Optimal Creation of Entanglement Using a Two--Qubit Gate

Abstract

We consider a general unitary operator acting on two qubits in a product state. We find the conditions such that the state of the qubits after the action is as entangled as possible. We also consider the possibility of using ancilla qubits to increase the entanglement.

9 pages, 1 figure

References in corpus (3)

• On the Entangling Power of Quantum Evolutions
• Limits for entanglement measures
• Entangling operations and their implementation using a small amount of entanglement

Cited by in corpus (293)

• Validating quantum computers using randomized model circuits
• Tachyon Dynamics in Open String Theory
• Quantum autoencoders for efficient compression of quantum data
• Optimal Quantum Circuits for General Two-Qubit Gates
• A geometric theory of non-local two-qubit operations
• Environment Induced Entanglement in Markovian Dissipative Dynamics
• Quantum Correlations in Systems of Indistinguishable Particles
• Quantum coherence in multipartite systems
• Thermalizing Quantum Machines: Dissipation and Entanglement
• A practical scheme for quantum computation with any two-qubit entangling gate
• A universal quantum circuit for two-qubit transformations with three CNOT gates
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Simulating quantum many-body dynamics on a current digital quantum computer
• Exact dynamics in dual-unitary quantum circuits
• Entanglement as a signature of quantum chaos
• Phonon decoherence of quantum entanglement: Robust and fragile states
• Quantum dynamics as a physical resource
• Open Quantum Dynamics: Complete Positivity and Entanglement
• Realisation of a programmable two-qubit quantum processor
• The entanglement membrane in chaotic many-body systems
• Single-photon logic gates using minimal resources
• Collision model for non-Markovian quantum dynamics
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Entangling oscillators through environment noise
• Maximum velocity quantum circuits
• Standard forms of noisy quantum operations via depolarization
• Topological Quantum Compiling with Reinforcement Learning
• Characterization of non-local gates
• Characterization of two-qubit perfect entanglers
• Interaction cost of non-local gates
• Optimal Entanglement Generation from Quantum Operations
• Quantum entanglement of unitary operators on bi-partite systems
• Entangling power and operator entanglement in qudit systems
• Local unitary equivalence and entanglement of multipartite pure states
• From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy
• Universal Quantum Computation through Control of Spin-Orbit Coupling
• Five Two-Qubit Gates Are Necessary for Implementing Toffoli Gate
• Ancilla-Driven Universal Quantum Computation
• Deterministic generation of large-scale entangled photonic cluster state from interacting solid state emitters
• Optimal conversion of non--local unitary operations
• Applications of coherent classical communication and the Schur transform to quantum information theory
• Minimum construction of two-qubit quantum operations
• Exact two-qubit universal quantum circuit
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Localization with random time-periodic quantum circuits
• Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula
• Entanglement generation and Hamiltonian simulation in Continuous-Variable Systems
• The Quantum Speed Limit of Optimal Controlled Phasegates for Trapped Neutral Atoms
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
• Symmetry from Entanglement Suppression
• Unitary quantum gates, perfect entanglers and unistochastic maps
• Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays
• Local Distinguishability of Multipartite Unitary Operations
• Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings
• Time Optimal Control of Coupled Qubits Under Non-Stationary Interactions
• Overhead for simulating a non-local channel with local channels by quasiprobability sampling
• Optimal two-qubit quantum circuits using exchange interactions
• Optimal dynamical control of many-body entanglement
• Optimal quantum circuit synthesis from Controlled-U gates
• Entangling power and local invariants of two-qubit gates
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Extreme dimensionality reduction with quantum modelling
• Long-lived spin entanglement induced by a spatially correlated thermal bath
• Restricted numerical range: a versatile tool in the theory of quantum information
• Stabilizing multiple topological fermions on a quantum computer
• Entanglement Cost of Nonlocal Measurements
• The entangling and disentangling power of unitary transformations are unequal
• Canonical Decompositions of n-qubit Quantum Computations and Concurrence
• Conditions for optimal construction of two-qubit non-local gates
• Compressed quantum computation using the IBM Quantum Experience
• Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
