@article {566, title = {Optimal fixed-point quantum search in an interacting Ising spin system}, journal = {Quantum Inf. Process.}, volume = {20}, year = {2021}, pages = {90}, abstract = {In Grover{\textquoteright}s search algorithm, a priori knowledge of the number of target states is needed to effectively find a solution. This is due to the inherent oscillatory nature of unitary gates in the algorithm. A fixed-point quantum search is introduced in [Phys. Rev. Lett. 113, 210501 (2014)] to mitigate this oscillation even without knowing the size of the target space. This is done by modifying the phase inversion and oracle of the original Grover{\textquoteright}s algorithm so that the phase can assume intermediate values in [-π,π]. Naturally, qubits in a quantum computer are interacting among themselves and this might introduce an error in the phase assignment. In this work, we used the Ising spin chain to simulate the interactions among the qubits and demonstrate how to implement the fixed-point quantum search. By inspecting the state vectors after some finite number of iterations, we found that the error is primarily due to the phase difference of the ideal target state with that of the final state. Further investigation shows that high fidelity between the ideal and real evolution can be achieved by using a low Rabi frequency.}, doi = {10.1007/s11128-021-03023-1}, author = {Neris I. Sombillo and Ronald S. Banzon and Cristine Villagonzalo} } @conference {493, title = {Effect of error tolerance probability to the fidelity of a 4-qubit quantum search simulation}, year = {2018}, month = {5{\textendash}9 Nov 2018}, pages = {P.16}, publisher = {2018 ICTP Asian Network School and Workshop on Complex Condensed Matter Systems}, address = {Suranaree University of Technology, Thailand}, abstract = {We simulate the optimized fixed-point quantum search (OFPQS) algorithm with first- and second-nearest neighbor interactions in a 4-qubit Ising spin system using a nonrefocusing technique. In order to perform a single qubit gate, we utilize the coupling interactions to control the neighboring spins. The phase-marking scheme of the OFPQS is implemented using a single rotation about the transverse axis instead of the usual rotation about the field axis. Furthermore, the state of the ancilla is initialized in a superposition of the basis states to avoid the generation of unwanted states. This procedure gives us a probability of finding the target state within the prescribed bound of the OFPQS. Based on this scheme, we investigate the effect of error tolerance probability of the OFPQS to the fidelity of the nonrefocusing implementation.}, url = {https://indico.cern.ch/event/745791/contributions/3202508/}, author = {Neris Sombillo and Ronald Banzon and Cristine Villagonzalo} } @inproceedings {sombillo, title = {Amplitude amplification of the marked states in quantum search simulation}, booktitle = {Proceedings of the 35th Samahang Pisika ng Pilipinas Physics Conference}, year = {2017}, month = {7{\textendash}10 June 2017}, pages = {SPP-2017-PB-17}, address = {Cebu City, Philippines}, abstract = {Yoder et al. [1] proposed a quantum search algorithm that prevents the system to move away from the marked states when the number of target states M is unknown. This method uses a recursive approach that makes the target state act as a fixed-point. We simulate the algorithm in an Ising spin chain with first- and second-nearest neighbor interaction. Our method involves a selective phase-shift rotation per iteration to obtain the target state. We find the probability of success for the fixed-point implementation to fluctuate only about a limited range of values within an indicated tolerance as compared to the large oscillations of the same for Grover{\textquoteright}s non-fixed-point algorithm.