Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0606023 · Physical Review A

Lower bounds for the fidelity of entangled-state preparation

Rolando D. Somma, John Chiaverini, Dana J. Berkeland

Published Nov 1, 2006• 21 citations
arXivHTMLPDF

Abstract

Estimating the fidelity of state preparation in multiqubit systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the corresponding experimental setup. In this paper we give simple expressions to estimate the fidelity of multiqubit state preparation for rotational-invariant, stabilizer, and generalized coherent states. We specifically discuss the GHZ-type and W-type states, and obtain efficiently measurable lower bounds for the fidelity. We use these techniques to estimate the fidelity of a quantum simulation of an Ising-like interaction model using two trapped ions. These results are directly applicable to experiments using fidelity-based entanglement witnesses, such as quantum simulations and quantum computation.

DOI
10.1103/physreva.74.052302

Related papers

Scalable Experimental Bounds for Entangled Quantum State Fidelities

Shamminuj Aktar, Andreas Bärtschi, Abdel‐Hameed A. Badawy +1 more

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 et al.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 \(\left|\smash{D_{N/2}^{N}} \right\rangle\) , 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.

arXiv:2210.03048•ACM Transactions on Quantum Computing•Nov 11, 2024•1 citation

Scalable Experimental Bounds for Dicke and GHZ States Fidelities

Shamminuj Aktar, Abdel‐Hameed A. Badawy, Andreas Bärtschi +1 more

Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is an important task for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as O(3N) for N-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma et al. [20] 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. For larger states, these bounds still need to be tight enough to provide reasonable estimations on NISQ devices.

ACM International Conference on Computing Frontiers (CF)•May 9, 2023•3 citations

Versatile Fidelity Estimation with Confidence

Akshay Seshadri, Martin Ringbauer, Jacob Spainhour +3 more

As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge is quantifying how close an experimentally prepared quantum state is to the desired one. Here we present a method to construct an estimator for the quantum state fidelity that is compatible with any measurement protocol. Our method provides a confidence interval on this estimator that is guaranteed to be nearly minimax optimal for the specified measurement protocol. For a well-chosen measurement scheme, our method is competitive in the number of measurement outcomes required for estimation. We demonstrate our method using simulations and experimental data from a trapped-ion quantum computer and compare the results to state-of-the-art techniques. Our method can be easily extended to estimate the expectation value of any observable, such as entanglement witnesses.

arXiv:2112.07925•Physical Review Letters•Jul 10, 2024•8 citations

Directly estimating the fidelity of measurement-based quantum computation

David T. Stephen, Michael Foss-Feig

In measurement-based quantum computation (MBQC), quantum circuits are implemented using adaptive measurements on an entangled resource state. In practice, the resource state will always be prepared with some noise, and it is crucial to understand the effect of this noise on the operation of MBQC. Typically, one measures the fidelity of the noisy resource state with the assumption that a high fidelity state means a high fidelity computation. However, the precise relationship between these two fidelities is not known. Here, we derive an expression that equates the average fidelity of the MBQC output state to a certain correlation function evaluated on the noisy resource state. Using this expression, we show that state fidelity provides a tight lower bound on average MBQC fidelity. Conversely, we also find that state fidelity can greatly underestimate average MBQC fidelity, implying that state fidelity is not a good indicator of MBQC performance in general. In response, we formulate an efficient method to directly estimate average MBQC fidelity by measuring the aforementioned correlation function. These results therefore improve our ability to characterize noisy resource states in quantum computers and benchmark MBQC performance.

quant-pharXiv:2603.13753•Mar 17, 2026•0 citations

Practical and efficient experimental characterization of multiqubit stabilizer states

Chiara Greganti, Marie-Christine Roehsner, Stefanie Barz +2 more

Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and the purpose of their use. Here we present a method that scales linearly with the number of qubits for characterizing stabilizer states. Our approach allows simultaneous extraction of information about the fidelity, the entanglement, and the nonlocality of the state and thus is of high practical relevance. We demonstrate the efficient applicability of our method by performing an experimental characterization of a photonic four-qubit cluster state and three- and four-qubit Greenberger-Horne-Zeilinger states. Our scheme can be directly extended to larger-scale quantum information tasks.

