Spectral quantum tomography

Helsen, Jonas; Battistel, Francesco; Terhal, Barbara M.

doi:10.1038/s41534-019-0189-0

Cited by 20 publications

(11 citation statements)

References 32 publications

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“…Firstly, by directly estimating a range of CUPs using the SWAP test [44]. These methods are detailed in Section V. Secondly, we consider how techniques for device benchmarking [35,45,46] can be used to estimate CUPs in a SPAM-robust way, see Sections VI A & VI B. We show that -with some assumptions -quantum CUP-sets can be estimated SPAM robustly on current devices (see Figure 1).…”

Section: A Structure and Main Results Of The Papermentioning

confidence: 99%

A simple formulation of no-cloning and no-hiding that admits efficient and robust verification

Girling¹,

Cirstoiu²,

Jennings³

2023

Preprint

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Incompatibility is a feature of quantum theory that sets it apart from classical theory, and the inability to clone an unknown quantum state is one of the most fundamental instances. The no-hiding theorem is another such instance that arises in the context of the black-hole information paradox, and can be viewed as being dual to no-cloning. Here, we formulate both of these fundamental features of quantum theory in a single form that is amenable to efficient verification, and that is robust to errors arising in state preparation and measurements. We extend the notion of unitarity -an average figure of merit that for quantum theory captures the coherence of a quantum channel -to general physical theories. Then, we introduce the notion of compatible unitarity pair (CUP) sets, that correspond to the allowed values of unitarities for compatible channels in the theory. We show that a CUP-set constitutes a simple 'fingerprint' of a physical theory, and that incompatibility can be studied through them. We derive information-disturbance constraints on quantum CUP-sets that encode both the no-cloning/broadcasting and no-hiding theorems of quantum theory. We then develop randomised benchmarking protocols that efficiently estimate quantum CUP-sets and provide simulations using IBMQ of the simplest instance. Finally, we discuss ways in which CUP-sets and quantum no-go theorems could provide additional information to benchmark quantum devices.

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Section: A Structure and Main Results Of The Papermentioning

confidence: 99%

A simple formulation of no-cloning and no-hiding that admits efficient and robust verification

Girling¹,

Cirstoiu²,

Jennings³

2023

Preprint

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“…This is a damping oscillating function. From the time series data O L at different depth L, we can extract the noisy eigenvalues via signal processing methods, such as matrix pencil method [66][67][68]. The imperfect initial state ρ and measurement operator O only affect the coefficients of signals rather than the noisy eigenvalues.…”

Section: The Csb Protocolmentioning

confidence: 99%

“…In step 3a, the noisy eigenvalues are estimated using the matrix pencil (MP) method [66][67][68]. MP method is well-suited for our task because MP involves a singular value decomposition (svd) of the data Hankel matrix.…”

Section: The Csb Protocolmentioning

confidence: 99%

Benchmarking universal quantum gates via channel spectrum

Zhuang

Chai

et al. 2023

Preprint

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Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a novel method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation.

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“…For the problem of computing multiple eigenvalues, the complexity is also polynomial in the number of distinct eigenvalues. Naturally, these complexities will be extremely large for typical cases where the gap is exponentially small in n. See [21,22] for related uses of the MP method in quantum computing.…”

Section: Related Workmentioning

confidence: 99%

Quantum eigenvalue estimation via time series analysis

Somma

2019

New J. Phys.

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We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ò, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ò.

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Spectral quantum tomography

Cited by 20 publications

References 32 publications

A simple formulation of no-cloning and no-hiding that admits efficient and robust verification

A simple formulation of no-cloning and no-hiding that admits efficient and robust verification

Benchmarking universal quantum gates via channel spectrum

Quantum eigenvalue estimation via time series analysis

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