Controlled-NOT gate with weakly coupled qubits: Dependence of fidelity on the form of interaction

Abstract

An approach to the construction of the CNOT quantum logic gate for a 4-dimensional coupled-qubit model with weak but otherwise arbitrary coupling has been given recently [M. R. Geller et al., Phys. Rev. A, 012320 (2010)]. How does the resulting fidelity depend on the form of qubit-qubit coupling? In this paper we calculate intrinsic fidelity curves (fidelity in the absence of decoherence versus total gate time) for a variety of qubit-qubit interactions, including the commonly occurring isotropic Heisenberg and XY models, as well as randomly generated ones. For interactions not too close to that of the Ising model, we find that the fidelity curves do not significantly depend on the form of the interaction, and we calculate the resulting interaction-averaged fidelity curve for the non-Ising-like cases and a criterion for determining its applicability.

6 pages, 5 figures, Accepted for publication in Phys. Rev. A

References in corpus (12)

• Decoherence, einselection, and the quantum origins of the classical
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• A geometric theory of non-local two-qubit operations
• Fidelity of quantum operations
• Realization of a photonic CNOT gate sufficient for quantum computation
• Robust CNOT gates from almost any interaction
• Purity and State Fidelity of Quantum Channels via Hamiltonians
• Quantum logic with weakly coupled qubits
• The distribution of quantum fidelities
• Generation of high-fidelity controlled-not logic gates by coupled superconducting qubits
• Controlled-NOT logic with nonresonant Josephson phase qubits
• Single-step controlled-NOT logic from any exchange interaction

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• Local quantum control of Heisenberg spin chains
• Quantum-control approach to realizing a Toffoli gate in circuit QED
• Robust single-qubit gates by composite pulses in three-level systems
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Pulse sequences for suppressing leakage in single-qubit gate operations
• High-Fidelity Entangling Gates for Quantum-Dot Hybrid Qubits Based on Exchange Interactions
• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Validity of resonant two-qubit gates in the ultrastrong coupling regime of circuit QED
• Fidelity of optically induced single-spin rotations in semiconductor quantum dots in the presence of nuclear spins
• Controlled-NOT logic gate for phase qubits based on conditional spectroscopy
• Role of hyperfine interaction for cavity-mediated coupling between spin qubits