arXiv:1502.06549•Physical Review A•Feb 20, 2015•9 citations

Compressed Sensing for Efficient Fidelity Estimation of GHZ States

Farrokh Labib, David Nicholaeff, Vincent Russo +1 more

Accurately characterizing multipartite entangled states is a critical challenge in quantum information processing. In this work, we focus on applying compressed sensing techniques to efficiently estimate the fidelity of Greenberger-Horne-Zeilinger (GHZ) states. By exploiting the inherent sparsity of these states, our compressed sensing protocol drastically reduces the measurement overhead traditionally required for state verification while maintaining high accuracy. To evaluate the practical performance of this approach, we test the protocol on GHZ states using both quantum simulators and Quantinuum's trapped-ion hardware. Furthermore, we implement error detection techniques during our hardware evaluations, demonstrating the robustness and viability of compressed sensing for fidelity estimation in noisy experimental environments.

quant-pharXiv:2604.27824•May 1, 2026•0 citations
Estimating the fidelity of state preparation in multiqubit systems is generally a time-consuming task. Nevertheless, this complexity can be reduced if the desired state can be characterized by certain symmetries measurable with the corresponding experimental setup. In this paper we give simple expressions to estimate the fidelity of multiqubit state preparation for rotational-invariant, stabilizer, and generalized coherent states. We specifically discuss the GHZ-type and W-type states, and obtain efficiently measurable lower bounds for the fidelity. We use these techniques to estimate the fidelity of a quantum simulation of an Ising-like interaction model using two trapped ions. These results are directly applicable to experiments using fidelity-based entanglement witnesses, such as quantum simulations and quantum computation.
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 et al.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 ∣DN/2N⟩\left|\smash{D_{N/2}^{N}} \right\rangle∣DN/2N​⟩ , 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.
Estimating the state preparation fidelity of highly entangled states on noisy intermediate-scale quantum (NISQ) devices is an important task for benchmarking and application considerations. Unfortunately, exact fidelity measurements quickly become prohibitively expensive, as they scale exponentially as O(3N) for N-qubit states, using full state tomography with measurements in all Pauli bases combinations. However, Somma et al. [20] 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. For larger states, these bounds still need to be tight enough to provide reasonable estimations on NISQ devices.
As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge is quantifying how close an experimentally prepared quantum state is to the desired one. Here we present a method to construct an estimator for the quantum state fidelity that is compatible with any measurement protocol. Our method provides a confidence interval on this estimator that is guaranteed to be nearly minimax optimal for the specified measurement protocol. For a well-chosen measurement scheme, our method is competitive in the number of measurement outcomes required for estimation. We demonstrate our method using simulations and experimental data from a trapped-ion quantum computer and compare the results to state-of-the-art techniques. Our method can be easily extended to estimate the expectation value of any observable, such as entanglement witnesses.
In measurement-based quantum computation (MBQC), quantum circuits are implemented using adaptive measurements on an entangled resource state. In practice, the resource state will always be prepared with some noise, and it is crucial to understand the effect of this noise on the operation of MBQC. Typically, one measures the fidelity of the noisy resource state with the assumption that a high fidelity state means a high fidelity computation. However, the precise relationship between these two fidelities is not known. Here, we derive an expression that equates the average fidelity of the MBQC output state to a certain correlation function evaluated on the noisy resource state. Using this expression, we show that state fidelity provides a tight lower bound on average MBQC fidelity. Conversely, we also find that state fidelity can greatly underestimate average MBQC fidelity, implying that state fidelity is not a good indicator of MBQC performance in general. In response, we formulate an efficient method to directly estimate average MBQC fidelity by measuring the aforementioned correlation function. These results therefore improve our ability to characterize noisy resource states in quantum computers and benchmark MBQC performance.
Vast developments in quantum technology have enabled the preparation of quantum states with more than a dozen entangled qubits. The full characterization of such systems demands distinct constructions depending on their specific type and the purpose of their use. Here we present a method that scales linearly with the number of qubits for characterizing stabilizer states. Our approach allows simultaneous extraction of information about the fidelity, the entanglement, and the nonlocality of the state and thus is of high practical relevance. We demonstrate the efficient applicability of our method by performing an experimental characterization of a photonic four-qubit cluster state and three- and four-qubit Greenberger-Horne-Zeilinger states. Our scheme can be directly extended to larger-scale quantum information tasks.
Accurately characterizing multipartite entangled states is a critical challenge in quantum information processing. In this work, we focus on applying compressed sensing techniques to efficiently estimate the fidelity of Greenberger-Horne-Zeilinger (GHZ) states. By exploiting the inherent sparsity of these states, our compressed sensing protocol drastically reduces the measurement overhead traditionally required for state verification while maintaining high accuracy. To evaluate the practical performance of this approach, we test the protocol on GHZ states using both quantum simulators and Quantinuum's trapped-ion hardware. Furthermore, we implement error detection techniques during our hardware evaluations, demonstrating the robustness and viability of compressed sensing for fidelity estimation in noisy experimental environments.