Session G35: Quantum Characterization, Verification, and Validation: Noise and Cross-Talk

Characterizing the statistics of the qubit frequency noise

Measurements of the qubit state brings in randomness, which is superposed on the noise in the qubit parameters. This complicates characterizing the noise. We show that not only the spectrum of the noise, but also its statistics can be revealed using periodically repeated Ramsey measurements. The method is based on studying two- and three-time correlators of the measurement outcomes. It allows identifying noise from a periodic frequency modulation and distinguishing a Gaussian from a non-Gaussian noise. It also identifies a characteristic footprint of the telegraph noise. We provide analytical expressions for the two-and three-time correlators for different kinds of noise. The results for commonly encountered types of noise, the Gaussian 1/f and  exponentially correlated noise, and for a telegraph noise are verified by numerical simulations.   

Modeling of environmental noise in transmon qubit using dynamical decoupling

Tackling decoherence is one of the core challenges in the field of quantum computing. For superconducting qubits, coupling to the environment results in several noise channels. A rigorous characterization of the open system dynamics at the circuit Hamiltonian level is essential for a better understanding of these noise processes. Here we model the open quantum system effects for a qubit derived from a transmon circuit Hamiltonian. We use the Redfield master equation with a hybrid bath consisting of both high and low frequency components to model the effects of environment. We develop a fitting procedure using dynamical decoupling to learn the behavior of noise and use it to reproduce the experiments on processors available through IBM Quantum Experience. We test our model with quantum state fidelity experiments for random initial states. We further reproduce the effects of applied time-dependent dynamical decoupling pulses. Our model predicts all the experimental results with an average relative error of less than 1%.   

High Fidelity Quantum Gates under random telegraph noise: Machine Learning Approach

Achieving high fidelity quantum gates under random telegraph noise (RTN) is of great interest for quantum computing. We have generated data for qubit driven by π, CORPSE, SCORPSE, symmetric and asymmetric pulses in presence of RTN and by using train-test model in machine learning algorithm within python environment, we report symmetric pulse provides large fidelity recovery against noise among all the other pulses for large noise correlation time, whereas π-pulse has small error among all the other pulses for small noise correlation time. Investigation of high fidelity quantum gate for small energy amplitudes of RTN may be useful for low temperature measurements, whereas large energy amplitudes of RTN may be useful for room temperature measurements of quantum error correction codes.   

Tomographic construction and prediction of superconducting qubit dynamics using the post-Markovian master equation

Non-Markovian noise presents a particularly relevant challenge in understanding and combating decoherence in quantum computers. Using tomographic constructed state dynamics of a superconducting qubit system, we show that we can construct a phenomenological dynamical model using the post-Markovian master equation (PMME). We experimentally test our protocol to characterize the free evolution of a single qubit in one of IBMQ's cloud-based quantum processors. The resultant PMME model characterizes the cross-talk effect due to the neighboring qubits, the timescales of the qubit decoherence and dissipation process, and quantifies the degree of non-Markovianity of the system. We also demonstrate that the constructed PMME model can predict future qubit dynamics for an arbitrary single-qubit state better than the standard Lindblad model. Our model construction protocol requires sampling the qubit evolution at multiple time points for only one qubit initial state; thus, it requires less data than the process tomography and machine learning methods. The PMME has a closed-form analytical solution, making it straightforward to find the best-fit PMME model parameters via the maximum likelihood estimation method. Our protocol provides a robust estimation method for a continuous dynamical model beyond the commonly assumed Markovian approximation, leading to more accurate modeling of noisy intermediate-scale quantum (NISQ) devices.   

Learning Noise via Dynamical Decoupling of Entangled Qubits

Arrays of superconducting qubits with frequency tunable couplers are capable of producing interesting quantum behavior. Key to this is the ability to produce high-fidelity entangling interactions between qubits. The quality of these interactions is limited by noise caused by system-environment interaction. Characterizing noise in entangled systems is difficult not only because of the large numbers of degrees of freedom but also due to the limited and imperfect available control. This makes achieving good correspondence between theory and experiments difficult. By comparing the behavior of isolated and entangled qubits, we establish that the dominating source of noise during our resonant, excitation preserving two-qubit gates is frequency fluctuations of the coupler, not the qubits themselves. We drive pairs of entangled qubits through CPMG-inspired pulse sequences and observe steps in the decay curves that cannot be produced by Gaussian noise. Via detailed modeling, we establish that this noise is well described by a few stand-alone random telegraph fluctuators which interact with the coupler via its flux bias and have a correlation time on the order of 0.1ms. We also explore spatial inter-qubit correlations in this noise that could be detrimental to multi-qubit algorithms.    

