| |
Records |
Links |
|
Author |
Nzongani, U.; Zylberman, J.; Doncecchi, C.E.; Perez, A.; Debbasch, F.; Arnault, P. |
|
| |
Title |
Quantum circuits for discrete-time quantum walks with position-dependent coin operator |
Type |
Journal Article |
| |
Year |
2023 |
Publication |
Quantum Information Processing |
Abbreviated Journal  |
Quantum Inf. Process. |
|
| |
Volume |
22 |
Issue |
7 |
Pages |
270 - 46pp |
|
| |
Keywords |
Quantum walks; Quantum circuits; Quantum simulation |
|
| |
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). |
|
| |
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; |
|
| |
Corporate Author |
|
Thesis |
|
|
| |
Publisher |
Springer |
Place of Publication |
|
Editor |
|
|
| |
Language |
English |
Summary Language |
|
Original Title |
|
|
| |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
|
| |
Series Volume |
|
Series Issue |
|
Edition |
|
|
| |
ISSN |
1570-0755 |
ISBN |
|
Medium |
|
|
| |
Area |
|
Expedition |
|
Conference |
|
|
| |
Notes |
WOS:001022408900002 |
Approved |
no |
|
| |
Is ISI |
yes |
International Collaboration |
yes |
|
| |
Call Number |
IFIC @ pastor @ |
Serial |
5587 |
|
| Permanent link to this record |
| |
|
| |
|
Author |
Jay, G.; Arnault, P.; Debbasch, F. |
|
| |
Title |
Dirac quantum walks with conserved angular momentum |
Type |
Journal Article |
| |
Year |
2021 |
Publication |
Quantum Studies-Mathematics and Foundations |
Abbreviated Journal |
Quantum Stud. Math. Found. |
|
| |
Volume |
8 |
Issue |
|
Pages |
419-430 |
|
| |
Keywords |
Quantum walks; Quantum simulation; Lattice field theory |
|
| |
Abstract |
A quantum walk (QW) simulating the flat (1+2)D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group SO(3), but rather of its double cover SU(2), the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to 4 pi. The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW. |
|
| |
Address |
[Jay, Gareth] Univ Western Australia, Phys Dept, Perth, WA 6009, Australia, Email: gareth.jay@uwa.edu.au; |
|
| |
Corporate Author |
|
Thesis |
|
|
| |
Publisher |
Springer |
Place of Publication |
|
Editor |
|
|
| |
Language |
English |
Summary Language |
|
Original Title |
|
|
| |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
|
| |
Series Volume |
|
Series Issue |
|
Edition |
|
|
| |
ISSN |
2196-5609 |
ISBN |
|
Medium |
|
|
| |
Area |
|
Expedition |
|
Conference |
|
|
| |
Notes |
WOS:000697709700001 |
Approved |
no |
|
| |
Is ISI |
yes |
International Collaboration |
yes |
|
| |
Call Number |
IFIC @ pastor @ |
Serial |
4975 |
|
| Permanent link to this record |
