We study quantum decoherence of single-qubit and two-qubit Aharonov-Anandan (AA) geometric phase gates realized in a multistep scheme. Each AA gate is also compared with the dynamical phase gate performing the same unitary transformation within the same time period and coupled with the same environment, which is modeled as harmonic oscillators. It is found that the fidelities and the entanglement protection of the AA phase gates are enhanced by the states being superpositions of different eigenstates of the environmental coupling, and the noncommutativity between the qubit interaction and the environmental coupling.
We study quantum decoherence of single-qubit and two-qubit Aharonov-Anandan (AA) geometric phase gates realized in a multistep scheme. Each AA gate is also compared with the dynamical phase gate performing the same unitary transformation within the same time period and coupled with the same environment, which is modeled as harmonic oscillators. It is found that the fidelities and the entanglement protection of the AA phase gates are enhanced by the states being superpositions of different eigenstates of the environmental coupling, and the noncommutativity between the qubit interaction and the environmental coupling.
Quantum computing in terms of geometric phases, i.e. Berry or Aharonov-Anandan phases, is fault-tolerant to a certain degree. We examine its implementation based on Zeeman coupling with a rotating field and isotropic Heisenberg interaction, which describe NMR and can also be realized in quantum dots and cold atoms. Using a novel physical representation of the qubit basis states, we construct π/8 and Hadamard gates based on Berry and Aharonov-Anandan phases. For two interacting qubits in a rotating field, we find that it is always impossible to construct a two-qubit gate based on Berry phases, or based on Aharonov-Anandan phases when the gyromagnetic ratios of the two qubits are equal. In implementing a universal set of quantum gates, one may combine geometric π/8 and Hadamard gates and dynamical gate.
Recently, it has been proposed to perform quantum computation through the Berry phase (adiabatic cyclic geometric phase) shift with NMR. This geometric quantum gate will hopefully be fault tolerant to certain types of error because of the geometric property of the Berry phase. Here we give a scheme to realize the NMR C-NOT gate through the Aharonov-Anandan phase (non-adiabatic cyclic phase) shift on the dynamic phase free evolution loop. In our scheme, the gate is run non-adiabatically, thus it is less affected by the decoherence. Moreover, in the scheme we have chosen the zero dynamic phase time evolution loop in obtaining the geometric phase shift; we need not perform any extra operation to cancel the dynamic phase.
Abstract Geometric quantum computation relies on the geometric phase that arises in adiabatic cyclic evolutions of non-degenerate quantum systems, enabling the design of robust quantum gates. However, the adiabatic condition requires long evolution times, making the system vulnerable to decoherence. In this work, we propose a scheme to realize fast and high-fidelity geometric quantum gates by applying the superadiabatic transitionless driving protocol within the dressed-state framework. We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field, focusing in particular on the nitrogen-vacancy center in diamond. We show how the dynamical phase can be canceled to obtain purely geometric operations. The robustness of the gates is assessed under systematic errors and environmental decoherence, demonstrating high fidelity even in regimes with strong fluctuations. Finally, we extend the protocol to construct nontrivial two-qubit gates, highlighting its feasibility for scalable quantum information processing.
Because of using geometric phases, nonadiabatic geometric gates have robustness against control errors.On the other hand, decoherence still affects nonadiabatic geometric gates, which is a key factor in reducing their fidelities.In this paper, we show that based on the system Hamiltonian that realizes a nonadiabatic geometric gate, one may construct a system Hamiltonian by the use of which not only the geometric feature of the nonadiabatic geometric gate is preserved, but also the system's coherence is protected.As a result, a coherence-protected nonadiabatic geometric gate is realized with this system Hamiltonian, and this gate has robustness against both control errors and decoherence.We further implement our scheme with nitrogen-vacancy centers and show that a universal set of coherence-protected nonadiabatic geometric gates can be realized.Our scheme does not need auxiliary systems or the encoding of logical qubits with physical qubits, which saves resources for the implementation.Due to the robustness against both control errors and decoherence, our scheme provides a promising way to realize high-fidelity quantum gates.
We introduce the nonadiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how this phase on one qubit can be monitored by a second qubit without any dynamical contribution. We also discuss how this geometric phase could be implemented with superconducting charge qubits. While the nonadiabatic geometric phase may circumvent many of the drawbacks related to the adiabatic (Berry) version of geometric gates, we show that the effect of fluctuations of the control parameters on nonadiabatic phase gates is more severe than for the standard dynamic gates. Similarly, fluctuations also affect to a greater extent quantum gates that use the Berry phase instead of the dynamic phase.
We investigate how to obtain a non-trivial geometric phase gate for a two-qubit spin chain, with Ising interaction in different magnetic fields. Indeed, one of the spins is driven by a time-varying rotating magnetic field, and the other is coupled with a static magnetic field in the direction of the rotation axis. This is an interesting problem both for the purpose of measuring the geometric phases and in quantum computing applications. It is shown that the static magnetic field does not change the adiabatic states of the system, and it does not affect the geometric phases, whereas it may be used to control the dynamic phases. In addition, by considering the exact two-spin adiabatic geometric phases, we find that a non-trivial two-spin unitary transformation, purely based on Berry phases, can be obtained by using two consecutive cycles with opposite directions of the magnetic fields, opposite signs of the interaction constant and the phase shift of the rotating magnetic field. In addition, in the non-adiabatic case, starting with a certain initial state, a cycle can be achieved and thus the Aharonov–Anandan phase is calculated.