With the advent of efficient quantum algorithms and technological advances, design of quantum circuits has gained importance. Minimization of the gate count and the number of gate levels are the two major objectives in quantum circuit design. The peculiar nature of quantum decoherence that leads to quantum errors mandates completion of all the quantum gate operations within a time bound, hence reduction in the gate count and the number of circuit levels leads to lowering the errors and the overall cost in quantum circuits. In this paper, we propose the design of adder circuits using CNOT and CkNOT gates, with significant reduction in gate count and number of gate levels over their existing counterparts in the literature. We then present a software model for evaluating errors in quantum computing circuits and employ it for evaluating the error performance of our proposed quantum adder circuits.With the advent of efficient quantum algorithms and technological advances, design of quantum circuits has gained importance. Minimization of the gate count and the number of gate levels are the two major objectives in quantum circuit design. The peculiar nature of quantum decoherence that leads to quantum errors mandates completion of all the quantum gate operations within a time bound, hence reduction in the gate count and the number of circuit levels leads to lowering the errors and the overall cost in quantum circuits. In this paper, we propose the design of adder circuits using CNOT and CkNOT gates, with significant reduction in gate count and number of gate levels over their existing counterparts in the literature. We then present a software model for evaluating errors in quantum computing circuits and employ it for evaluating the error performance of our proposed quantum adder circuits.

International Conference on Electronic DesignDec 1, 20089 citations

Robustness of Quantum Signal Processing and Resource-aware Polynomial Design

Thiago O. Maciel, Giancarlo Camilo, Allan Tosta +3 more

Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant $L_\star$ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on $L_\star$ , and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, $T$ -gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H $_6$ molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled $T$ -gate count by $51.9\%$ -- $56.7\%$ relative to the standard analytical polynomial obtained from an error-function approximation.Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant $L_\star$ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on $L_\star$, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, $T$-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H$_6$ molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled $T$-gate count by $51.9\%$--$56.7\%$ relative to the standard analytical polynomial obtained from an error-function approximation.

quant-pharXiv:2610.03885Oct 6, 20260 citations

Gate Errors in Solid-State Quantum Computer Architectures

X. Hu, S. Das Sarma

Springer eBooksJan 1, 20044 citations

Phase Estimation

Andreas Wichert

The Kitaev's Phase Estimation Algorithm (also referred to as quantum eigenvalue estimation algorithm) is a quantum algorithm to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator. We explain the algorithm and indicate an example of the determination of the eigenvalue of the T gate. Then we introduce the quantum counting algorithm that is based on the quantum phase estimation algorithm and on the Grover's search algorithm. Quantum counting algorithm is a quantum algorithm for counting the number of solutions for a given search problem.The Kitaev's Phase Estimation Algorithm (also referred to as quantum eigenvalue estimation algorithm) is a quantum algorithm to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator. We explain the algorithm and indicate an example of the determination of the eigenvalue of the T gate. Then we introduce the quantum counting algorithm that is based on the quantum phase estimation algorithm and on the Grover's search algorithm. Quantum counting algorithm is a quantum algorithm for counting the number of solutions for a given search problem.

Chapman & Hall/CRC eBooksNov 28, 20230 citations

L_\star

of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on

L_\star

, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance,

T

-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H

_6

molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled

T

-gate count by

51.9\%

56.7\%

relative to the standard analytical polynomial obtained from an error-function approximation.