1Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France
2Dipartimento di Fisica e Astronomia “G. Galilei”, Universita` di Padova, I-35131 Padova, Italy
3Padua Quantum Technologies Research Center, Universita` degli Studi di Padova
4Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova, I-35131 Padova, Italy
5Dipartimento di Fisica, Universita` di Bari, I-70126 Bari, Italy
6Université Paris-Saclay, Inria, CNRS, LMF, 91190 Gif-sur-Yvette, France
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Abstract
This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step $Delta_t=Delta_x$. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.
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Cited by
[1] Ugo Nzongani, Julien Zylberman, Carlo-Elia Doncecchi, Armando Pérez, Fabrice Debbasch, and Pablo Arnault, “Quantum circuits for discrete-time quantum walks with position-dependent coin operator”, Quantum Information Processing 22 7, 270 (2023).
[2] Nicolás Medina Sánchez and Borivoje Dakić, “Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics”, arXiv:2306.05919, (2023).
[3] Edoardo Centofanti, Alessandro Bisio, and Paolo Perinotti, “A massless interacting Fermionic Cellular Automaton exhibiting bound states”, arXiv:2304.14687, (2023).
[4] Ugo Nzongani and Pablo Arnault, “Adjustable-depth quantum circuit for position-dependent coin operators of discrete-time quantum walks”, arXiv:2304.10460, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2023-11-08 16:19:08). The list may be incomplete as not all publishers provide suitable and complete citation data.
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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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