Readout Errors Research Articles

Quantum readout error mitigation via deep learning

Quantum computing devices are inevitably subject to errors. To leverage quantum technologies for computational benefits in practical applications, quantum algorithms and protocols must be implemented reliably under noise and imperfections. Since noise and imperfections limit the size of quantum circuits that can be realized on a quantum device, developing quantum error mitigation techniques that do not require extra qubits and gates is of critical importance. In this work, we present a deep learning-based protocol for reducing readout errors on quantum hardware. Our technique is based on training an artificial neural network (NN) with the measurement results obtained from experiments with simple quantum circuits consisting of singe-qubit gates only. With the NN and deep learning, non-linear noise can be corrected, which is not possible with the existing linear inversion methods. The advantage of our method against the existing methods is demonstrated through quantum readout error mitigation experiments performed on IBM five-qubit quantum devices.

Correlations in Noisy Measurements

Although a measurement on the computational basis is devised in quantum computing, e.g., cloud-based quantum computing services, a quantum measurement in a realistic scenario is noisy. In particular, a measurement readout error in the era of noisy-intermediate-scale-quantum technologies is significant. In this work, we consider measurements on multiple qubits in a realistic scenario and present a method of analyzing noise in the measurement. Correlations existing in a noisy measurement are of particular interest so that local and crosstalk errors are introduced: the existence of correlations in a measurement in cloud-based quantum computing services is verified. We then present quantification of local and crosstalk errors and apply it to a noisy measurement in a cloud-based quantum computing service. Our results that analyze measurement errors can be used to mitigate these errors.

High-Fidelity Indirect Readout of Trapped-Ion Hyperfine Qubits.

We propose and demonstrate a protocol for high-fidelity indirect readout of trapped ion hyperfine qubits, where the state of a ^{9}Be^{+} qubit ion is mapped to a ^{25}Mg^{+} readout ion using laser-driven Raman transitions. By partitioning the ^{9}Be^{+} ground-state hyperfine manifold into two subspaces representing the two qubit states and choosing appropriate laser parameters, the protocol can be made robust to spontaneous photon scattering errors on the Raman transitions, enabling repetition for increased readout fidelity. Wedemonstrate combined readout and back-action errors for the two subspaces of 1.2_{-0.6}^{+1.1}×10^{-4} and 0_{-0}^{+1.9}×10^{-5} with 68%confidence while avoiding decoherence of spectator qubits due to stray resonant light that is inherent to direct fluorescence detection.

Model-free readout-error mitigation for quantum expectation values

Measurements on current quantum processors are subject to hardware imperfections that lead to readout errors. These errors manifest themselves as a bias in quantum expectation values. Here, we consider a very simple method that forces the bias in the expectation value to appear as a multiplicative factor that can be measured directly and removed at the cost of an increase in the sampling complexity for the observable. This method was previously discussed by Karalekas et al. [Quantum Sci. Technol. 5, 024003 (2020)] for the product of single-qubit readout-error models. Here, we formally analyze the method and show that it can be applied to general noise models. In particular, we show the method does not need to assume any specific form of the noise model and requires only that the noise is ``weak'' to avoid excessive sampling overhead. We prove bounds relating the error in the expectation value to the sample complexity.

Experimental Bayesian estimation of quantum state preparation, measurement, and gate errors in multiqubit devices

We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of each qubit's state preparation, readout, and gate errors, analyze the stability of these errors as a function of time, and demonstrate easily implemented approaches for mitigating different errors before a quantum computation experiment. On the investigated devices we find non-negligible qubit reset errors that cannot be parametrized as a diagonal mixed state, but manifest as a coherent phase of a superposition with a small contribution from the qubit's excited state. We are able to mitigate such errors by applying pre-rotations on the initialized qubits, which we demonstrate with multi-qubit entangled states. Our results demonstrate that Bayesian estimation can resolve small parameters - including those pertaining to quantum gate errors - with a high relative accuracy, at a lower measurement cost as compared with standard characterization approaches.

Real-time simulation of light-driven spin chains on quantum computers

In this work, we study the real-time evolution of periodically driven (Floquet) systems on a quantum computer using IBM quantum devices. We consider a driven Landau-Zener model and compute the transition probability between the Floquet steady states as a function of time. We find that for this simple one-qubit model, Floquet states can develop in real time, as indicated by the transition probability between Floquet states. Next, we model light-driven spin chains and compute the time-dependent antiferromagnetic order parameter. We consider models arising from light coupling to the underlying electrons as well as those arising from light coupling to phonons. For the two-spin chains, the quantum devices yield time evolutions that match the effective Floquet Hamiltonian evolution for both models once readout error mitigation is included. For three-spin chains, zero-noise extrapolation yields a time dependence that follows the effective Floquet time evolution. Therefore, the current IBM quantum devices can provide information on the dynamics of small Floquet systems arising from light drives once error mitigation procedures are implemented.

