Single-step controlled-NOT logic from any exchange interaction
arXiv:0705.1784 · doi:10.1063/1.2806489
Abstract
A self-contained approach to studying the unitary evolution of coupled qubits is introduced, capable of addressing a variety of physical systems described by exchange Hamiltonians containing Rabi terms. The method automatically determines both the Weyl chamber steering trajectory and the accompanying local rotations. Particular attention is paid to the case of anisotropic exchange with tracking controls, which is solved analytically. It is shown that, if computational subspace is well isolated, any exchange interaction can always generate high-fidelity, single-step controlled-NOT (CNOT) logic, provided that both qubits can be individually manipulated. The results are then applied to superconducting qubit architectures, for which several CNOT gate implementations are identified. The paper concludes with consideration of two CNOT gate designs having high efficiency and operating with no significant leakage to higher-lying non-computational states.
12 pages + 7 figures; revised version; title changed
References in corpus (28)
- Time Optimal Control in Spin Systems
- A geometric theory of non-local two-qubit operations
- Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
- Complete controllability of quantum systems
- Spectroscopy on two coupled flux qubits
- Quantum logic gates for coupled superconducting phase qubits
- Tunable coupling of superconducting qubits
- Controllable coupling between flux qubits
- Time Optimal Unitary Operations
- Protocol for universal gates in optimally biased superconducting qubits
- Diffraction limited optics for single atom manipulation
- Entangling flux qubits with a bipolar dynamic inductance
- Time-optimal control of a two-level dissipative quantum system
- Complete controllability of finite-level quantum systems
- Fast two-bit operations in inductively coupled flux qubits
- Superconducting Phase Qubit Coupled to a Nanomechanical Resonator: Beyond the Rotating-Wave Approximation
- Universal Leakage Elimination
- Robust CNOT gates from almost any interaction
- Spectroscopy of capacitively coupled Josephson-junction qubits
- Optimized design of universal two-qubit gates
- Generation of quantum logic operations from physical Hamiltonians
- Theory of measurement crosstalk in superconducting phase qubits
- Two-level quantum dynamics, integrability and unitary NOT gates
- Hamiltonian for coupled flux qubits
- Non-holonomic Quantum Devices
- Mesoscopic entanglement of atomic ensembles through non-resonant stimulated Raman scattering
- A unified approach to realize universal quantum gates in a coupled two-qubit system with fixed always-on coupling
- Tunneling out of metastable vacuum in a system consisting of two capacitively coupled phase qubits
Cited by in corpus (5)
- Maximally entangling tripartite protocols for Josephson phase qubits
- Quantum logic with weakly coupled qubits
- Controlled-NOT gate with weakly coupled qubits: Dependence of fidelity on the form of interaction
- Controlled-NOT logic with nonresonant Josephson phase qubits
- Controlled-NOT logic gate for phase qubits based on conditional spectroscopy