Characterizing d-dimensional quantum channels by means of quantum process tomography

Varga, J. J. M.; Rebón, Lorena; Stefano, Quimey Pears; Iemmi, Claudio

doi:10.1364/ol.43.004398

Cited by 8 publications

(10 citation statements)

References 21 publications

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“…Specifically, quantum computing on higher-dimensional systems can be more efficient than on qubits [7,14,18]. Ultimate success of quantum computing, both qubitand qudit-based, depends on being scalable, which, in turn, requires components meeting fault-tolerance conditions [19].Unitary-gate randomized benchmarking (URB) is the preferred technique to characterize unitary-gate performance due to its efficiency [20,21], which is robust against state-preparation-and-measurement (SPAM) errors and exponentially superior to the alternative of quantum process tomography (QPT) [22,23]. URB estimates average fidelity between real and ideal implementation of all 24 Clifford gates in C 2 , which normalizes the Pauli group…”

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confidence: 99%

“…Unitary-gate randomized benchmarking (URB) is the preferred technique to characterize unitary-gate performance due to its efficiency [20,21], which is robust against state-preparation-and-measurement (SPAM) errors and exponentially superior to the alternative of quantum process tomography (QPT) [22,23]. URB estimates average fidelity between real and ideal implementation of all 24 Clifford gates in C 2 , which normalizes the Pauli group…”

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confidence: 99%

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Randomized benchmarking for qudit Clifford gates

Jafarzadeh

Sanders

et al. 2020

New J. Phys.

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We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending singleand multi-qubit URB to single-and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.Quantum computing and quantum communication typically focuse on quantum information encoded and processed with quantum bit (qubit) strings, but replacing qubits by higher-dimensional qudit strings [1,2] can be advantageous [3] for quantum simulation [4], quantum algorithms [5-7], quantum error correction [8-10], universal optics-based quantum computation [11], quantum communication [12, 13] and fault-tolerant quantum computation [14, 15]. Qudit quantum-information process could reduce space requirements and exploit natural properties such as orbital angular momentum for photons [16], superconductors [4] and neutral atoms [17]. Specifically, quantum computing on higher-dimensional systems can be more efficient than on qubits [7,14,18]. Ultimate success of quantum computing, both qubitand qudit-based, depends on being scalable, which, in turn, requires components meeting fault-tolerance conditions [19].Unitary-gate randomized benchmarking (URB) is the preferred technique to characterize unitary-gate performance due to its efficiency [20,21], which is robust against state-preparation-and-measurement (SPAM) errors and exponentially superior to the alternative of quantum process tomography (QPT) [22,23]. URB estimates average fidelity between real and ideal implementation of all 24 Clifford gates in C 2 , which normalizes the Pauli group

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confidence: 99%

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confidence: 99%

Randomized benchmarking for qudit Clifford gates

Jafarzadeh

Sanders

et al. 2020

New J. Phys.

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“…Introduction.-Parameter reconstruction from datasets is a preliminary task in the study of natural sciences. In quantum theory, proper reconstruction of quantum states [1][2][3][4][5], quantum channels [6][7][8][9], interferometric phases [10,11], etc., is the root to successful executions of all quantum-information protocols [12][13][14][15]. A parameter estimator must be accompanied by an appropriate error certification to ascertain its reliability for future physical predictions.…”

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confidence: 99%

Probing Bayesian Credible Regions Intrinsically: A Feasible Error Certification for Physical Systems

Teo

Jeong

2019

Phys. Rev. Lett.

