Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data

Hong, Cheng-Lin; Tsai, Ting Yen; Chou, Jyh‐Pin; Chen, Peng‐Jen; Tsai, Pei-Kai; Chen, Yu‐Cheng; Kuo, En-Jui; Srolovitz, David J.; Hu, Alice; Cheng, Yuan‐Chung; Goan, Hsi‐Sheng

doi:10.1103/prxquantum.3.020360

Cited by 7 publications

(8 citation statements)

References 55 publications

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“…As our algorithm is designed for an orthonormal basis set, we used the Löwdin symmetric orthonormalization of the atomic orbitals to get a basis of orthonormal atomic orbitals. In principle, this step will be circumvented by using already orthonormal basis sets such as plane waves or Daubechies wavelets [61,62]. They usually require much more basis functions but this is not a problem for Q-DFT as they are mapped on only log 2 (N ) qubits.…”

Section: Methodsmentioning

confidence: 99%

Toward density functional theory on quantum computers?

2023

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Quantum Chemistry and Physics have been pinpointed as killer applications for quantum computers, and quantum algorithms have been designed to solve the Schrödinger equation with the wavefunction formalism. It is yet limited to small systems, as their size is dictated by the number of qubits available. Computations on large systems rely mainly on mean-field-type approaches such as density functional theory, for which no quantum advantage has been envisioned so far. In this work, we question this a priori by proposing a counter-intuitive mapping from the non-interacting to an auxiliary interacting Hamiltonian that may provide the desired advantage.

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Section: Methodsmentioning

confidence: 99%

Toward density functional theory on quantum computers?

2023

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“…The computational cost reported in lemma 4 is indeed the cost of executing USHIFT in equation (8). We use a controlled version of this operation as in the circuit shown in figure 3.…”

Section: Complexity Of Key Subroutinesmentioning

confidence: 99%

“…With the wavelet transforms' diverse utility and extensive use in classical computing, a natural expectation is that a quantum analog of such transforms will find applications in quantum computing, especially for developing faster quantum algorithms and quantum data compression. Wavelets have already been used in quantum physics and computation [5][6][7][8][9][10][11][12]. However, prior works on developing a quantum analog for wavelet transforms are limited to a few representative cases [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Efficient quantum algorithm for all quantum wavelet transforms

Bagherimehrab,

Aspuru-Guzik

2024

Quantum Sci. Technol.

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Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet transform is specified by a sequence of numbers associated with the type of wavelet used and an order parameter specifying the length of the sequence. While the quantum Fourier transform, a quantum analog of the classical Fourier transform, has been pivotal in quantum computing, prior works on quantum wavelet transforms (QWTs) were limited to the second and fourth order of a particular wavelet, the Daubechies wavelet. Here we develop a simple yet efficient quantum algorithm for executing any wavelet transform on a quantum computer. Our approach is to decompose the kernel matrix of a wavelet transform as a linear combination of unitaries (LCU) that are compilable by easy-to-implement modular quantum arithmetic operations and use the LCU technique to construct a probabilistic procedure to implement a QWT with a known success probability. We then use properties of wavelets to make this approach deterministic by a few executions of the amplitude amplification strategy. We extend our approach to a multilevel wavelet transform and a generalized version, the packet wavelet transform, establishing computational complexities in terms of three parameters: the wavelet order M, the dimension N of the transformation matrix, and the transformation level d. We show the cost is logarithmic in N, linear in d and superlinear in M. Moreover, we show the cost is independent of M for practical applications. Our proposed quantum wavelet transforms could be used in quantum computing algorithms in a similar manner to their well-established counterpart, the quantum Fourier transform.

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“…[29][30][31][32][33] The development of VQE is an extremely active research field. Notable recent progress includes the development of new variational ansa ¨tze, [34][35][36] adaptations of spatial and spin symmetries, 37 optimizing qubit measurement efficiency, [38][39][40][41] techniques for reducing qubit resources, 42,43 error mitigation strategies, 44,45 and development of quantum simulators. 46 Researchers are actively leveraging these algorithmic advancements to assess the potential of VQE in studying molecular systems, including applications related to electronic ground states, [47][48][49] excited states, [50][51][52] and vibrations.…”

Section: Introductionmentioning

confidence: 99%