Multiqubit Spatially Correlated Noise Characterization

Spatiotemporally correlated noise and its impact on error correcting schemes such as the surface code are of critical interest for quantum information processing research. We propose and validate a quantum noise spectroscopy protocol to measure spatially correlated noise on two qubits. Our scheme reconstructs the real and imaginary part of the power spectrum using two fixed total time pulse sequences and performing single qubit and joint two-qubit measurements to separately resolve spatially correlated noise processes from the individual noise spectra of the participating qubits. We inject noise by using a technique known as Schrodinger Wave Autoregressive Moving Average, developed by our group [1], to generate phase error on the qubit control line. Our results demonstrate that our protocol is a way to characterize spatially correlated noise in a quantum device and inform error correction algorithms.

[1] Murphy, Andrew, et al. "Universal Dephasing Noise Injection via Schrodinger Wave Autoregressive Moving Average Models." arXiv preprint arXiv:2102.03370 (2021).   

Dephasing-Robust Characterization of Temporally-Correlated Qubit Control Noise

Precise control of quantum systems is a requirement for quantum technologies spanning fields from quantum metrology to quantum computing. A major factor limiting control fidelity is noise due to fluctuations in control fields.  To design optimally robust control sequences, it is first necessary to have a high-accuracy characterization of the statistical properties of control noise. Previous approaches to characterize control noise are limited by their vulnerability to low-frequency dephasing noise, which can overwhelm the target control noise signal and prevent reliable characterization. In this work, we apply optimized narrowband quantum control sequences to probe fine spectral features of amplitude control noise while simultaneously suppressing dephasing noise. This extends the spectroscopy of control noise to experimentally relevant settings where dephasing is strong relative to control noise, such as superconducting qubits.   

Distinguishing multi-spin interactions from lower order effects

Multi-spin interactions can be engineered with artificial quantum spins. However, it is challenging to verify such interactions experimentally. We describe two methods to characterize $n$-local coupling of $n$ spins. First, we analyze the variation of the transition energy of the static system as a function of local spin fields. Generally accessible measurement techniques are used to distinguish $n$-local interactions between up to five spins from lower-order contributions in the presence of noise and spurious fields and couplings. Second, we show a detection technique that relies on time-dependent driving of the coupling term. Generalizations to larger system sizes are analyzed for both static and dynamic detection methods, and we find that the dynamic method is asymptotically optimal when increasing the system size. The proposed methods enable robust exploration of multi-spin interactions across a broad range of both coupling strengths and qubit modalities.   

Analysis of Randomized Benchmarking with Realistic Noise

Recently, a leakage-detecting (“blind”) randomized benchmarking (RB) technique has been employed to characterize overall error and, via interleaving, errors for specific gates, in 6-dot arrays of silicon quantum dots operated as exchange-only qubits [Andrews et al., Nature Nano. 14, 747 (2019)].  Here, we analytically compute functional forms for these RB decays using the group Fourier transform convolutional analysis described in Merkel et al., arXiv:1804.05951. Our analysis includes gate-dependent errors caused by composite pulses and control and environmental noise, as well as leakage. The effects of both Markovian and non-Markovian noise are analyzed, with excellent agreement found between simulations and group Fourier transform theory. We find that, for exchange-only qubits at least, Markovian and non-Markovian noise-induced RB decays are qualitatively similar.   

Measurement efficient automated multi-level qudit pulse optimization on quantum devices

Harnessing the existing higher levels in the cQED qudit can significantly increase the resourcefulness of NISQ era quantum devices. However, increased deviations and complexity in the modeling of higher levels, make it challenging to tune up high-fidelity gates on a qudit. We investigate using a model-free pulse optimization of a U(3) gate. We demonstrate that parameterizing the pulse with Hanning windowed basis functions allows for more efficient optimization, as they reduce the number of parameters required, and ensure strict bandwidth limits. We also simplify the cost function and use only state populations instead of full state tomography, reducing the number of measurements required at each evaluation. Our optimization protocol starts with no prior knowledge about the ideal pulse parameters and obtains a gate error of 2e-3 which is primarily coherence limited. Unlike traditional model-based optimization, this model-free approach enables optimization of multi-qutrit gates and is directly applicable to other qubit architectures including protected qubits.   

Estimating gate-set properties from random sequences

With quantum devices for computing and simulation increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations.