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Standard computation of size and credibility of a Bayesian credible region for certifying any point estimator of an unknown parameter (such as a quantum state, channel, phase, etc.) requires selecting points that are in the region from a finite parameter-space sample, which is infeasible for a large dataset or dimension as the region would then be extremely small. We solve this problem by introducing the in-region sampling theory to compute both region qualities just by sampling appropriate functions over the region itself using any Monte Carlo sampling method. We take in-region sampling to the next level by understanding the credible-region capacity (an alternative description for the region content to size) as the average l p -norm distance (p > 0) between a random region point and the estimator, and present analytical formulas for p = 2 to estimate both the capacity and credibility for any dimension and sufficiently large dataset without Monte Carlo sampling, thereby providing a quick alternative to Bayesian certification. All results are discussed in the context of quantum-state tomography.Introduction.-Parameter reconstruction from datasets is a preliminary task in the study of natural sciences. In quantum theory, proper reconstruction of quantum states [1-5], quantum channels [6-9], interferometric phases [10,11], etc., is the root to successful executions of all quantum-information protocols [12][13][14][15]. A parameter estimator must be accompanied by an appropriate error certification to ascertain its reliability for future physical predictions. Bootstrapping or resampling [16,17], which generates mock data from collected ones to obtain "error-bars", can result in highly overoptimistic "error-bar" lengths [18] that do not accurately characterize the estimator. From the principles of hypothesis testing, one can instead construct Bayesian credible regions [19,20] based on the collected data. These credible regions are distinct from the frequentists' confidence regions [21][22][23], which are constructed from the complete (often assumed) distribution of estimators that includes all unobserved ones in the experiment.A credible region R, which is a Bayesian error region constructed from experimentally observed data D, requires the specification of its size and credibility, which is the probability that the true parameter is inside R. It is well-known from [19] that the latter is readily derived so long as the functional behavior of the former with the shape of R is known. As the size of R is defined as the volume fraction of the full parameter space R 0 , its computation conventionally requires one to first obtain a large sample of points in R 0 , and later discard (usually very many) points that are outside R. Acquiring a sufficiently large sample of R 0 for a subsequently accurate sample filtering is doable with a number of Monte Carlo (MC) methods [24,25], most notably the Hamiltonian Markov-chain MC, provided that R is not small. In practice, however, when data sample-size N becomes even moderately large...

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“…* quimeyps@df.uba.ar Among the several physical implementations of a quantum state, photonic systems are ideally to be used for quantum communications applications [20]. Particularly, the discretized transverse momentum of single photons was used to define photonic quantum states, usually called slit states [21][22][23][24]. This is a very versatile option for the encoding of quantum states that allows to achieve high dimensional Hilbert spaces, easily in relation to other codifications.…”

Section: Introductionmentioning

confidence: 99%

Determination of spatial quantum states by using point diffraction interferometry

Stefano¹,

Rebón²,

Iemmi³

2020

J. Opt.

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We present a method to reconstruct pure spatial qudits of arbitrary dimension d, which is based on a point diffraction interferometer. In the proposed scheme, the quantum states are codified in the discretized transverse position of a photon field, once they are sent through an aperture consisting in d rectangular regions, with an extra region that provides a phase reference. To characterize these photonic quantum states, the complete phase wavefront is reconstructed through a phase-shifting technique. Combined with a multipixel detector, the acquisition can be parallelized, and only four interferograms are required to reconstruct any pure qudit, independently of the dimension d. We tested the method experimentally, for reconstructing states of dimension d = 6 randomly chosen. A mean fidelity values of 0.95 is obtained. Additionally, we develop an experimental scheme that allows to estimate phase aberrations affecting the wavefront upon propagation, and thus improve the quantum state estimation. In that regard, we present a proof-of-principle demonstration that shows the possibility to correct the influence of turbulence in a free-space communication, recovering mean fidelity values comparable to the propagation free of turbulence.

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Characterizing d-dimensional quantum channels by means of quantum process tomography

Cited by 8 publications

References 21 publications

Randomized benchmarking for qudit Clifford gates

Randomized benchmarking for qudit Clifford gates

Probing Bayesian Credible Regions Intrinsically: A Feasible Error Certification for Physical Systems

Determination of spatial quantum states by using point diffraction interferometry

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