Qubit Quantum Metrology with Limited Measurement Resources

• URL: http://arxiv.org/abs/2108.02876v1
• Date: Thu, 5 Aug 2021 22:39:33 GMT
• Title: Qubit Quantum Metrology with Limited Measurement Resources
• Authors: Jason Saunders and Jean-Francois Van Huele
• Abstract summary: We find that entanglement between qubits always decreases the uncertainty of an estimation. In noiseless systems, the quantum advantage decreases as fewer qubits are used in the estimation. We also find that the presence of strong dephasing noise removes the quantum advantage completely.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement resources by the Quantum Cramer-Rao Bound, but no general description exists for the regime of limited measurement resources. We address this problem by defining a Bayesian quantifier for uncertainty suitable for the regime of limited resources, and by developing a mathematical description for a parameter-estimation procedure which uses qubit probes to estimate a rotation angle induced on them. We simulate the qubit estimation scheme in the regime of limited resources using a single class of probe states. We find that, in noiseless systems, entanglement between qubits always decreases the uncertainty of the estimation; however, the quantum advantage decreases as fewer qubits are used in the estimation. We also find that the presence of strong dephasing noise removes the quantum advantage completely, regardless of the number of qubit probes used.

Related papers

• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states. It is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• Error mitigated shadow estimation based on virtual distillation [6.354965487736348]
  Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements. We introduce an error-mitigated shadow estimation approach based on virtual distillation, tailored for applications in near-term quantum devices.
  arXiv  Detail & Related papers  (2024-02-29T03:31:18Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs [0.0]
  We consider the problem of estimating the quantum state of a qubit in a quantum processing unit without conducting direct measurements of it. We implement and test the circuit using the quantum computer of the Technical Research Centre of Finland as well as an IBM quantum computer.
  arXiv  Detail & Related papers  (2023-08-15T09:27:52Z)
• Quantum metrology in the finite-sample regime [0.6299766708197883]
  In quantum metrology, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram'er-Rao bound. We propose to quantify the quality of a protocol by the probability of obtaining an estimate with a given accuracy.
  arXiv  Detail & Related papers  (2023-07-12T18:00:04Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Universal cost bound of quantum error mitigation based on quantum estimation theory [0.0]
  We present a unified approach to analyzing the cost of various quantum error mitigation methods on the basis of quantum estimation theory. We derive for a generic layered quantum circuit under a wide class of Markovian noise that, unbiased estimation of an observable encounters an exponential growth with the circuit depth in the lower bound on the measurement cost. Our results contribute to the understanding of the physical limitations of quantum error mitigation and offer a new criterion for evaluating the performance of quantum error mitigation techniques.
  arXiv  Detail & Related papers  (2022-08-19T15:04:36Z)
• Error-Mitigated Quantum Metrology via Virtual Purification [0.0]
  We propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise.
  arXiv  Detail & Related papers  (2021-12-03T11:07:50Z)
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [58.720142291102135]
  We define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. Our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation.
  arXiv  Detail & Related papers  (2021-09-27T12:56:01Z)
• Quantum verification and estimation with few copies [63.669642197519934]
  The verification and estimation of large entangled systems represents one of the main challenges in the employment of such systems for reliable quantum information processing. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity) and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography.
  arXiv  Detail & Related papers  (2021-09-08T18:20:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.