Mixed-state Pauli-channel parameter estimation

Collins, David C.

doi:10.1103/physreva.87.032301

Cited by 14 publications

(5 citation statements)

References 47 publications

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“…1-4 by the probability p, can be known to some extent, to appreciate whether its increase is pro¯table and have control on its tuning when implemented. For this purpose, estimation techniques can be employed [47][48][49], which to some extent rest on the same principles as those reported in Sec. 2.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Resonance with Unital Quantum Noise

2019

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The fundamental quantum information processing task of estimating the phase of a qubit is considered. Following quantum measurement, the estimation efficiency is evaluated by the classical Fisher information which determines the best performance limiting any estimator and achievable by the maximum likelihood estimator. The estimation process is analyzed in the presence of decoherence represented by essential quantum noises that can affect the qubit and belonging to the broad class of unital quantum noises. Such a class especially contains the bit-flip, the phase-flip, the depolarizing noises, or the whole family of Pauli noises. As the level of noise is increased, we report the possibility of non-standard behaviors where the estimation efficiency does not necessarily deteriorate uniformly, but can experience non-monotonic variations. Regimes are found where higher noise levels prove more favorable to estimation. Such behaviors are related to stochastic resonance effects in signal estimation, shown here feasible for the first time with unital quantum noises. The results provide enhanced appreciation of quantum noise or decoherence, manifesting that it is not always detrimental for quantum information processing.

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Section: Discussionmentioning

confidence: 99%

Stochastic Resonance with Unital Quantum Noise

2019

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“…with (p 0 , p x , p y , p z ), a probability distribution satisfying the normalization condition p 0 + p x + p y + p z = 1, and the four Kraus operators Λ k = √ p k σ k . Pauli noises form a useful class of quantum noise that has been considered in many contexts of application, for instance for detection [22] or estimation [23][24][25] with quantum signals, or for investigating specific properties of quantum noises [26,27]. The class of Pauli noises of Equation (1) in particular contains important noises [20] such as the bit-flip noise when (p 0 , p x , p y , p z ) = (1 − p x , p x , 0, 0), the phase-flip noise when (p 0 , p x , p y , p z ) = (1 − p z , 0, 0, p z ), the bitphase-flip noise when (p 0 , p x , p y , p z ) = (1 − p y , 0, p y , 0), and the depolarizing noise when (p 0 , p x , p y , p z ) = (1 − p, p/3, p/3, p/3) parametrized by the probability p = 1 − p 0 .…”

Section: Quantum Pauli Noisementioning

confidence: 99%

Simulating Quantum Pauli Noise with Three Independently Controlled Pauli Gates

Chapeau-Blondeau

2024

Electronics

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A quantum Pauli noise is a nonunitary process that alters the state of a qubit by random application of the four Pauli operators. We investigate a four-qubit quantum circuit, consisting of a pipeline of three independently controlled Pauli gates, for simulating the general class of qubit Pauli noises. The circuit with a fixed architecture is controllable by three separable quantum states from three auxiliary qubits in order to adjust the parameters of the targeted Pauli noise on the principal qubit. Important Pauli noises such as bit flip, phase flip, bit phase flip, and depolarizing noise are readily simulated, along with an infinite subset of other Pauli noises. However, the quantum circuit with its simple and fixed architecture cannot simulate all conceivable Pauli noises, and a characterization is proposed, in the parameter space of the Pauli noises, denoting those that are simulable by the circuit and those that are not. The circuit is a useful tool to contribute to controlled simulation, on current or future quantum processors, of nonunitary processes of noise and decoherence.

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“…Because of the important role played by Pauli channels, it is of great interest to study the estimation of these objects in an efficient and practical way. Despite a long line of research [18][19][20][21][22][23][24][25][26], the ultimate sample complexity for Pauli channel estimation has not yet been fully characterized.…”

Section: Introductionmentioning

confidence: 99%

Quantum advantages for Pauli channel estimation

et al. 2022

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We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices. The specific task we consider is to simultaneously learn all the eigenvalues of an n-qubit Pauli channel to ±ε precision. We give an estimation protocol with an n-qubit ancilla that succeeds with high probability using only O(n/ε 2 ) copies of the Pauli channel, while proving that any ancilla-free protocol (possibly with adaptive control and channel concatenation) would need at least (2 n/3 ) rounds of measurement. We further study the advantages provided by a small number of ancillas. For the case that a k-qubit ancilla (k n) is available, we obtain a sample complexity lower bound of (2 (n−k)/3 ) for any nonconcatenating protocol, and a stronger lower bound of (n2 n−k ) for any nonadaptive, nonconcatenating protocol, which is shown to be tight. We also show how to apply the ancilla-assisted estimation protocol to a practical quantum benchmarking task in a noise-resilient and sample-efficient manner, given reasonable noise assumptions. Our results provide a practically interesting example for quantum advantages in learning and also bring insights for quantum benchmarking.

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Mixed-state Pauli-channel parameter estimation

Cited by 14 publications

References 47 publications

Stochastic Resonance with Unital Quantum Noise

Stochastic Resonance with Unital Quantum Noise

Simulating Quantum Pauli Noise with Three Independently Controlled Pauli Gates

Quantum advantages for Pauli channel estimation

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