• Hybrid Optimization Schemes for Quantum Control
• Optimal two-qubit gate for generation of random bipartite entanglement
• Weak measurement and control of entanglement generation
• On the efficiency of nonlocal gates generation
• Witness of mixed separable states useful for entanglement creation
• Lower bounds on the complexity of simulating quantum gates
• Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
• Optimal compression of quantum many-body time evolution operators into brickwall circuits
• The maximally entangled set of 4-qubit states
• D-Branes, Tachyons and K-Homology
• Extending matchgates into universal quantum computation
• Entanglement cost of implementing controlled-unitary operations
• Entanglement capability of self-inverse Hamiltonian evolution
• Realization of a General Three-Qubit Quantum Gate
• Matrix realignment and partial transpose approach to entangling power of quantum evolutions
• Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control
• Quantum Channel Capacities with Passive Environment Assistance
• Catalysis in non--local quantum operations
• Quantum processing by remote quantum control
• Localized State in a Two-Dimensional Quantum Walk on a Disordered Lattice
• Classical capacities of quantum channels with environment assistance
• Quantum Optimal Control via Semi-Automatic Differentiation
• A constructive algorithm for the Cartan decomposition of SU(2^N)
• Entangling capacity and distinguishability of two-qubit unitary operators
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Probabilistically implementing nonlocal operation using non-maximally entangled state
• Smooth optimal control with Floquet theory
• Dynamically Correcting a CNOT Gate for any Systematic Logical Error
• Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer
• Unitary transformations can be identified locally
• Discording power of quantum evolutions
• Designing calibration and expressivity-efficient instruction sets for quantum computing
• Deterministic teleportation of electrons in a quantum dot nanostructure
• Gate simulation and lower bounds on the simulation time
• Complete set of operational measures for the characterization of 3-qubit entanglement
• Two-step phantom relaxation of out-of-time-ordered correlations in random circuits
• Entanglement consumption of instantaneous nonlocal quantum measurements
• Quantum channel detection
• Circuits of space and time quantum channels
• Fixed-Depth Two-Qubit Circuits and the Monodromy Polytope
• Quantum logic with weakly coupled qubits
• Directly accessible entangling gates for capacitively coupled singlet-triplet qubits
• Relation between classical communication capacity and entanglement capability for two-qubit unitary operations
• Certainty relations, mutual entanglement and non-displacable manifolds
• Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates
• Channel kets, entangled states, and the location of quantum information
• Entanglement changing power of two-qubit unitary operations
• Numerical analysis of quantum circuits for state preparation and unitary operator synthesis
• Bipartite unitary gates and billiard dynamics in the Weyl chamber
• Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments
• Network coding for distributed quantum computation over cluster and butterfly networks
• Local Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations Acting on Two-Qudits by LOCC
• Pauli semigroups and unistochastic quantum channels
• Characterizing the geometrical edges of nonlocal two-qubit gates
• Quantum computation over the butterfly network
• Entangling characterization of (SWAP)1/m and Controlled unitary gates
• Efficient Implementation of Controlled-Rotations by Using Entanglement
• Here comes the SU(N): multivariate quantum gates and gradients
• Noncompletely Positive Quantum Maps Enable Efficient Local Energy Extraction in Batteries
• Implementing two-qubit gates at the quantum speed limit
• Three-fold way of entanglement dynamics in monitored quantum circuits
• Computational power of matchgates with supplementary resources
• Quantum circuit synthesis using Householder transformations
• Dynamics of entanglement in qubit-qutrit with x component of DM interaction
• Remote entanglement preparation
• Quantum-classical eigensolver using multiscale entanglement renormalization
• Simulating a single qubit channel using a mixed state environment
• Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2
• Exact CNOT Gates with a Single Nonlocal Rotation for Quantum-Dot Qubits
• Quantifying Spatial Correlations of General Quantum Dynamics
• Optimal synthesis into fixed XX interactions
• Quantum simulations of molecular systems with intrinsic atomic orbitals
• Discrimination of two-qubit unitaries via local operations and classical communication
• Fractionalized Prethermalization in a Driven Quantum Spin Liquid
• Formation of Multipartite Entanglement Using Random Quantum Gates
