Qubits as Edge State Detectors:
Illustration Using the SSH Model
Meri Zaimi, Christian Boudreault, Nouédyn Baspin, Hichem Eleuch,
Richard MacKenzie, and Michael Hilke
Abstract As is well known, qubits are the fundamental building blocks of quantum
computers, and more generally, of quantum information. A major challenge in
the development of quantum devices arises because the information content in
any quantum state is rather fragile, as no system is completely isolated from its
environment. Generally, such interactions degrade the quantum state, resulting in a
loss of information.
Topological edge states are promising in this regard because they are in ways
more robust against noise and decoherence. But creating and detecting edge states
can be challenging. We describe a composite system consisting of a two-level
system (the qubit) interacting with a finite Su–Schrieffer–Heeger chain (a hopping
model with alternating hopping parameters) attached to an infinite chain. In this
model, the dynamics of the qubit changes dramatically depending on whether or not
M. Zaimi
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: meri.zaimi@umontreal.ca
C. Boudreault
Département des sciences de la nature, Collège militaire royal de Saint-Jean,
Saint-Jean-sur-Richelieu, QC, Canada
e-mail: Christian.Boudreault@cmrsj-rmcsj.ca
N. Baspin · M. Hilke
Department of Physics, McGill University, Montréal, QC, Canada
e-mail: nouedyn.baspin@mail.mcgill.ca; hilke@physics.mcgill.ca
H. Eleuch
Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi
University, Abu Dhabi, United Arab Emirates
Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX,
USA
R. MacKenzie ()
Département de physique, Université de Montréal, Montréal, QC, Canada
e-mail: richard.mackenzie@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_59
633
Illustration Using the SSH Model
Meri Zaimi, Christian Boudreault, Nouédyn Baspin, Hichem Eleuch,
Richard MacKenzie, and Michael Hilke
Abstract As is well known, qubits are the fundamental building blocks of quantum
computers, and more generally, of quantum information. A major challenge in
the development of quantum devices arises because the information content in
any quantum state is rather fragile, as no system is completely isolated from its
environment. Generally, such interactions degrade the quantum state, resulting in a
loss of information.
Topological edge states are promising in this regard because they are in ways
more robust against noise and decoherence. But creating and detecting edge states
can be challenging. We describe a composite system consisting of a two-level
system (the qubit) interacting with a finite Su–Schrieffer–Heeger chain (a hopping
model with alternating hopping parameters) attached to an infinite chain. In this
model, the dynamics of the qubit changes dramatically depending on whether or not
M. Zaimi
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: meri.zaimi@umontreal.ca
C. Boudreault
Département des sciences de la nature, Collège militaire royal de Saint-Jean,
Saint-Jean-sur-Richelieu, QC, Canada
e-mail: Christian.Boudreault@cmrsj-rmcsj.ca
N. Baspin · M. Hilke
Department of Physics, McGill University, Montréal, QC, Canada
e-mail: nouedyn.baspin@mail.mcgill.ca; hilke@physics.mcgill.ca
H. Eleuch
Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi
University, Abu Dhabi, United Arab Emirates
Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX,
USA
R. MacKenzie ()
Département de physique, Université de Montréal, Montréal, QC, Canada
e-mail: richard.mackenzie@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_59
633