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Register a new userEfficient characterization of correlated SPAM errors
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State preparation and measurement (SPAM) errors limit the performance of many gate-based quantum computing architecures, but are partly correctable after a calibration step that requires, for an exact implementation on a register of $n$ qubits, $2^n$ additional characterization experiments, as well as classical post-processing. Here we introduce an approximate but efficient method for SPAM error characterization requiring the {it classical} processing of $2^n ! times 2^n$ real matrices, but only $O(n^2)$ measurements. The technique assumes that multi-qubit measurement errors are dominated by pair correlations, which are estimated with $n(n-1)k/2$ two-qubit experiments, where $k$ is a parameter related to the accuracy. We demonstrate the technique on the IBM and Rigetti online superconducting quantum computers, allowing comparison of their SPAM errors in both magnitude and degree of correlation. We also study the correlations as a function of the registers geometric layout. We find that the pair-correlation model is fairly accurate on linear arrays of superconducting qubits. However qubits arranged in more closely spaced two-dimensional geometries exhibit significant higher-order (such as 3-qubit) SPAM error correlations.
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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.
State preparation and measurement (SPAM) errors limit the performance of near-term quantum computers and their potential for practical application. SPAM errors are partly correctable after a calibration step that requires, for a complete implementation on a register of $n$ qubits, $2^n$ additional measurements. Here we introduce an approximate but efficient method for multiqubit SPAM error characterization and mitigation requiring the classical processing of $2^n ! times 2^n$ matrices, but only $O(4^k n^2)$ measurements, where $k=O(1)$ is the number of qubits in a correlation volume. We demonstrate and validate the technique using an IBM Q processor on registers of 4 and 8 superconducting qubits.
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that are capable of implementing a universal set of gates with error rates below approximately 1%, requirements compatible with experimental reality. Consequently, a number of authors are attempting to squeeze additional performance out of the surface code. We describe an optimal complexity error suppression algorithm, parallelizable to O(1) given constant computing resources per unit area, and provide evidence that this algorithm exploits correlations in the error models of each gate in an asymptotically optimal manner.
The central challenge in building a quantum computer is error correction. Unlike classical bits, which are susceptible to only one type of error, quantum bits (qubits) are susceptible to two types of error, corresponding to flips of the qubit state about the $X$- and $Z$-directions. While the Heisenberg Uncertainty Principle precludes simultaneous monitoring of $X$- and $Z$-flips on a single qubit, it is possible to encode quantum information in large arrays of entangled qubits that enable accurate monitoring of all errors in the system, provided the error rate is low. Another crucial requirement is that errors cannot be correlated. Here, we characterize a superconducting multiqubit circuit and find that charge fluctuations are highly correlated on a length scale over 600~$mu$m; moreover, discrete charge jumps are accompanied by a strong transient suppression of qubit energy relaxation time across the millimeter-scale chip. The resulting correlated errors are explained in terms of the charging event and phonon-mediated quasiparticle poisoning associated with absorption of gamma rays and cosmic-ray muons in the qubit substrate. Robust quantum error correction will require the development of mitigation strategies to protect multiqubit arrays from correlated errors due to particle impacts.
Crosstalk is a leading source of failure in multiqubit quantum information processors. It can arise from a wide range of disparate physical phenomena, and can introduce subtle correlations in the errors experienced by a device. Several hardware characterization protocols are able to detect the presence of crosstalk, but few provide sufficient information to distinguish various crosstalk errors from one another. In this article we describe how gate set tomography, a protocol for detailed characterization of quantum operations, can be used to identify and characterize crosstalk errors in quantum information processors. We demonstrate our methods on a two-qubit trapped-ion processor and a two-qubit subsystem of a superconducting transmon processor.
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