Generation of quantum logic operations from physical Hamiltonians

Abstract

We provide a systematic analysis of the physical generation of single- and two-qubit quantum operations from Hamiltonians available in various quantum systems for scalable quantum information processing. We show that generation of one-qubit operations can be transformed into a steering problem on the Bloch sphere, whereas the two-qubit problem can be generally transformed into a steering problem in a tetrahedron representing all the local equivalence classes of two-qubit operations (the Weyl chamber). We use this approach to investigate several physical examples for the generation of two-qubit operations. The steering approach provides useful guidance for the realization of various quantum computation schemes.

17 pages, 8 figures

References in corpus (34)

• Quantum Computation with Quantum Dots
• Elementary gates for quantum computation
• Coupled quantum dots as quantum gates
• NMR Techniques for Quantum Control and Computation
• Two-Bit Gates are Universal for Quantum Computation
• Universal Quantum Computation with the Exchange Interaction
• Electron Spin Resonance Transistors for Quantum Computing in Silicon-Germanium Heterostructures
• Time Optimal Control in Spin Systems
• Josephson-Junction Qubits with Controlled Couplings
• A geometric theory of non-local two-qubit operations
• Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
• Universal Control of Decoupled Quantum Systems
• Robust dynamical decoupling with bounded controls
• Design and proof of concept for silicon-based quantum dot quantum bits
• Practical design and simulation of silicon-based quantum dot qubits
• Natural two-qubit gate for quantum computation using the XY interaction
• Scalable quantum computing with Josephson charge qubits
• Hydrogenic Spin Quantum Computing in Silicon: A Digital Approach
• Quantum Computation in Quantum-Hall Systems
• Creating Decoherence-Free Subspaces with Strong and Fast Pulses
• Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
• Quantum cellular automata quantum computing with endohedral fullerenes
• Optimal simulation of two-qubit Hamiltonians using general local operations
• Physical Optimization of Quantum Error Correction Circuits
• Quantum Information Processing with Ferroelectrically Coupled Quantum Dots
• Gate control of spin dynamics in III-V semiconductor quantum dots
• Entangling flux qubits with a bipolar dynamic inductance
• Combined encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing
• Characterization of non-local gates
• On Quantum Control via Encoded Dynamical Decoupling
• Minimum construction of two-qubit quantum operations
• Optimal quantum circuit synthesis from Controlled-U gates
• Optimal multiqubit operations for Josephson charge qubits
• Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer

Cited by in corpus (15)

• Quantum-control approach to realizing a Toffoli gate in circuit QED
• Scheme for direct measurement of a general two-qubit Hamiltonian
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Generation of high-fidelity controlled-not logic gates by coupled superconducting qubits
• Quantum logic with weakly coupled qubits
• Directly accessible entangling gates for capacitively coupled singlet-triplet qubits
• Precision characterisation of two-qubit Hamiltonians via entanglement mapping
• Constrained optimization of sequentially generated entangled multiqubit states
• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Simplified Approach to Implementing Controlled-Unitary Operations in a Two-Qubit System
• Fast macroscopic-superposition-state generation by coherent driving
• Single-step controlled-NOT logic from any exchange interaction
• Entanglement dynamics of two Ising-coupled qubits with nonperpendicular local driving fields
• Improving quantum gate fidelities using optimized Euler angles
• Optimal generation of single-qubit operation from an always-on interaction by algebraic decoupling