}, url = {http://paperview.spp-online.org/proceedings/article/view/142}, author = {Neris Sombillo and Ronald Banzon and Cristine Villagonzalo} } @conference {420, title = {Fixed-point quantum search as implemented in an Ising spin system}, year = {2017}, month = {26{\textendash}29 June 2017}, pages = {50}, publisher = {6th Adiabatic Quantum Computing Conference}, address = {Tokyo, Japan}, abstract = {The fixed-point quantum search provides a solution to the oscillation problem in a quantum search algorithm through the variation of oracle and inversion phases at each iteration. We simulate the fixed-point algorithm in an Ising spin system with first- and second-nearest neighbor interactions. Since the oracle and the inversion operator acts on O(2), then the oracle qubit is required to be in a superposition of states at the start of the simulation. This provides a way to implement the rotation required in the variation of phases at each iteration. Results show that the probability of success calculated from the algorithm and obtained from the simulation gives a similar behavior which effectively damps the oscillation. We also investigate the effect of tolerance on the fidelity as we increase the number of iterations.}, url = {http://www.smapip.is.tohoku.ac.jp/~aqc2017/program.html}, author = {Neris I Sombillo and Ronald S. Banzon and Cristine Villagonzalo} } @article {377, title = {Measurement-enhanced quantum search}, journal = {AIP Conf. Proc. (8th Jagna International Workshop)}, volume = {1871}, year = {2017}, pages = {020002}, abstract = {The oscillatory nature of the unitary Grover operator makes quantum searching difficult if one has no prior knowledge of the number of target states in the database. In this work, we coupled the database to an external qubit to transfer the target state in a space where the quantum search operation is not applied. This is followed by a measurement of the external and the ancilla qubit which result to a mixed state with a higher probability of finding the target state. The algorithm is simulated in a spin chain having first and second order neighbor interactions. The result shows that the oscillation is suppressed and the probability of success generally increased with iteration number.}, doi = {10.1063/1.4996512}, url = {http://aip.scitation.org/doi/10.1063/1.4996512}, author = {Neris I Sombillo and Ronald Banzon and Cristine Villagonzalo} } @inproceedings {312, title = {Near-resonant approximation in quantum search simulation}, booktitle = {Proceedings of the 34th Samahang Pisika ng Pilipinas Physics Congress}, year = {2016}, month = {18{\textendash}21 Aug 2016}, pages = {SPP-2016-2C-01}, address = {University of the Philippines Visayas, Iloilo City}, abstract = {
The simulation of a quantum search algorithm in an Ising spin chain is equivalent to solving a system of 2^L coupled first order differential equations with L being the number of qubits. The near-resonant approximation can be used to simplify the evolution of the states in the database. In this work, we compare the simulation of a quantum search algorithm using the exact evolution according to Schr{\"o}dinger equation and using the near-resonant approximation. Our results show that the error of the near-resonant approximation is comparable to that of the exact evolution in terms of the fidelity measure. The advantage gained in having this small error at the near-resonant approximation is its faster execution time relative to the exact case.
}, author = {Neris D Ilano and Ronald Banzon and Cristine Villagonzalo} } @inproceedings {320, title = {A critically damped quantum search may not necessarily be optimal}, booktitle = {Proceedings of the AQIS Conference 2015}, year = {2015}, month = {24{\textendash}30 Aug 2015}, pages = {147-148}, address = {Korea Institute for Advanced Study, Seoul}, abstract = {We explore the rate at which the target state is obtained in a damped quantum search of an Ising system. As the number of target states is reduced, the damped quantum search gives a higher probability of success than that of the classical search. For any system in general, a new damping parameter was obtained from an optimization of the damped quantum search. Application of the optimum damping parameter per iteration on the damped quantum search shows a significant improvement of the probability of success over the critically damped quantum search.