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On the Irresistible Efficiency of Signal Processing Methods in Quantum Computing
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We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits for the Discrete Cosine and Sine Transforms, and for the Discrete Hartley transform. We show that at most O(log^2 N) elementary quantum gates are necessary to implement any of those transforms for input sequences of length N.
Forward citations
Cited by 2 Pith papers
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Encoding Choices and Fault-Tolerant Resource Estimates for Digital Quantum Hamiltonian Descent
For digital quantum Hamiltonian descent, binary amplitude encoding uses O(d log N) qubits and fewer R_z rotations than one-hot encoding in all tested benchmarks, making it the preferred starting point for fault-tolera...
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QRTlib: A Library for Fast Quantum Real Transforms
A new Qiskit library implements quantum Hartley, cosine, and sine transforms, with an LCU-based Hartley circuit whose leading gate-complexity term is four times smaller than the previous best.
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