Optimal probes and error-correction schemes in multi-parameter quantum metrology

Górecki, Wojciech; Zhou, Sisi; Jiang, Liang; Demkowicz-Dobrzański, Rafał

doi:10.22331/q-2020-07-02-288

Cited by 46 publications

(51 citation statements)

References 70 publications

(128 reference statements)

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“…Recent work shows that it is possible to measure H at the Heisenberg limit using an error-correcting code if H cannot be expressed as a linear combination of correctable noise operators [100][101][102][103][104]. But if the physical charge T A is a sum of local charges, the Eastin-Knill theorem poses a challenge to the application of error-correcting techniques; namely, error correction prevents probe states from evolving, obscuring the signal.…”

Section: Discussionmentioning

confidence: 99%

Continuous Symmetries and Approximate Quantum Error Correction

et al. 2020

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Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here, we study the compatibility of these two important principles. If a logical quantum system is encoded into n physical subsystems, we say that the code is covariant with respect to a symmetry group G if a G transformation on the logical system can be realized by performing transformations on the individual subsystems. For a G-covariant code with G a continuous group, we derive a lower bound on the errorcorrection infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems n or the dimension d of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with n or d as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem for quantum computation: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large d (using random codes) or n (using codes based on W states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.

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Section: Discussionmentioning

confidence: 99%

Continuous Symmetries and Approximate Quantum Error Correction

et al. 2020

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“…Beyond these direct applications, it provides a crucial fundamental milestone of experimental witnessing of intrinsic properties of highly nonclassical states applicable to a broad spectrum of modern applications of quantum-enhanced control and measurement of mechanical motion including the optical frequency metrology [38,39], quantum error correction [8,[15][16][17], tests of quantum thermodynamical phenomena [40,41], or gravitational wave detection [42]. Together with the recent demonstration of viable preparation of states with properties suggesting their proximity to number states with up to |n ∼ 100 on the same experimental platform [9], presented approach will allow for optimization and comparison of these quantum states across different sensing scenarios with a clearly identifiable fundamental and application relevance [43,44]. We foresee a further enhancement of the presented states approaching idealized Fock states by operating the experiment at a much higher trapping frequencies, which will allow for speed up of the state preparation procedure and minimization of the corresponding thermalization process duration.…”

Section: Discussionmentioning

confidence: 99%

Quantum non-Gaussianity of multi-phonon states of a single atom

Podhora,

Lachman,

Pham

et al. 2021

Preprint

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Quantum non-Gaussian mechanical states from inherently nonlinear quantum processes are already required in a range of applications spanning from quantum sensing up to quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates -Fock states. Despite the progress in their preparation, the remaining imperfections can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant in the applications. We derive the most challenging hierarchy of quantum non-Gaussian criteria for the individual mechanical Fock states and demonstrate its implementation on the characterization of single trapped-ion oscillator states up to 10 phonons. We analyze the depth of quantum non-Gaussian features under mechanical heating and predict their application in quantum sensing. These results uncover that the crucial quantum non-Gaussian features are demanded to reach quantum advantage in the applications.

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“…To regain the quantum advantage, one needs to combine quantum error correction with quantum sensing. Indeed, if the noise acts sufficiently different than the signal, we can retain the Heisenberg scaling by using a metrological code [57,58]. For certain noise models, scalings between standard and Heisenberg scaling can be achieved [59].…”

Section: Quantifying Sensing Performance the Classicalmentioning

confidence: 99%

Fisher Information in Noisy Intermediate-Scale Quantum Applications

Meyer

2021

Quantum

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The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

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Optimal probes and error-correction schemes in multi-parameter quantum metrology

Cited by 46 publications

References 70 publications

Continuous Symmetries and Approximate Quantum Error Correction

Continuous Symmetries and Approximate Quantum Error Correction

Quantum non-Gaussianity of multi-phonon states of a single atom

Fisher Information in Noisy Intermediate-Scale Quantum Applications

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