• Time Reversal and n-qubit Canonical Decompositions
• Entanglement Transitions in Unitary Circuit Games
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• 2QAN: A quantum compiler for 2-local qubit Hamiltonian simulation algorithms
• Towards Large-Scale Quantum Computation
• Bounds on Instantaneous Nonlocal Quantum Computation
• Hamiltonian Simulation of Quantum Beats in Radical Pairs Undergoing Thermal Relaxation on Near-term Quantum Computers
• Measures of operator entanglement of two-qubit gates
• Tailoring many-body entanglement through local control
• The canonical Naimark extension for the Pauli quantum roulette wheel
• Quantum entangling power of adiabatically connected hamiltonians
• Entangling power of two-qubit gates on mixed states
• Mediated gates between spin qubits
• Conditional entropy production and quantum fluctuation theorem of dissipative information: Theory and experiments
• A Toffoli Gate Decomposition via Echoed Cross-Resonance Gates
• Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction
• Control aspects of holonomic quantum computation
• Efficient quantum computation within a disordered Heisenberg spin-chain
• Bipartite quantum measurements with optimal single-sided distinguishability
• Optimal Entangling Capacity of Dynamical Processes
• Automatic quantum circuit encoding of a given arbitrary quantum state
• Tensor Network Methods for Invariant Theory
• Exactly solvable many-body dynamics from space-time duality
• The source and accessible entanglement of few-body systems
• On the distribution of entanglement changes produced by unitary operations
• Experimental Validation of Enhanced Information Capacity by Quantum Switch in Accordance with Thermodynamic Laws
• Capability of local operations and classical communication for distinguishing bipartite unitary operations
• Hybrid quantum learning with data re-uploading on a small-scale superconducting quantum simulator
• Relations for classical communication capacity and entanglement capability of two-qubit operations
• Fast protocols for local implementation of bipartite nonlocal unitaries
• Maximally entangled mixed states for a fixed spectrum do not always exist
• Diagonal unitary and orthogonal symmetries in quantum theory II: Evolution operators
• Quantum circuit synthesis via a random combinatorial search
• Identifying Flakiness in Quantum Programs
• Strongly coupled quantum Otto cycle with single qubit bath
• Quantum Causal Inference with Extremely Light Touch
• Optimal realization of Yang-Baxter gate on quantum computers
• Programmable quantum channels and measurements
• Delocalization power of global unitary operations on quantum information
• On the practicality of time-optimal two-qubit Hamiltonian simulation
• A simple representation of quantum process tomography
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Variational Quantum Support Vector Machine based on $\Gamma$ matrix expansion and Variational Universal-Quantum-State Generator
• Broadcasting of quantum correlations in qubit-qudit systems
• Dissipative Quantum Dynamics and Optimal Control using Iterative Time Ordering: An Application to Superconducting Qubits
• Bell-CHSH Violation Under Global Unitary Operations: Necessary and Sufficient conditions
• Optimal Simulation of a Perfect Entangler
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Two-party LOCC convertibility of quadpartite states and Kraus-Cirac number of two-qubit unitaries
• Restrictions on the Schmidt rank of bipartite unitary operators beyond dimension two
• Dual unitaries as maximizers of the distance to local product gates
• Localization and integrability breaking in weakly interacting Floquet circuits
• Quantum-phase synchronization
• Quantum Resource Control for noisy EPR-steering with qubit measurements
• Entangling power of two-qubit unitary operations
• All maximally entangling unitary gates
• QContext: Context-Aware Decomposition for Quantum Gates
• Classification of joint quantum measurements based on entanglement cost of localization
• Construction of perfect tensors using biunimodular vectors
• Adversarial vs cooperative quantum estimation
• Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach
• Process estimation in presence of time-invariant memory effects
• Riemannian quantum circuit optimization based on matrix product operators
• Optimal transfer of an unknown state via a bipartite operation
• Amplitude Damping for single-qubit System with single-qubit mixed-state Environment
• Matrix-product unitaries: Beyond quantum cellular automata
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Experimental implementation of arbitrary entangled operations
• Resource Theory of Non-absolute Separability
• Entanglement Distribution and Entangling Power of Quantum Gates
• Quantum Process Tomography of Unitary Maps from Time-Delayed Measurements
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Lower bounds for communication capacities of two-qudit unitary operations
