Efficient quantum algorithms for $GHZ$ and $W$ states, and implementation on the IBM quantum computer

Abstract

We propose efficient algorithms with logarithmic step complexities for the generation of entangled $GH{Z}_N$ and $W_N$ states useful for quantum networks, and we demonstrate an implementation on the IBM quantum computer up to $N=16$. Improved quality is then investigated using full quantum tomography for low-$N$ GHZ and W states. This is completed by parity oscillations and histogram distance for large $N$ GHZ and W states respectively. We are capable to robustly build states with about twice the number of quantum bits which were previously achieved. Finally we attempt quantum error correction on GHZ using recent schemes proposed in the literature, but with the present amount of decoherence they prove detrimental.

References in corpus (16)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• 14-qubit entanglement: creation and coherence
• Large-scale silicon quantum photonics implementing arbitrary two-qubit processing
• A blueprint for demonstrating quantum supremacy with superconducting qubits
• The General Quantum Interference Principle and the Duality Computer
• Adding control to arbitrary unknown quantum operations
• Efficient Scheme for Initializing a Quantum Register with an Arbitrary Superposed State
• Scalable in-situ qubit calibration during repetitive error detection
• A Case for Variability-Aware Policies for NISQ-Era Quantum Computers
• Deterministic Local Expansion of W States
• Automated Error Correction in IBM Quantum Computer and Explicit Generalization
• Photonic multipartite entanglement conversion using nonlocal operations
• Decoherence of up to 8-qubit entangled states in a 16-qubit superconducting quantum processor
• A brief introduction to multipartite entanglement
• Multipartite entanglement

Cited by in corpus (69)

• A Race Track Trapped-Ion Quantum Processor
• Noise Resilience of Variational Quantum Compiling
• Variational Quantum State Eigensolver
• Verifying Multipartite Entangled GHZ States via Multiple Quantum Coherences
• Machine learning of noise-resilient quantum circuits
• Speed limits and locality in many-body quantum dynamics
• Efficient encoding of the weighted MAX k-CUT on a quantum computer using QAOA
• The Quantum Alternating Operator Ansatz on Maximum k-Vertex Cover
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
• Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
• Tripartite entanglement: Foundations and applications
• A Divide-and-Conquer Approach to Dicke State Preparation
• Solving hadron structures using the basis light-front quantization approach on quantum computers
• Short-Depth Circuits for Dicke State Preparation
• Optimal Verification of Greenberger-Horne-Zeilinger States
• Comparative study of variations in quantum approximate optimization algorithms for the Traveling Salesman Problem
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Algebraic Bethe Circuits
• Preparation of an Exciton Condensate of Photons on a 53-Qubit Quantum Computer
• Modeling Noisy Quantum Circuits Using Experimental Characterization
• Verification of phased Dicke states
• High-fidelity interconversion between Greenberger-Horne-Zeilinger and $W$ states through Floquet-Lindblad engineering in Rydberg atom arrays
• Deterministic preparation of W states via spin-photon interactions
• Efficiently improving the performance of noisy quantum computers
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Pairwise tomography networks for many-body quantum systems
• Classification of four-qubit entangled states via Machine Learning
• A Tool For Debugging Quantum Circuits
• Optimal protocols for quantum metrology with noisy measurements
• Entanglement and scattering in quantum electrodynamics: S-matrix information from an entangled spectator particle
• Finding Small and Large k-Clique Instances on a Quantum Computer
• Experimental sample-efficient quantum state tomography via parallel measurements
• Benchmarking near-term quantum devices with the Variational Quantum Eigensolver and the Lipkin-Meshkov-Glick model
• Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance
• Quantum secret aggregation utilizing a network of agents
• A Multiparty Quantum Private Equality Comparison scheme relying on $|GH{Z}_3⟩$ states
• Experimental validation of the Kibble-Zurek Mechanism on a Digital Quantum Computer
• Graph state representation of the toric code
• Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D
• An entanglement-based protocol for simultaneous reciprocal information exchange between 2 players
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Efficient preparation of entangled states in cavity QED with Grover's algorithm
• Efficient factored gradient descent algorithm for quantum state tomography
• Symmetric quantum states: a review of recent progress
• On Actual Preparation of Dicke State on a Quantum Computer
• Reconstructing Thermal Quantum Quench Dynamics from Pure States
• One-to-Many Simultaneous Secure Quantum Information Transmission
• Generating multipartite nonlocality to benchmark quantum computers
• Quantum State Preparation Using an Exact CNOT Synthesis Formulation
• A Quantum Approach to News Verification from the Perspective of a News Aggregator
• A distributed and parallel $(k,n)$ QSS scheme with verification capability
• A novel $2$ \& $3$ player scheme for Quantum Direct Communication
• Quantum Shadows: The Dining Information Brokers
• Spreading entanglement through pairwise exchange interactions
• Efficient Sparse State Preparation via Quantum Walks
• Deterministic carving of quantum states with Grover's algorithm
• Quantum advantage in temporally flat measurement-based quantum computation
• Characteristics, Implementation and Applications of Special Perfect Entangler Circuits
• IF-QAOA: A Penalty-Free Approach to Accelerating Constrained Quantum Optimization
• Scalable Experimental Bounds for Entangled Quantum State Fidelities
• Spectral stabilizability
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• A Novel Scalable Quantum Protocol for the Dining Cryptographers Problem
• Delocalized Excitation Transfer in Open Quantum Systems with Long-Range Interactions
• Enhanced Compressive Threshold Quantum State Tomography for Qudit Systems
• Multipartite Entanglement Distribution in Quantum Networks using Subgraph Complementations
• Efficient QAOA Architecture for Solving Multi-Constrained Optimization Problems
• Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers
• Ptychographic estimation of pure multiqubit states in a quantum device