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Author |
Nzongani, U.; Zylberman, J.; Doncecchi, C.E.; Perez, A.; Debbasch, F.; Arnault, P. |
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Title |
Quantum circuits for discrete-time quantum walks with position-dependent coin operator |
Type |
Journal Article |
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Year |
2023 |
Publication |
Quantum Information Processing |
Abbreviated Journal |
Quantum Inf. Process. |
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Volume  |
22 |
Issue |
7 |
Pages |
270 - 46pp |
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Keywords |
Quantum walks; Quantum circuits; Quantum simulation |
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Abstract |
The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode 2(n) position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. Themain idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent 2 x 2-block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error epsilon (in terms of the spectral norm), the depth and size of which scale as O(1/epsilon). A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position). |
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Address |
[Nzongani, Ugo; Doncecchi, Carlo-Elia; Arnault, Pablo] Univ Paris Saclay, CNRS, INRIA, Lab Methodes Formelles,ENS Paris Saclay, F-91190 Gif Sur Yvette, France, Email: ugo.nzongani@universite-paris-saclay.fr; |
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Springer |
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English |
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ISSN |
1570-0755 |
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Conference |
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Notes |
WOS:001022408900002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5587 |
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Author |
Aguiar, P.; Rafecas, M.; Ortuño, J.E.; Kontaxakis, G.; Santos, A.; Pavia, J.; Rosetti, M. |
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Title |
Geometrical and Monte Carlo projectors in 3D PET reconstruction |
Type |
Journal Article |
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Year |
2010 |
Publication |
Medical Physics |
Abbreviated Journal |
Med. Phys. |
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Volume |
37 |
Issue |
11 |
Pages |
5691-5702 |
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Keywords |
3D PET; iterative reconstruction; list-mode reconstruction; ray-tracing techniques; Monte Carlo simulation; system response matrix |
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Abstract |
Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk. Methods: Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET. Results: The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors. Conclusions: The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible. |
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Address |
[Aguiar, Pablo] Univ Santiago de Compostela, Dept Fis Particulas, Complexo Hosp Univ Santiago de Compostela, Fdn IDICHUS IDIS, Santiago De Compostela, Spain, Email: pablo.aguiar.fernandez@sergas.es |
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Amer Assoc Physicists Medicine Amer Inst Physics |
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English |
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ISSN |
0094-2405 |
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Notes |
ISI:000283747600015 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ elepoucu @ |
Serial |
338 |
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Author |
Arnault, P.; Macquet, A.; Angles-Castillo, A.; Marquez-Martin, I.; Pina-Canelles, V.; Perez, A.; Di Molfetta, G.; Arrighi, P.; Debbasch, F. |
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Title |
Quantum simulation of quantum relativistic diffusion via quantum walks |
Type |
Journal Article |
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Year |
2020 |
Publication |
Journal of Physics A |
Abbreviated Journal |
J. Phys. A |
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Volume |
53 |
Issue |
20 |
Pages |
205303 - 39pp |
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Keywords |
noisy quantum walks; noisy quantum systems; decoherence; Lindblad equation; quantum simulation; relativistic diffusions; telegraph equation |
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Abstract |
Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position. |
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Address |
[Arnault, Pablo; Angles-Castillo, Andreu; Marquez-Martin, Ivan; Pina-Canelles, Vicente; Perez, Armando; Di Molfetta, Giuseppe] Univ Valencia, Dept Fis Teor, Dr Moliner 50, Burjassot 46100, Spain, Email: pablo.arnault@ic.uv.es |
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Publisher |
Iop Publishing Ltd |
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English |
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ISSN |
1751-8113 |
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Notes |
WOS:000531359000001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4390 |
