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Quantum Implementation of Non-unitary Operations with Biorthogonal Representations Cover

Quantum Implementation of Non-unitary Operations with Biorthogonal Representations

Quantum Information & Computation
Volume 25 (2025): Issue 2 (May 2025)
By: Efstratios Koukoutsis,  Panagiotis Papagiannis,  Kyriakos Hizanidis,  Abhay K. Ram,  George Vahala,  óscar Amaro,  Llucas I Iñigo Gamiz and  Dimosthenis Vallis  
Open Access
|May 2025

Figures & Tables

Figure 1.

The quantum circuit implementation of quantum operations (33)–(41) that produce the output state |Ψ〉out ∝V^|Ψ〉. The controlled operation represents a series of 2𝒩 multi-qubit controlled operations according to the definition of U^select in Eq. (36).
The quantum circuit implementation of quantum operations (33)–(41) that produce the output state |Ψ〉out ∝V^|Ψ〉. The controlled operation represents a series of 2𝒩 multi-qubit controlled operations according to the definition of U^select in Eq. (36).

Figure 2.

Quantum circuit implementation of non-unitary operator V^ in Eq. (49), following the procedure of Eq. (54). The measurement outcome in the first register is conditioned on the 0-bit value.
Quantum circuit implementation of non-unitary operator V^ in Eq. (49), following the procedure of Eq. (54). The measurement outcome in the first register is conditioned on the 0-bit value.

Figure 3.

The LCU quantum circuit of Eq. (60), implementing the non-unitary operator V^ in Eq. (49).
The LCU quantum circuit of Eq. (60), implementing the non-unitary operator V^ in Eq. (49).

Figure 4.

The implementation quantum circuit for the non-unitary operator V^ in Eq. (62) with κ1 > 0. Notice that because V^>=1^ the circuit is considerably simple.
The implementation quantum circuit for the non-unitary operator V^ in Eq. (62) with κ1 > 0. Notice that because V^>=1^ the circuit is considerably simple.

Figure 5.

Synergistic quantum implementation of V^|Ψ〉 using the LCU and biorthogonal unitary implementations U^A and U^B for the non-unitary components V^A and V^B, respectively.
Synergistic quantum implementation of V^|Ψ〉 using the LCU and biorthogonal unitary implementations U^A and U^B for the non-unitary components V^A and V^B, respectively.
DOI: https://doi.org/10.2478/qic-2025-0007 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
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Language: English
Page range: 141 - 155
Submitted on: Dec 24, 2024
Accepted on: Mar 5, 2025
Published on: May 26, 2025
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
biorthogonal quantum mechanics,
dilation methods,
non-unitary gates,
non-Hermitian systems
Related subjects:
Physics,
Quantum physics

© 2025 Efstratios Koukoutsis, Panagiotis Papagiannis, Kyriakos Hizanidis, Abhay K. Ram, George Vahala, óscar Amaro, Llucas I Iñigo Gamiz, Dimosthenis Vallis, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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