transformed Hamiltonians and the analysis of parameter representation to distinguish between eigenvectors. The algorithm is showcased through applications to the 1D Heisenberg system and the LiH molecular system, highlighting its potential for both near-term quantum devices and fault-tolerant quantum devices. The paper also explores the scalability of the method and its performance across various settings, setting the stage for more resource-efficient quantum computations that are both accurate and fast. The findings presented here mark a new insight into hybrid algorithms, offering a pathway to overcoming current computational challenges., Comment: add fig.3

During the noisy intermediate-scale quantum (NISQ) era, quantum computational approaches refined to overcome the challenge of limited quantum resources are highly valuable. However, the accuracy of the molecular properties predicted by most of the quantum computations nowadays is still far off (not within chemical accuracy) compared to their corresponding experimental data. Here, we propose a promising qubit-efficient quantum computational approach to calculate the harmonic vibrational frequencies of a large set of neutral closed-shell diatomic molecules with results in great agreement with their experimental data. To this end, we construct the accurate Hamiltonian using molecular orbitals, derived from density functional theory to account for the electron correlation and expanded in the Daubechies wavelet basis set to allow an accurate representation in real space grid points, where an optimized compact active space is further selected so that only a reduced small number of qubits is sufficient to yield an accurate result. To justify the approach, we benchmark the performance of the Hamiltonians spanned by the selected molecular orbitals by first transforming the molecular Hamiltonians into qubit Hamiltonians and then using the exact diagonalization method to calculate the results, regarded as the best results achievable by quantum computation. Furthermore, we show that the variational quantum circuit with the chemistry-inspired UCCSD ansatz can achieve the same accuracy as the exact diagonalization method except for systems whose Mayer bond order indices are larger than 2. For those systems, we demonstrate that the heuristic hardware-efficient RealAmplitudes ansatz, even with a shorter circuit depth, can provide a significant improvement over the UCCSD ansatz, verifying that the harmonic vibrational frequencies could be calculated accurately by quantum computation in the NISQ era., Comment: 17 pages, 5 figures plus 11-page supplemental material

Particle-conserved subspace encoding reduces resources for quantum simulations, but a scalable and resource-minimal protocol for $M$ modes and $N$ particles, $\mathcal{O}(N\log M)$ qubits and $\mathcal{O}(Poly(M))$ measurements bases, has remained unknown. We demonstrate optimal encoding with classical parity check code generated by the Randomized Linear Encoder and propose the Fermionic Expectation Decoder for scalable probability decoding in $\mathcal{O}(M^4)$ bases. The protocol is tested with variational quantum eigensolver on LiH in the STO-3G and 6-31G basis, and $\text{H}_2$ potential energy curve in the 6-311G* basis.

Although quantum computation (QC) is regarded as a promising numerical method for computational quantum chemistry, current applications of quantum-chemistry calculations on quantum computers are limited to small molecules. This limitation can be ascribed to technical problems in building and manipulating more qubits and the associated complicated operations of quantum gates in a quantum circuit when the size of the molecular system becomes large. As a result, reducing the number of required qubits is necessary to make QC practical. Currently, the minimal STO-3G basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals. Nonetheless, the accuracy of using STO-3G is generally low and thus cannot provide useful predictions. We propose to adopt Daubechies wavelet functions as an accurate and efficient method for QCs of molecular electronic properties. We demonstrate that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian, while keeping the number of spin orbitals minimal. With the improved Hamiltonian through Daubechies wavelets, we calculate vibrational frequencies for H$_2$ and LiH using quantum-computing algorithm to show that the results are in excellent agreement with experimental data. As a result, we achieve quantum calculations in which accuracy is comparable with that of the full configuration interaction calculation using the cc-pVDZ basis set, whereas the computational cost is the same as that of a STO-3G calculation. Thus, our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient QCs of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers., Comment: 14 pages, 5 figures, Accepted by PRX Quantum

Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for ground-state preparation. We also dig for the source of acceleration of the imaginary-time process under Lyapunov control with theoretical understanding and dynamic process visualization. To make the method accessible in the noisy intermediate-scale quantum era, we further propose a variational form of the algorithm that could work with shallow quantum circuits. Through numerical experiments on a broad spectrum of realistic models, including molecular systems, 2D Heisenberg models, and Sherrington-Kirkpatrick models, we show that imaginary-time control may substantially accelerate the imaginary time evolution for all systems and even generate orders of magnitude acceleration (suggesting exponential-like acceleration) for challenging molecular Hamiltonians involving small energy gaps as impressive special cases. Finally, with a proper selection of the control Hamiltonian, the new variational quantum algorithm does not incur additional measurement costs compared to the original variational quantum imaginary-time algorithm., Comment: 25 pages, 19 figures

We study the effect of strain on the physical properties of the nitrogen antisite-vacancy pair in hexagonal boron nitride ($h$-BN), a color center that may be employed as a quantum bit in a two-dimensional material. With group theory and ab-initio analysis we show that strong electron-phonon coupling plays a key role in the optical activation of this color center. We find a giant shift on the zero-phonon-line (ZPL) emission of the nitrogen antisite-vacancy pair defect upon applying strain that is typical of $h$-BN samples. Our results provide a plausible explanation for the experimental observation of quantum emitters with similar optical properties but widely scattered ZPL wavelengths and the experimentally observed dependence of the ZPL on the strain., Comment: 7 pages, 3 figures

Shallow nitrogen-vacancy (NV) center in diamond is promising in quantum sensing applications however its sensitivity has been limited by surface terminators and defects. There is an immediate quest to find suitable diamond surfaces for NV sensors. In this work, the surface terminators of (113) diamond to host shallow NV centers are studied by means of first principles calculations. Results indicate that complete oxygen termination of (113) diamond creates positive electron affinity with neither strain on the surface nor in-gap levels. This is a very surprising result as the commonly employed oxygenated (001) diamond surface is often defective due to the disorder created by the strain of ether groups at the surface that seriously undermine the coherence properties of the shallow NV centers. The special atomic configurations on (113) diamond surface are favorable for oxygen bonding, in contrast to (001) and (111) diamond surfaces. These simulations imply that oxygenated diamond (113) surface can be produced by conventional diamond chemical vapor deposition growth. Combining this with the ~73% preferential alignment of as-grown NV centers in (113) oriented diamond, oxygenated (113) diamond is presently supposed to be the most prospective host for NV quantum sensors., Comment: 4 figures