Interaction cost of non-local gates

Abstract

We introduce the interaction cost of a non-local gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and quantum information, depends on the specific interaction, and allows to compare in an operationally meaningful manner any two non-local gates. In the case of a two-qubit system, an analytical expression for the interaction cost of any unitary operation given any coupling Hamiltonian is obtained. One gate may be more time-consuming than another for any possible interaction. This defines a partial order structure in the set of non-local gates, that compares their degree of non-locality. We analytically characterize this partial order in a region of the set of two-qubit gates.

revtex, 4 pages, no pictures, typos corrected, small changes in nomenclature

Cited by in corpus (57)

• Training Schrödinger's cat: quantum optimal control
• A universal quantum circuit for two-qubit transformations with three CNOT gates
• Natural two-qubit gate for quantum computation using the XY interaction
• Quantum Computing with NMR
• Entanglement as a signature of quantum chaos
• Quantum dynamics as a physical resource
• Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
• Time Optimal Unitary Operations
• Characterization of non-local gates
• Speed limits for quantum gates in multi-qubit systems
• Optimal Entanglement Generation from Quantum Operations
• Entangling power and operator entanglement in qudit systems
• Entanglement of superconducting qubits via microwave fields: classical and quantum regimes
• Applications of coherent classical communication and the Schur transform to quantum information theory
• Entanglement generation and Hamiltonian simulation in Continuous-Variable Systems
• Optimizing for an arbitrary perfect entangler: I. Functionals
• Local Distinguishability of Multipartite Unitary Operations
• Entanglement flow in multipartite systems
• Skyrmion Qubits: Challenges For Future Quantum Computing Applications
• Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions
• Circuit Transformations for Quantum Architectures
• Quantum Brachistochrone for Mixed States
• Programmable networks for quantum algorithms
• Conditions for optimal construction of two-qubit non-local gates
• Symmetry criteria for quantum simulability of effective interactions
• Lower bounds on the complexity of simulating quantum gates
• Elliptic functions and efficient control of Ising spin chains with unequal couplings
• Entanglement capability of self-inverse Hamiltonian evolution
• Matrix realignment and partial transpose approach to entangling power of quantum evolutions
• Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
• Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
• Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer
• Gate simulation and lower bounds on the simulation time
• Unitary Gate Synthesis for Continuous Variable Systems
• Advantages and limitations of quantum routing
• Quantum Control via Geometry: An explicit example
• Mean of continuous variables observable {\it via} measurement on single qubit
• Reversible simulation of bipartite product Hamiltonians
• Implementing two-qubit gates at the quantum speed limit
• Simulating Hamiltonian dynamics using many-qudit Hamiltonians and local unitary control
• Quantum brachistochrone problem for two spins-1/2 with anisotropic Heisenberg interaction
• Quantum routing with fast reversals
• Extended quantum Maxwell demon acting over macroscopic distances
• Continuous-variable quantum non-demolishing interaction at a distance
• Time-optimal polarization transfer from an electron spin to a nuclear spin
• Compensating for non-linear distortions in controlled quantum systems
• Fast protocols for local implementation of bipartite nonlocal unitaries
• On the practicality of time-optimal two-qubit Hamiltonian simulation
• A general formulation of time-optimal quantum control and optimality of singular protocols
• Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach
• Nearly optimal time-independent reversal of a spin chain
• Entanglement Distribution and Entangling Power of Quantum Gates
• Quantum Speed Limits from Symmetries in Quantum Control
• Entanglement magnification induced by local manipulations
• Optimal generation of entanglement under local control
• Hierarchies among genuine multipartite entangling capabilities of quantum gates
• Imperfect Entangling Power of Quantum Gates