The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold symmetry axis. These rings are found to exibit two bands of excitons. A simplified mathematical description of the exciton states is given in Hu, X. & Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will show, by suitable labeling of the lowest energy (Qy) excited states of individual BChls, that the resulting exciton states are the quantum Fourier transform of the BChls excited states. For Rs. molischianum ring exciton states will be modeled as the four qubit quantum Fourier transform and the explicit circuit will be derived. Exciton states for Rps. acidophila ring cannot be modeled with an integer number of qubits. Both quantum Fourier transforms are instances of the hidden subgroup problem and this opens up a possibility that both purple bacteria implement an efficient quantum circuit for light harvesting.The LH-II of purple bacteria Rhodospirillum (Rs.) molischianum and Rhodopseudomonas (Rps.) acidophila adopts a highly symmetrical ring shape, with a radius of about 7 nm. In the case of Rps. acidophila the ring has a ninefold symmetry axis, and in LH-II from Rs. molischianum the ring has an eightfold symmetry axis. These rings are found to exibit two bands of excitons. A simplified mathematical description of the exciton states is given in Hu, X. & Schulten, K. (1997) Physics Today 50, 28-34. Using this description, we will show, by suitable labeling of the lowest energy (Qy) excited states of individual BChls, that the resulting exciton states are the quantum Fourier transform of the BChls excited states. For Rs. molischianum ring exciton states will be modeled as the four qubit quantum Fourier transform and the explicit circuit will be derived. Exciton states for Rps. acidophila ring cannot be modeled with an integer number of qubits. Both quantum Fourier transforms are instances of the hidden subgroup problem and this opens up a possibility that both purple bacteria implement an efficient quantum circuit for light harvesting.

arXiv:quant-ph/0702203Bulletin of the American Physical SocietyFeb 22, 20071 citation

Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms

Chaowen Guan, Akshit Katiyar

We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\in[-1,1]$ , and hence non-uniform in the angle $θ=\arccos x$ , a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter $κ$ of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting $\varepsilon$ -accurate block encoding has $O(1)$ normalization and uses $O(L)$ qubits and $\widetilde O(L^2)$ gates, where $L=\log N+\log(1/\varepsilon)$ . We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\in[-1,1]$, and hence non-uniform in the angle $θ=\arccos x$, a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter $κ$ of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting $\varepsilon$-accurate block encoding has $O(1)$ normalization and uses $O(L)$ qubits and $\widetilde O(L^2)$ gates, where $L=\log N+\log(1/\varepsilon)$. We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.

quant-pharXiv:2609.40277Oct 1, 20260 citations

Quantum Fourier Transform I

Hiu Yung Wong

Springer eBooksJun 21, 20230 citations

STABILITY OF THE QUANTUM FOURIER TRANSFORMATION ON THE ISING QUANTUM COMPUTER

G. L. Celardo, Carlos Pineda, Marko Žnidarič

We analyze the influence of errors on the implementation of the quantum Fourier transformation. Two kinds of errors are studied: (i) systematic errors due to off-resonant transitions and (ii) errors due to an external perturbation. The scaling of errors with system parameters and the number of qubits is analyzed. To suppress off-resonant transitions, we use correcting pulses while in order to suppress errors due to an external perturbation, we use an improved quantum Fourier transformation algorithm. As a result, the fidelity of quantum computation is increased by several orders of magnitude and is thus stable in a much wider range of physical parameters.We analyze the influence of errors on the implementation of the quantum Fourier transformation. Two kinds of errors are studied: (i) systematic errors due to off-resonant transitions and (ii) errors due to an external perturbation. The scaling of errors with system parameters and the number of qubits is analyzed. To suppress off-resonant transitions, we use correcting pulses while in order to suppress errors due to an external perturbation, we use an improved quantum Fourier transformation algorithm. As a result, the fidelity of quantum computation is increased by several orders of magnitude and is thus stable in a much wider range of physical parameters.

International Journal of Quantum InformationSep 1, 20057 citations

We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in

x\in[-1,1]

, and hence non-uniform in the angle

θ=\arccos x

, a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter

κ

of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting

\varepsilon

-accurate block encoding has

O(1)

normalization and uses

O(L)

qubits and

\widetilde O(L^2)

gates, where

L=\log N+\log(1/\varepsilon)

. We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.