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Author |
Hornillos, M.B.G.; Gorlychev, V.; Caballero, R.; Cortes, G.; Poch, A.; Pretel, C.; Calvino, F.; Tain, J.L.; Algora, A.; Agramunt, J.; Cano-Ott, D.; Martinez, T.; Mendoza, E.; Rissanen, J.; Aysto, J.; Jokinen, A.; Eronen, T.; Moore, I.; Penttila, H. |
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Title |
Monte Carlo Simulations for the Study of a Moderated Neutron Detector |
Type |
Journal Article |
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Year |
2011 |
Publication |
Journal of the Korean Physical Society |
Abbreviated Journal |
J. Korean Phys. Soc. |
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Volume |
59 |
Issue |
2 |
Pages |
1573-1576 |
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Keywords |
Monte Carlo simulations; GEANT4; MCNPX; Beta delayed neutron emission; Neutron detector |
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Abstract |
This work presents the Monte Carlo simulations performed with the MCNPX and GEANT4 codes for the design of a BEta deLayEd Neutron detector, BELEN-20. This detector will be used for the study of beta delayed neutron emission and consists of a block of polyethylene with dimensions 90 x 90 x 80 cm(3) and 20 cylindrical (3)He gas counters. The results of these simulations have been validated experimentally with a (252)Cf source in the laboratory at UPC, Barcelona. Also the first experiment with this detector has been carried out in November 2009 in JYFL, Finland. In this experiment the neutron emission probability after beta decay of the fission products (88)Br, (94,95)Rb, and (138)I has been measured; this data is still under analysis. Simulations with MCNPX and GEANT4 have been performed in order to obtain the efficiency of the BELEN-20 detector for each of the above nuclei using the neutron energy distribution corresponding to each nucleus. |
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Address |
[Hornillos, MBG; Gorlychev, V; Caballero, R; Cortes, G; Poch, A; Pretel, C; Calvino, F] Univ Politecn Cataluna, Seccio Engn Nucl, E-08028 Barcelona, Spain, Email: belen.gomez@upc.edu |
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Korean Physical Soc |
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English |
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ISSN |
0374-4884 |
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Notes |
WOS:000294080700028 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ elepoucu @ |
Serial |
733 |
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Author |
n_TOF Collaboration (Mendoza, E. et al); Giubrone, G.; Tain, J.L. |
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Title |
Improved Neutron Capture Cross Section Measurements with the n_TOF Total Absorption Calorimeter |
Type |
Journal Article |
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Year |
2011 |
Publication |
Journal of the Korean Physical Society |
Abbreviated Journal |
J. Korean Phys. Soc. |
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Volume |
59 |
Issue |
2 |
Pages |
1813-1816 |
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Keywords |
ND2010; Nuclear data; n_TOF; Background; Monte Carlo; Neutron; Time of flight; Cross section; Calorimeter; Shielding; Simulation; Total absorption; Gamma ray; Neutron capture |
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Abstract |
The n_TOF collaboration operates a Total Absorption Calorimeter (TAC) [1] for measuring neutron capture cross-sections of low-mass and/or radioactive samples. The results obtained with the TAC have led to a substantial improvement of the capture cross sections of (237)Np and (240)Pu [2]. The experience acquired during the first measurements has allowed us to optimize the performance of the TAC and to improve the capture signal to background ratio, thus opening the way to more complex and demanding measurements on rare radioactive materials. The new design has been reached by a series of detailed Monte Carlo simulations of complete experiments and dedicated test measurements. The new capture setup will be presented and the main achievements highlighted. |
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Address |
[Mendoza, E; Becares, V; Casado, A; Cano-Ott, D; Fernandez-Ordonez, M; Gonzalez-Romero, E; Guerrero, C; Martinez, T; Vidriales, JJ] Ctr Invest Energet Medioambientales & Tecnol, Madrid 28040, Spain, Email: emilio.mendoza@ciemat.es |
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Publisher |
Korean Physical Soc |
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English |
Summary Language |
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Series Volume |
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Series Issue |
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ISSN |
0374-4884 |
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Conference |
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Notes |
WOS:000294080700086 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ elepoucu @ |
Serial |
738 |
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