In this work, we show that by measuring random gate sequences, one can accurately and efficiently estimate a wealth of different properties of noisy implementations of gate sets. This simple experimental protocol is independent of the properties one intends to estimate. It generates `sequence  shadows' from which gate-set properties can be extracted, through classical post-processing, in a state preparation and measurement error robust way. Our schemes include protocols to extract many average gate fidelities with respect to arbitrary unitary channels. This - as a special case - emulates (interleaved) randomized benchmarking, but is vastly more general in its applicability. We establish that the sequence estimation scheme can be used as a primitive for partial, compressive and full process tomography, and the learning of Pauli noise. This gives rise to channel variants of shadow estimation with close-to optimal performance guarantees. Finally, we discuss applications to the engineering cycle for the optimization of quantum gates, for instance as a novel method to diagnose crosstalk.   

Neural Network Based Qubit Environment Characterization

The exact microscopic structure of the environments that produces $1/f$ noise in superconducting qubits remains largely unknown, hindering our ability to have robust simulations and harness the noise. In this paper we show how it is possible to infer information about such an environment based on a single measurement of the qubit coherence, circumventing any need for separate spectroscopy experiments. Similarly to other spectroscopic techniques, the qubit is used as a probe which interacts with its environment. The complexity of the relationship between the observed qubit dynamics and the impurities in the environment makes this problem ideal for machine learning methods - more specifically neural networks. With our algorithm we are able to reconstruct the parameters of the most prominent impurities in the environment, as well as differentiate between different environment models, paving the way towards a better understanding of $1/f$ noise in superconducting circuits.   

The Learning and Compiled Calibration of Clock Cycle Errors in QuantumComputing Architectures

The performance of quantum computers is inhibited by the occurrence of physical errors during computation.

For this reason, the development of increasingly sophisticated error suppression and error characterization techniques is central to the progress of quantum computing.

Error distributions are considerably influenced by the precise gate scheduling across the entire quantum processing unit.

To account for this holistic feature, we may ascribe each error profile to a (clock) cycle, which is a detailed list of instructions performed over the whole chip.

A celebrated technique known as randomized compiling introduces some randomness within cycles' instructions, which yields effective cycles with simpler, stochastic error signatures.

In the present work, we leverage known Pauli channel estimation techniques to derive a highly efficient and scalable method to estimate with Heisenberg-like precision the marginal error distribution associated with any effective cycle of interest.

Furthermore, we develop a fast compilation-based calibration method to identify and suppress local coherent error sources occurring in any effective cycle of interest.

We performed both protocols on IBM-Q 5-qubit devices.

Via our calibration scheme, we obtained up to a 5-fold improvement of the circuit performance.   

Flux crosstalk as an optimization problem

Flux crosstalk is an important control issue for scaling up quantum computers based on superconducting qubits. The number of measurements required to calibrate crosstalk usually scales at least quadratically with the number of control channels, and becomes worse when the circuit elements interact strongly. Here we propose a new method for calibrating flux crosstalk for superconducting circuits. Using the fundamental property that superconducting circuits respond periodically to external fluxes, crosstalk calibration of N flux channels can be treated as N independent optimization problems, with the optimization metric being the periodicity of a measured signal. We show experimental results on a small-scale quantum annealer, which indicates that the optimization problem is convex given reasonable initial estimates of the crosstalk, and can thus be efficiently solved.   

Optimal Quantum State Tomography with Noisy Gates

For limited scenarios, depending on projector rank and system size, optimal measurement schemes for efficient QST are known.  In the case of errorless non-degenerate measurements, using mutually unbiased bases yields the optimal QST scheme [1]. Measuring one out of N qubits becomes optimal if the measurement operators project on mutually unbiased subspaces [2]. However, in the general case, the optimal measurement scheme for efficient QST is not known and, oftentimes, it may need to be numerically approximated. This problem can be generalized as a framework for customized efficient QST. Here, we extend this framework to investigate the effect of noise on the optimal QST measurement sets using two noise models:  the depolarizing channel, and over- and under-rotation in two-qubit gates. We demonstrate the benefit of using entangling gates for the efficient QST measurement schemes for two qubits at realistic noise levels, by comparing the fidelity of reconstruction of our optimized QST measurement set to the state-of-the-art scheme using only product bases.

[1] Wootters, Fields, Ann. Phys. 191, 363 (1989)

[2] Bodmann, Haas, Proc. Amer. Math. Soc. 146, 2601 (2018)