}, url = {http://aqis-conf.org/2015/program/}, author = {Neris D Ilano and Ronald Banzon and Cristine Villagonzalo} } @conference {350, title = {Effect of varying the position of the ancilla qubit and the coupling constants in the simulation of Grover{\textquoteright}s quantum search algorithm}, year = {2015}, month = {7{\textendash}11 Jan 2015}, pages = {P-62}, publisher = {9th International Conference on Computational Physics}, address = {National University of Singapore}, abstract = {We simulate Grover{\textquoteright}s algorithm in an Ising spin chain quantum computer with spatially-dependent coupling constant. The interaction to the nearest and second-nearest neighbor of the spins is considered. The behavior of the fidelity as a function of the number of Grover iteration during the algorithm is determined. For a fixed location of the ancilla qubit, the overall fidelity decreases as we increase the size of the database. Also, as we vary the coupling constant per neighbor, we obtain a high fidelity for a given number of iteration. The simulation of the algorithm using a classical computer system restricts the size of the database that gives a high fidelity result.}, url = {http://www.physics.nus.edu.sg/iccp9/}, author = {Neris D Ilano and Cristine Villagonzalo and Ronald Banzon} } @inproceedings {ilano-spp-2015, title = {Simulation of Grover{\textquoteright}s algorithm with position-variation of the ancilla qubit}, booktitle = {Proceedings of the 33rd Samahang Pisika ng Pilipinas Physics Congress}, year = {2015}, month = {3{\textendash}6 Jun 2015}, pages = {SPP-2015-2B-06}, address = {University of Northern Philippines, Vigan City}, abstract = {
We simulate Grover{\textquoteright}s quantum search algorithm in an Ising spin chain quantum computer with nearest and second-nearest neighbor interactions. We determine the optimum Rabi frequency that satisfies the 2πk method by selecting a high fidelity value in the frequency scan for each database size. Also, we vary the position of the ancilla qubit and investigate the effect on the fidelity for different sizes of the database. The behavior of the fidelity as a function of the number of Grover iterations during the algorithm is considered. For a fixed location of the ancilla qubit, the overall fidelity decreases as we increase the size of the database.
}, author = {Neris D Ilano and Ronald S. Banzon and Cristine Villagonzalo} } @conference {ilano-qpcmp-2015, title = {Simulation of the quantum search algorithm in an Ising spin system}, year = {2015}, month = {22{\textendash}23 Apr 2015}, publisher = {Workshop on Theories in Quantum Phenomena and Condensed Matter Physics}, address = {University of the Philippines Los Ba{\~n}os, Laguna}, url = {https://imsp.uplb.edu.ph/index.php/component/content/article/17-imsp-news/research/370-workshop-on-theories-in-quantum-phenomena-and-condensed-matter-physics}, author = {Neris D Ilano} } @conference {354, title = {Simulation of Grover{\textquoteright}s algorithm with spatially-dependent coupling constant}, year = {2014}, month = {16{\textendash}25 Sep 2014}, pages = {19}, publisher = {Okinawa School in Physics: Coherent Quantum Dynamics}, address = {Okinawa Institute of Science and Technology, Japan}, abstract = {We simulate Grover{\textquoteright}s algorithm in an Ising spin chain quantum computer with spatially-dependent coupling constant. The simulation shows that the tendency of two distinct states to transition from the same initial state is reduced. The fidelity with the ideal result and the probability of finding the target state are also investigated.}, url = {https://groups.oist.jp/cqd/participants-0}, author = {Neris D Ilano and Cristine Villagonzalo and Ronald Banzon} } @inproceedings {ilano-spp-2014, title = {Working precision in a simulation of Grover{\textquoteright}s algorithm in an Ising spin system}, booktitle = {Proceedings of the 32nd Samahang Pisika ng Pilipinas Physics Congress}, year = {2014}, month = {17{\textendash}20 Oct 2014}, pages = {SPP2014-5A-2}, address = {University of the Philippines Diliman, Quezon City}, abstract = {
We consider the simulation of Grover{\textquoteright}s algorithm in an Ising nuclear spin chain computer with first- and second-nearest neighbor interaction. We calculate the fidelity, a measure of the accuracy of the state, as a function of π/2- and π-pulses and investigate the precision of the success probability of the target state. The fidelity is constrained by the set working precision of the computer system, hence we simulate the algorithm using different working precisions. A reduction of precision is also observed as you increase the number of iterations that restricts the size of the database to effectively simulate the algorithm. The amount of decrease is dependent on the decomposition of pulses.
