Robust Extraction of Tomographic Information via Randomized Benchmarking

Kimmel, Shelby; Silva, Marcus; Ryan, Colm A.; Johnson, Blake; Ohki, Thomas A.

doi:10.1103/physrevx.4.011050

Cited by 126 publications

(155 citation statements)

References 38 publications

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“…in the process matrix formalism for a single qubit [28]. The infidelity is particularly convenient for our algorithm because the trace is a linear function of the channel.…”

Section: A Infidelity-optimized Decodingmentioning

confidence: 99%

Hard decoding algorithm for optimizing thresholds under general Markovian noise

Chamberland

Wallman

et al. 2017

Phys. Rev. A

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Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several errorcorrecting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.

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“…in the process matrix formalism for a single qubit [28]. The infidelity is particularly convenient for our algorithm because the trace is a linear function of the channel.…”

Section: A Infidelity-optimized Decodingmentioning

confidence: 99%

Hard decoding algorithm for optimizing thresholds under general Markovian noise

Chamberland

Wallman

et al. 2017

Phys. Rev. A

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“…The fidelity of a state ρ to a pure state ψ is Tr y y r ñá (| | ) [15,[39][40][41]. The fidelity of the output of the actual gate ac  to the output of the ideal gate id  for a given input state yñ | is therefore…”

Section: Average Gate Fidelitymentioning

confidence: 99%

Bounding quantum gate error rate based on reported average fidelity

2015

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Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender optimism that fault-tolerant quantum computing is within reach, the connection of average gate fidelity with fault-tolerance requirements is not direct. Here we use reported average gate fidelity to determine an upper bound on the quantum-gate error rate, which is the appropriate metric for assessing progress towards fault-tolerant quantum computation, and we demonstrate that this bound is asymptotically tight for general noise. Although this bound is unlikely to be saturated by experimental noise, we demonstrate using explicit examples that the bound indicates a realistic deviation between the true error rate and the reported average fidelity. We introduce the Pauli distance as a measure of this deviation, and we show that knowledge of the Pauli distance enables tighter estimates of the error rate of quantum gates. lb 0

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“…Extracting fidelity information can often be useful in diagnosing performance and problems with a device in lieu of full characterization [22]. Moreover, randomized benchmarking has also been used to extract information about the completely positive and unital parts of linear maps [23].Here, using near-optimal data processing together with prior information, we accelerate the data processing used in benchmarking experiments, such that to achieve the accuracy demanded of benchmarking protocols, we require orders of magnitude less experimental data. We also extend results on the achievable estimation quality in the presence of finite sampling [24] and prior information, then show that our accelerated methods are nearly optimal.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Accelerated randomized benchmarking

2015

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Quantum information processing offers promising advances for a wide range of fields and applications, provided that we can efficiently assess the performance of the control applied in candidate systems. That is, we must be able to determine whether we have implemented a desired gate, and refine accordingly. Randomized benchmarking reduces the difficulty of this task by exploiting symmetries in quantum operations. Here, we bound the resources required for benchmarking and show that, with prior information, we can achieve several orders of magnitude better accuracy than in traditional approaches to benchmarking. Moreover, by building on state-of-the-art classical algorithms, we reach these accuracies with near-optimal resources. Our approach requires an order of magnitude less data to achieve the same accuracies and to provide online estimates of the errors in the reported fidelities. We also show that our approach is useful for physical devices by comparing to simulations.Quantum information processing devices offer great promise in a variety of different fields, including chemistry and material science, data analysis and machine learning [1][2][3][4], as well as cryptography [5]. Over the past few years, proposals have been advanced for quantum information processing past the classical scale, based on nodebased architectures [6,7]. In addition, rapid progress has been made towards experimental implementations that might allow for developing such devices [8,9]. An impediment in this effort, however, is presented by the difficulty of calibrating and diagnosing quantum devices.In particular, in the development of quantum information processing, an important experimental challenge is to efficiently characterize the quality with which we can control a quantum system. By characterizing the quality of a quantum gate that is implemented by a control pulse, we can then reason about the utility of that gate for quantum information processing tasks. For instance, we can estimate the feasibility of and the resources required to implement error correction using that control by comparing to proven and numerically estimated fault-tolerance thresholds [10,11]. Alternately, we can adjust our control sequences to account for differences between our control model and the actual system.In cases where only the quality of a quantum gate or set of gates is required, randomized benchmarking has proven to be a useful means of extracting this information with relatively little experimental effort [12]. This has been demonstrated in a variety of experimental settings [9,[13][14][15][16][17][18][19]. Randomized benchmarking has also been used to improve gate fidelities by characterizing cross-talk [20] or distortions [21]. Extracting fidelity information can often be useful in diagnosing performance and problems with a device in lieu of full characterization [22]. Moreover, randomized benchmarking has also been used to extract information about the completely positive and unital parts of linear maps [23].Here, using near-optimal data proces...

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Robust Extraction of Tomographic Information via Randomized Benchmarking

Cited by 126 publications

References 38 publications

Hard decoding algorithm for optimizing thresholds under general Markovian noise

Hard decoding algorithm for optimizing thresholds under general Markovian noise

Bounding quantum gate error rate based on reported average fidelity

Accelerated randomized benchmarking

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