Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstates: A New Approach to Quantum Computation

Shi-Biao Zheng

Published Aug 17, 2005• 95 citations
Publisher

Abstract

We propose a new approach to quantum phase gates via the adiabatic evolution. The conditional phase shift is neither of dynamical nor geometric origin. It arises from the adiabatic evolution of the dark state itself. Taking advantage of the adiabatic passage, this kind of quantum logic gates is robust against moderate fluctuations of experimental parameters. In comparison with the geometric phase gates, it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle. Thus, the procedure is simplified, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided. We illustrate such a kind of quantum logic gates in the ion trap system. The idea can also be realized in other systems, opening a new perspective for quantum information processing.

DOI
10.1103/physrevlett.95.080502

Related papers

Comment on Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstate

Hua Zhong Li

In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is discovered. The origin of this phase is the adiabatic evolution of a dark state. I would like to point out that these claims are questionable. The so called new phase gate was based on a phase which was nothing new but has been known for decades. It is something which has no physical meaning and is not observable. It was also pointed out by [quant-ph/0509150v1] that [Phy. Rev. Lett. 95, 080502 (2005)] was incorrect and the phase is the known geometric phase. Here we present a totally different argument.

arXiv:0707.3612•Jul 24, 2007•0 citations

Comment on “Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstates: A New Approach to Quantum Computation”

Ognyan Oreshkov, John Calsamiglia

In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the Hamiltonian does not follow a cyclic change. He further argues that "in comparison with the adiabatic geometric gates, the nontrivial cyclic loop is unnecessary, and thus the errors in obtaining the required solid angle are avoided, which makes this new kind of phase gates superior to the geometric gates." In this Comment, we point out that geometric operations, including adiabatic holonomies, can be induced by noncyclic Hamiltonians, and show that Zheng's gate is geometric. We also argue that the nontrivial loop responsible for the phase shift is there, and it requires the same precision as in any adiabatic geometric gate.

arXiv:0910.5694•Physical Review Letters•Oct 29, 2009•1 citation

Nongeometric multiqubit conditional phase gates by adiabatic evolution for trapped ions

Xinglai Zhang, Xun‐Li Feng, Chunfeng Wu +1 more

We propose a scheme for realizing controlled multiqubit quantum phase gates via the adiabatic evolution for trapped ions. Leveraging on the adiabatic operation, the scheme is tolerant to ambient noise and insensitive to the randomness of moderate fluctuations in experimental parameters. In our scheme, the ions are illuminated by lasers tuned to the first lower vibrational sideband or quasiresonant transition, the vibrational mode is not utilized as a data bus, and dark state evolution is required. The required gate operation time does not increase with the increasing number of qubits. This leads to a more efficient implementation of multiqubit gates than that of a series of one-qubit and two-qubit operations for quantum circuits and quantum algorithms.

Physical Review A•Mar 19, 2009•5 citations

Tunable Nongeometric Phase Gates for Two Hot Ions via Adiabatic Evolution of Dark States

Zheng Shi-Biao

We propose a scheme for implementing nongeometric phase gates for two trapped ions via adiabatic passage of dark states. During the operation, the vibrational mode is only virtually excited, thus the scheme is insensitive to heating. Furthermore, the spontaneous emission is suppressed since the ions are always in the electronic ground states. The scheme is robust against small fluctuations of parameters, and the conditional phase is tunable.

Chinese Physics Letters•Nov 29, 2006•1 citation

Rydberg-interaction gates via adiabatic passage and phase control of driving fields

Huai‐Zhi Wu, Xi-Rong Huang, Chang‐Sheng Hu +2 more

In this paper we propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques and currently developed approaches of phase control, a feasible proposal for implementation of a geometric phase gate is presented, where the conditional phase shift (Berry phase) is achieved by adiabatically and cyclically changing the parameters of the driving fields. Here we find that the geometric phase acquired is related to the way how the relative phase is modulated. In the second scheme, the system Hamiltonian is adiabatically changed in a noncyclic manner, so that the acquired conditional phase is not a Berry phase. A detailed analysis of the experimental feasibility and the effect of decoherence is also given. The proposed schemes provide new perspectives for adiabatic manipulation of interacting Rydberg systems with tailored phase modulation.

arXiv:1803.05145•Physical Review A•Aug 23, 2017•39 citations

Quantum logic gates by adiabatic passage

X. Lacour, Nicolas Sangouard, S. Guérin +1 more

We present adiabatic passage techniques for the realisation of one and two-qubit quantum Gates. These methods use evolution along dark-states of the system, avoiding decoherence effects such as spontaneous emission. The advantage of these methods is their robustness: they are insensitive to the fluctuations of the parameters and to partial knowledge of the system.

Journal de Physique IV (Proceedings)•Oct 1, 2006•1 citation
We propose a new approach to quantum phase gates via the adiabatic evolution. The conditional phase shift is neither of dynamical nor geometric origin. It arises from the adiabatic evolution of the dark state itself. Taking advantage of the adiabatic passage, this kind of quantum logic gates is robust against moderate fluctuations of experimental parameters. In comparison with the geometric phase gates, it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle. Thus, the procedure is simplified, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided. We illustrate such a kind of quantum logic gates in the ion trap system. The idea can also be realized in other systems, opening a new perspective for quantum information processing.
In a recent letter [Phy. Rev. Lett. 95, 080502 (2005)], it is claimed that based on a new kind of quantum mechanical phase of wave function which is neither dynamical nor geometrical a new kind of phase gate for quantum computation is discovered. The origin of this phase is the adiabatic evolution of a dark state. I would like to point out that these claims are questionable. The so called new phase gate was based on a phase which was nothing new but has been known for decades. It is something which has no physical meaning and is not observable. It was also pointed out by [quant-ph/0509150v1] that [Phy. Rev. Lett. 95, 080502 (2005)] was incorrect and the phase is the known geometric phase. Here we present a totally different argument.
In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the Hamiltonian does not follow a cyclic change. He further argues that "in comparison with the adiabatic geometric gates, the nontrivial cyclic loop is unnecessary, and thus the errors in obtaining the required solid angle are avoided, which makes this new kind of phase gates superior to the geometric gates." In this Comment, we point out that geometric operations, including adiabatic holonomies, can be induced by noncyclic Hamiltonians, and show that Zheng's gate is geometric. We also argue that the nontrivial loop responsible for the phase shift is there, and it requires the same precision as in any adiabatic geometric gate.
We propose a scheme for realizing controlled multiqubit quantum phase gates via the adiabatic evolution for trapped ions. Leveraging on the adiabatic operation, the scheme is tolerant to ambient noise and insensitive to the randomness of moderate fluctuations in experimental parameters. In our scheme, the ions are illuminated by lasers tuned to the first lower vibrational sideband or quasiresonant transition, the vibrational mode is not utilized as a data bus, and dark state evolution is required. The required gate operation time does not increase with the increasing number of qubits. This leads to a more efficient implementation of multiqubit gates than that of a series of one-qubit and two-qubit operations for quantum circuits and quantum algorithms.
In this paper we propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques and currently developed approaches of phase control, a feasible proposal for implementation of a geometric phase gate is presented, where the conditional phase shift (Berry phase) is achieved by adiabatically and cyclically changing the parameters of the driving fields. Here we find that the geometric phase acquired is related to the way how the relative phase is modulated. In the second scheme, the system Hamiltonian is adiabatically changed in a noncyclic manner, so that the acquired conditional phase is not a Berry phase. A detailed analysis of the experimental feasibility and the effect of decoherence is also given. The proposed schemes provide new perspectives for adiabatic manipulation of interacting Rydberg systems with tailored phase modulation.