Scalable Experimental Bounds for Entangled Quantum State Fidelities

Abstract

Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is important for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as $O(3^N)$ for $N$-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma and others [PhysRevA.74.052302] established that the complexity could be drastically reduced when looking at fidelity lower bounds for states that exhibit symmetries, such as Dicke States and GHZ States. These bounds must still be tight enough for larger states to provide reasonable estimations on NISQ devices. For the first time and more than 15 years after the theoretical introduction, we report meaningful lower bounds for the state preparation fidelity of all Dicke States up to $N=10$ and all GHZ states up to $N=20$ on Quantinuum H1 ion-trap systems using efficient implementations of recently proposed scalable circuits for these states. Our achieved lower bounds match or exceed previously reported exact fidelities on superconducting systems for much smaller states. Furthermore, we provide evidence that for large Dicke States $D_{N/2}^N$, we may resort to a GHZ-based approximate state preparation to achieve better fidelity. This work provides a path forward to benchmarking entanglement as NISQ devices improve in size and quality.

References in corpus (26)

• On the Measurement of Qubits
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Direct Fidelity Estimation from Few Pauli Measurements
• The randomized measurement toolbox
• Resource-Aware Quantum Programming with General Recursion and Quantum Control
• Maximum Likelihood, Minimum Effort
• Reliable Quantum State Tomography
• Toolbox for entanglement detection and fidelity estimation
• Optimal verification of entangled states with local measurements
• Efficient quantum algorithms for $GHZ$ and $W$ states, and implementation on the IBM quantum computer
• Deterministic Preparation of Dicke States
• Experimental Estimation of Quantum State Properties from Classical Shadows
• General framework for verifying pure quantum states in the adversarial scenario
• Efficient Verification of Hypergraph States
• Statistical Methods for Quantum State Verification and Fidelity Estimation
• Optimal verification and fidelity estimation of maximally entangled states
• Optimal Verification of Two-Qubit Pure States
• Efficient verification of bipartite pure states
• Optimal verification of general bipartite pure states
• Efficient verification of Dicke states
• Experimental Optimal Verification of Entangled States using Local Measurements
• A Divide-and-Conquer Approach to Dicke State Preparation
• Direct Fidelity Estimation of Quantum States using Machine Learning
• Optimal Verification of Greenberger-Horne-Zeilinger States
• Towards the standardization of quantum state verification using optimal strategies
• Lower bounds for the fidelity of entangled state preparation