Self-consistent quantum process tomography

Merkel, Seth; Gambetta, Jay; Smolin, John A.; Poletto, Stefano; Córcoles, Antonio; Johnson, Blake; Ryan, Colm A.; Steffen, Matthias

doi:10.1103/physreva.87.062119

Cited by 297 publications

(340 citation statements)

References 33 publications

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“…We estimate that our systematic errors are of order B2-3%. A rigorous error bound on fidelity in the presence of systematic noise is still the subject of future study 29 . In Fig.…”

Section: Resultsmentioning

confidence: 99%

Implementing a strand of a scalable fault-tolerant quantum computing fabric

et al. 2014

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With favourable error thresholds and requiring only nearest-neighbour interactions on a lattice, the surface code is an error-correcting code that has garnered considerable attention. At the heart of this code is the ability to perform a low-weight parity measurement of local code qubits. Here we demonstrate high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. With high-fidelity gates, we generate entanglement distributed across three superconducting qubits in a lattice where each code qubit is coupled to two bus resonators. Via high-fidelity measurement of the syndrome qubit, we deterministically entangle the code qubits in either an even or odd parity Bell state, conditioned on the syndrome qubit state. Finally, to fully characterize this parity readout, we develop a measurement tomography protocol. The lattice presented naturally extends to larger networks of qubits, outlining a path towards fault-tolerant quantum computing.

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“…We estimate that our systematic errors are of order B2-3%. A rigorous error bound on fidelity in the presence of systematic noise is still the subject of future study 29 . In Fig.…”

Section: Resultsmentioning

confidence: 99%

Implementing a strand of a scalable fault-tolerant quantum computing fabric

et al. 2014

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“…A variety of techniques have emerged including randomised benchmarking (RB), 1,2 purity benchmarking, 3 process tomography, [4][5][6][7] adaptive methods, 8 and gate-set tomography (GST). 9,10 Each protocol has relative strengths and weaknesses; for instance, RB has low experimental overhead but only provides average information about gate performance, while process tomography provides more information at the cost of unfavourable scaling in measurement overhead. 11 Despite their differences, these protocols share the common theme that they were originally developed and mathematically formalised assuming that error processes are statistically independent and do not exhibit strong correlations in time.…”

Section: Introductionmentioning

confidence: 99%

Experimental quantum verification in the presence of temporally correlated noise

et al. 2018

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Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171 Yb + ion-qubit and inject engineered noise /σ z ð Þto probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlatedσ z errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlatedσ x orσ y errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.

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“…However, this is not the case. Correlations such as Equation (4) can be determined without individual expectation values because equations like TrρΣ a i = Tr ρ a Σ i express a very special factorizability of the data, Equation (3). We thus proceed with the following operational definition: we say that data S a i is effectively (SPAM) uncorrelated when we can express it as a simple matrix equation:…”

Section: A the Born Rule Revisitedmentioning

confidence: 99%

“…Third, when P and W exist, they are in general not unique because one could just as well use P G and G -1 W where G is an n 2 × n 2 real invertible matrix. The components of G are gauge degrees of freedom which have been referred to as SPAM gauge [3,8,9] or blame gauge [1].…”

Section: A the Born Rule Revisitedmentioning

confidence: 99%

“…[3] Any practice which takes into account SPAM errors will be generically referred to as SPAM tomography. Several works have come out in SPAM tomography [3][4][5][6][7][8][9][10] particular to the task of making estimates in spite of such conditions, all of which speak to the notion of a "self-consistent tomography." Of course, such works assume that any and all SPAM errors are uncorrelated.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonholonomic tomography. II. Detecting correlations in multiqudit systems

Jackson¹,

Enk²

2017

Phys. Rev. A

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In the context of quantum tomography, quantities called partial determinants [1] were recently introduced. PDs (partial determinants) are explicit functions of the collected data which are sensitive to the presence of state-preparation-and-measurement (SPAM) correlations. In this paper, we demonstrate further applications of the PD and its generalizations. In particular we construct methods for detecting various types of SPAM correlation in multiqudit systems -e.g. measurementmeasurement correlations. The relationship between the PDs of each method and the correlations they are sensitive to is topological. We give a complete classification scheme for all such methods but focus on the explicit details of only the most scalable methods, for which the number of settings scales as O(d 4 ). This paper is the second of a two part series where the first paper[2] is about a theoretical perspective for the PD, particularly its interpretation as a holonomy.

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Self-consistent quantum process tomography

Cited by 297 publications

References 33 publications

Implementing a strand of a scalable fault-tolerant quantum computing fabric

Implementing a strand of a scalable fault-tolerant quantum computing fabric

Experimental quantum verification in the presence of temporally correlated noise

Nonholonomic tomography. II. Detecting correlations in multiqudit systems

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