Turbocharging Quantum Tomography

154

119

With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of 99.95% with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between unitary and non-unitary errors in quantum gates by interleaving repetitions of a target gate within a randomized benchmarking sequence. The benchmarking fidelity decays quadratically with the number of interleaved gates for unitary errors but linearly for non-unitary, allowing us to separate systematic coherent errors from decoherent effects. With this protocol we show that the fidelity of the gates is not limited by unitary errors, but by another drive-activated source of decoherence such as amplitude fluctuations.Accurate characterization of control gates is an essential task for developing any quantum computing device. Quantum process tomography (QPT) [1][2][3] has been the standard method for characterizing quantum gates because, ideally, it produces a full reconstruction of the quantum process. In practice however, QPT suffers from many drawbacks, the most inimical being its exponential scaling in the number of quantum bits (qubits) comprising the system and that it is limited by state preparation and measurement (SPAM) errors. Various methods such as randomized benchmarking (RB) [4][5][6][7] and gate set tomography (GST) [8,9] have recently been developed to help overcome these limitations. RB is both insensitive to SPAM errors and efficient [10]. However, it only extracts a single piece of information, the average gate fidelity. GST on the other hand helps to overcome limitations from SPAM errors by reconstructing an entire library of gates in a self-consistent manner. The price paid for this self-consistent reconstruction is an even worse scaling than QPT.As control calibration techniques continue to improve and quantum gates approach the fidelity required for fault tolerant quantum computation, it becomes both important and difficult to verify the presence of increasingly small errors. Error verification constitutes a critical first step in a debugging routine since different physical mechanisms can lead to different error types. QPT and GST are often poor choices for error verification since they are time consuming and contain so much information that backing out the presence of specific error types on small scales can be a challenge in itself. In addition, SPAM errors in QPT sets a lower limit on the detectable error strengths [8]. At the other end of the spectrum, while standard RB is efficient the information it contains about the gate is typically not enough to perform any sort of useful error verification. An extension of standard RB, interleaved randomized benchmarking, consists of interleaving a target gate in a benchmarking sequence and provides bounds on the error for the gate of interest [11,12]. Interleaved benchmarking can identify gates that are poorly calibrated, but does not reveal if the errors are due to decoherence, over-/underrotations, or offresona...

mentioning

confidence: 99%

Characterizing errors on qubit operations via iterative randomized benchmarking

Sheldon¹,

Bishop²,

Magesan³

et al. 2016

154

119

“…We considered a simple version of "gate-set tomography" [13], in which only state preparations and measurements (SPAM) are performed, and no gates in between. As a special case we considered in detail qubits in M unknown states measured by N unknown two-outcome detectors.…”

Section: Discussionmentioning

confidence: 99%

“…Such questions have become of interest in the context of debugging quantum devices that are meant to serve as fault tolerant quantum computers. The requirements on fault tolerance are quite stringent and more and more precise tools for analyzing tomography experiments have been developed very recently [13][14][15]. Correlations between errors are particularly bad for fault tolerance, hence our focus on detecting correlated SPAM errors.…”

Section: Introductionmentioning

confidence: 99%

Detecting correlated errors in state-preparation-and-measurement tomography

Jackson

Enk

2015

Whereas in standard quantum state tomography one estimates an unknown state by performing various measurements with known devices; and whereas in detector tomography one estimates the POVM elements of a measurement device by subjecting to it various known states, we consider here the case of SPAM (state preparation and measurement) tomography where neither the states nor the measurement device are assumed known. For d-dimensional systems measured by d-outcome detectors, we find there are at most d 2 (d 2 − 1) "gauge" parameters that can never be determined by any such experiment, irrespective of the number of unknown states and unknown devices. For the case d = 2 we find new gauge-invariant quantities that can be accessed directly experimentally and that can be used to detect and describe SPAM errors. In particular, we identify conditions whose violations detect the presence of correlations between SPAM errors. From the perspective of SPAM tomography, standard quantum state tomography and detector tomography are protocols that fix the gauge parameters through the assumption that some set of fiducial measurements is known or that some set of fiducial states is known, respectively.

“…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%

Nonholonomic tomography. II. Detecting correlations in multiqudit systems

Jackson¹,

Enk²

2017

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.