Variational quantum packaged deflation for arbitrary excited states

Wen, Jingwei; Lv, Dingshun; Yung, Man‐Hong; Long, Gui‐Lu

doi:10.1002/que2.80

Cited by 17 publications

(10 citation statements)

References 40 publications

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“…Comparison results showed that the proposed comparators have an overall advantage over the known comparators without quantum measurements for T-count, T-depth, CNOT-count, and circuit width. Some algorithms have been proposed for NISQ devices [40], [41]. For instance, a quantum convolutional neural network (QCNN) on NISQ devices is implemented by multiple control gates [41].…”

Section: Discussionmentioning

confidence: 99%

The Optimization and Application of 3-Bit Hermitian Gates and Multiple Control Toffoli Gates

2022

IEEE Trans. Quantum Eng.

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The well-known 3-bit Hermitian gate (a Toffoli gate) has been implemented using Clifford + T circuits. Compared with the Peres gate, its implementation circuit requires more controlled-NOT (CNOT) gates. However, the Peres gate is not Hermitian. This paper reports four 3-bit Hermitian gates named LI gates. Whose realized circuits have the same T-count, Tdepth, and CNOT-count as the Peres gate. Furthermore, two decomposition methods of a multiple control Toffoli (MCT) gate are proposed for different primary optimization goals. Then, we design the equality, less-than, and full comparators with the minimum circuit width using proposed Hermitian gates and optimized MCT gates. A fault-tolerant circuit is required for robust quantum computing. Clifford+T circuits are accepted solutions for fault-tolerant implementation. Considering T-count, T-depth, CNOT-count, and circuit width as the primary optimization goals, we design the optimized Clifford + T circuits of three comparators using LI gates and optimized MCT gates. Comparison and analysis show that the proposed comparators have better overall performances for T-count, T-depth, CNOTcount, and circuit width than the best-known comparators without quantum measurements.

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Section: Discussionmentioning

confidence: 99%

The Optimization and Application of 3-Bit Hermitian Gates and Multiple Control Toffoli Gates

2022

IEEE Trans. Quantum Eng.

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“…In summary, we propose a robust quantum search algorithm with both the advantage of simple search operators, and high success rate over a wide range of

values. Therefore, it provides many potential applications [ 28 , 29 , 30 , 31 , 32 ] in future quantum computing.…”

Section: Discussionmentioning

confidence: 99%

Robust Quantum Search with Uncertain Number of Target States

Zhu

Wang

Bao

et al. 2021

Entropy

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The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given λ=M/N, where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity ON as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio M/N. In particular, for a database with an uncertainty in the ratio M±MN, our algorithm will find the target states with a success rate no less than 96%.

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“…Unfortunately, the extension of the VQE algorithm to the excited state is not trivial, as a variational estimation of the excited-state energies can only be defined under orthogonal constraints. Such constraints have been considered by adding penalization terms to the Hamiltonian, thus leading to the state-specific variational quantum deflation (VQD) algorithm − where each state is determined by a separate minimization (or only two minimizations in total if the first one is performed on a state-average ensemble). Other extensions can treat excited states on the same footing, but still favor the ground state. − However, the proper description of conical intersections or avoided crossings requires a democratic description of both the ground and excited states.…”

Section: Theorymentioning

confidence: 99%

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

Yalouz

Koridon

Senjean

et al. 2022

J. Chem. Theory Comput.

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We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH 2 NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

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Variational quantum packaged deflation for arbitrary excited states

Cited by 17 publications

References 40 publications

The Optimization and Application of 3-Bit Hermitian Gates and Multiple Control Toffoli Gates

The Optimization and Application of 3-Bit Hermitian Gates and Multiple Control Toffoli Gates

Robust Quantum Search with Uncertain Number of Target States

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

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