scholarly journals Uniform approximation by (quantum) polynomials

2011 ◽  
Vol 11 (3&4) ◽  
pp. 215-225
Author(s):  
Andrew Drucker ◽  
Ronald de Wolf
Keyword(s):  
Approximation Theory ◽  
Uniform Approximation ◽  
Quantum Algorithms ◽  
Continuous Functions ◽  
Quantum Phase ◽  
Phase Estimation ◽  
Classical Theorem ◽  
Quantitative Version ◽  
Quantum Counting ◽  
Approximation Of Continuous Functions

We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectively on quantum counting and on quantum phase estimation.

scholarly journals Photonic scheme of quantum phase estimation for quantum algorithms via cross-Kerr nonlinearities under decoherence effect

2019 ◽  
Vol 27 (21) ◽  
pp. 31023 ◽  
Author(s):  
Changho Hong ◽  
Jino Heo ◽  
Min-Sung Kang ◽  
Jingak Jang ◽  
Hyun-Jin Yang ◽  
...  
Keyword(s):  
Quantum Algorithms ◽  
Quantum Phase ◽  
Phase Estimation ◽  
Decoherence Effect

Quantum phase estimation and quantum counting with qudits

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
Hristo S. Tonchev ◽  
Nikolay V. Vitanov
Keyword(s):  
Quantum Phase ◽  
Phase Estimation ◽  
Quantum Counting

scholarly journals Quantum phase estimation with arbitrary constant-precision phase shift operators

2012 ◽  
Vol 12 (9&10) ◽  
pp. 864-875
Author(s):  
Hamed Ahmadi ◽  
Chen-Fu Chiang
Keyword(s):  
Phase Shift ◽  
Arbitrary Constant ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Phase ◽  
Phase Estimation ◽  
Shift Operators ◽  
Physical Implementation ◽  
Alternative Approach ◽  
Original Approach

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In this paper, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach.

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