• Matchgate quantum computing and non-local process analysis
• Characterization of Nonlocal Resources Under Global Unitary Action
• Numerical Analysis of the Capacities for Two-Qubit Unitary Operations
• Entangling power, gate typicality, and measurement-induced phase transitions
• Testing quantum computers with the protocol of quantum state matching
• Noise effects and tomography of remote entangled spins in quantum dots
• Estimation of two-qubit interactions through channels with environment assistance
• Efficient generation of random multipartite entangled states using time optimal unitary operations
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• The statistics of the entanglement changes generated by the Hadamard-CNOT quantum circuit
• Universal quantum circuit for n-qubit quantum gate: A programmable quantum gate
• Correlation between resource-generating capacities of quantum gates
• Sinkhorn-Knopp Theorem for PPT states
• Tristochastic operations and convolutions of quantum states
• Local Gradient Optimization of Modular Entangling Sequences
• Geometric representations of braid and Yang-Baxter gates
• Entanglement and Irreversibility in the Approach to Thermal Equilibrium
• Noise Effects on Entanglement Distribution by Separable State
• Capturing the Page Curve and Entanglement Dynamics of Black Holes in Quantum Computers
• Classification of Schmidt-rank-two multipartite unitary gates by singular number
• Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Images
• Polyadic braid operators and higher braiding gates
• Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach
• Time optimal control in coupled spin systems: a second order analysis
• Extracting the spin excitation spectrum of a fermionic system using a quantum processor
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• Stroboscopically Robust Gates For Capacitively Coupled Singlet-Triplet Qubits
• Single-Copy Certification of Two-Qubit Gates without Entanglement
• Characteristics, Implementation and Applications of Special Perfect Entangler Circuits
• Local gradient optimization of leakage-suppressing entangling sequences
• Distributed implementation of standard oracle operators
• Entanglement magnification induced by local manipulations
• Coassociative grammar, periodic orbits and quantum random walk over Z
• Non-locality of conjugation symmetry: characterization and examples in quantum network sensing
• Entangling power of symmetric multiqubit systems: a geometrical approach
• Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm
• Three-Qubit State Preparation: Classification and Explicit Circuits
• Achieving fast and robust perfect entangling gates via reinforcement learning
• On the most efficient unitary transformation for programming quantum channels
• Symmetrization and Entanglement of Arbitrary States of Qubits
• Numerical search for universal entanglers in C3xC4 and C4xC4
• Variational-toolbox-based separability detection of multiqubit states
• Optimal generation of entanglement under local control
• Breaking absolute separability with quantum switch
• Quantifying electron-nuclear spin entanglement dynamics in central-spin systems using one-tangles
• Nonexistence of maximally entangled mixed states for a fixed spectrum
• Nonlocal characteristics and argand diagram of two-qubit gates
• Detection of nonabsolute separability in quantum states and channels through moments
• Hierarchies among genuine multipartite entangling capabilities of quantum gates
• Entanglement structure for finite system under dual-unitary dynamics
• Quantum correlations in composite systems under global unitary operations
• Robust entanglement buffers based on SWAP interactions
• Quantum teleportation and Birman-Murakami-Wenzl algebra
• Achievability of two qubit gates using linear optical elements and post-selection
• A triality pattern in entanglement theory
• Software mitigation of coherent two-qubit gate errors
• More global randomness from less-random local gates
• Comparing globalness of bipartite unitary operations: delocalization power, entanglement cost, and entangling power
• Distributed Quantum Dense Coding Enhanced With Non-classical Routing
• Entangling capabilities of Symmetric two qubit gates
• Topological Tenfold Classification and the Entanglement of Two Qubits
• Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations
• Quantum reading of quantum information
• The Computational Power of Non-interacting Particles
• Quantum Finite-Depth Memory Channels: Case Study
• Universal Optimal Gates Regarding Quantum Entanglement and Discord Generating
• Imperfect Entangling Power of Quantum Gates
• How much is a quantum controller controlled by the controlled system?
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Operator-Schmidt decomposition and the geometrical edges of two-qubit gates
• Benchmarking quantum devices beyond classical capabilities