}, author = {Neris D Ilano and Cristine Villagonzalo and Ronald S. Banzon} } @inproceedings {ilano-spp-2013, title = {The effect of the Hadamard gate decomposition in the simulation of Grover{\textquoteright}s algorithm}, booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress}, year = {2013}, month = {23{\textendash}25 Oct 2013}, pages = {SPP2013-5B-2}, address = {University of San Carlos, Cebu City}, abstract = {
Simulation of Grover{\textquoteright}s algorithm in an Ising nuclear spin chain computer with first- and second-nearest neighbor interaction is considered. The most frequently used quantum gate in the algorithm is the Hadamard gate. We investigate the effect of its decomposition into several rotation matrices and numerically calculate the fidelity and probability of success of finding the target state. Using an appropriate decomposition, we obtain a high fidelity for different numbers of iterations. The probability of finding the target state also increased and is much closer to the ideal result.
}, author = {Neris D Ilano and Cristine Villagonzalo and Ronald S. Banzon} } @inproceedings {242, title = {The effect of RF distribution on the implementation of quantum CN gate in an Ising spin chain}, booktitle = {Proceedings of the 30th Samahang Pisika ng Pilipinas Physics Congress}, year = {2012}, month = {22{\textendash}24 Oct 2012}, pages = {SPP-2012-056}, address = {De La Salle Health Sciences Institute, Dasmari{\~n}as, Cavite}, abstract = {
We consider the dynamics of an Ising spin quantum computer with a radio frequency (RF) pulse distribution. The effect of the frequency spread decreases the resonant transition probability and increases thenear-resonant transition probability. Also, we apply the 2πk method to suppress the near-resonant transition. However, it has an unwanted effect on the probability of the resonant transition. It turns out that the desirable result can be obtained if we use the lowest possible value of k.
}, author = {Neris D Ilano and Cristine Villagonzalo and Ronald S. Banzon} } @inproceedings {ilano-spp-2011, title = {Optimizing the damped quantum search algorithm}, booktitle = {Proceedings of the 29th Samahang Pisika ng Pilipinas National Physics Congress}, year = {2011}, month = {24{\textendash}26 Oct 2011}, pages = {SPP2011-4A-4}, address = {University of the Philippines Diliman, Quezon City}, abstract = {
An optimization of the damped quantum search is introduced by calculating the damping parameter that gives the minimum probability of failure per iteration. The resulting damping parameter is compared with the critical damping. The result shows that the optimized damping is generally not equal to the critical damping if the degeneracy of the target state is not comparable to the size of the database. The probability of failure for the optimized damping and critical damping does not differ significantly for the first two iterations. This difference is relatively large for the third iteration. This suggests that for greater number of iterations, the critically damped search is not optimized.
}, url = {https://paperview.spp-online.org/proceedings/article/view/3135}, author = {Neris D Ilano and Ronald S. Banzon and Cristine Villagonzalo} } @inproceedings {ilano-spp-2009, title = {Damped quantum search in an Ising spin system}, booktitle = {Proceedings of the 27th Samahang Pisika ng Pilipinas Physics Congress}, year = {2009}, month = {28{\textendash}30 Oct 2009}, pages = {SPP-2009-006}, address = {Development Academy of the Philippines Convention Center, Tagaytay City}, abstract = {
We seek on 8 and a 12 spins Ising systems at least one of their eigenstates of a certain eigenvalue by applying the damped quantum search. In particular, without the knowledge of the number of degeneracy, it requires 150 queries to find at least one of the characteristic states having an eigenvalue of -11ε in a database of 4096 items with a probability of 99.1\%. The average number of queries are compared with that of the undamped quantum search. It is found that for a small number of target states, the damped quantum search still preserves the quantum results, while for a large number of target states the classical limit is approached. Moreover, the damped quantum search is shown to increase monotonically as the number of iteration is increased.
}, author = {Neris D Ilano and Ronald S. Banzon and Cristine Villagonzalo} }