Parasitic Coupling in 3D Sequential Integration: The Example of a Two-Layer 3D Pixel

In this paper, we present a thorough analysis of parasitic coupling effects between different electrodes for a 3D Sequential Integration circuit example comprising stacked devices. More specifically, this study is performed for a Back-Side Illuminated, 4T–APS, 3D Sequential Integration pixel with both its photodiode and Transfer Gate at the bottom tier and the other parts of the circuit on the top tier. The effects of voltage bias and 3D inter-tier contacts are studied by using TCAD simulations. Coupling-induced electrical parameter variations are compared against variations due to temperature change, revealing that these two effects can cause similar levels of readout error for the top-tier readout circuit. On the bright side, we also demonstrate that in the case of a rolling shutter pixel readout, the coupling effect becomes nearly negligible. Therefore, we estimate that the presence of an inter-tier ground plane, normally used for electrical isolation, is not strictly mandatory for Monolithic 3D pixels.

Characterizing the Reproducibility of Noisy Quantum Circuits.

The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.

Active readout-error mitigation

Mitigating errors is a significant challenge for near term quantum computers. One of the most important sources of errors is related to the readout of the quantum state into a classical bit stream. A variety of techniques have been proposed to mitigate these errors with post-hoc corrections. We propose a complementary scheme to actively reduce readout errors on a shot-by-shot basis by encoding single qubits, immediately prior to readout, into multi-qubit states. The computational resources of our technique are independent of the circuit depth and fully compatible with current hardware error rates and connectivity. We analyze the potential of our approach using two types of error-correcting codes and, as a proof of principle, demonstrate an 80% improvement in readout error on the IBMQ Mumbai quantum computer.

100‐Layer Error‐Free 5D Optical Data Storage by Ultrafast Laser Nanostructuring in Glass

AbstractThe demand for energy efficient data storage technologies with high capacity and long life span is increasingly growing due to the explosion of digital information in modern society. Here, a 5D optical data storage with high capacity and ultralong lifetime is realized by femtosecond‐laser‐induced anisotropic nanopore structures (type X modification) in silica glass. The ultrahigh transmission of this birefringent modification, >99% in the visible range, allows recording and retrieving thousands of layers of multibit digital data practically. Type X formation is associated with moderate free carrier density produced close to the energy threshold of avalanche ionization. Higher retardance with increased repetition rate at low pulse energy is attributed to accumulation of defects (nonbridging oxygen hole centers), enabling rapid imprinting of voxels by megahertz‐rate pulses. Data recording of 7 bits per voxel, i.e., 25 azimuth angles and 22 retardance levels is experimentally demonstrated with readout error as small as 0.6%. Furthermore, “The Hitchhiker's Guide to the Galaxy” by Douglas Adams is optically recorded with a data writing speed of 8 kB s−1 in 100 layers of voxels and the proven data readout accuracy of 100%.

Measurement Crosstalk Errors in Cloud-Based Quantum Computing

Quantum technologies available currently contain noise in general, often dubbed noisy intermediate-scale quantum (NISQ) systems. We here present the verification of noise in measurement readout errors in cloud-based quantum computing services, IBMQ and Rigetti, by directly performing quantum detector tomography, and show that there exist measurement crosstalk errors. We provide the characterization and the quantification of noise in a quantum measurement of multiple qubits. We remark that entanglement is found as a source of crosstalk errors in a measurement of three qubits.

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices.

We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high-energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g. when variational quantum eigensolvers are used. This article is part of the theme issue 'Quantum technologies in particle physics'.

Quantum random number generator using a cloud superconducting quantum computer based on source-independent protocol

Quantum random number generator (QRNG) relies on the intrinsic randomness of quantum mechanics to produce true random numbers which are important in information processing tasks. Due to the presence of the superposition state, a quantum computer can be used as a true random number generator. However, in practice, the implementation of the quantum computer is subject to various noise sources, which affects the randomness of the generated random numbers. To solve this problem, we propose a scheme based on the quantum computer which is motivated by the source-independent QRNG scheme in optics. By using a method to estimate the upper bound of the superposition state preparation error, the scheme can provide certified randomness in the presence of readout errors. To increase the generation rate of random bits, we also provide a parameter optimization method with a finite data size. In addition, we experimentally demonstrate our scheme on the cloud superconducting quantum computers of IBM.

Qubit readout error mitigation with bit-flip averaging.

Quantum computers are becoming increasingly accessible and may soon outperform classical computers for useful tasks. However, qubit readout errors remain a substantial hurdle to running quantum algorithms on current devices. We present a scheme to more efficiently mitigate these errors on quantum hardware and numerically show that our method consistently gives advantage over previous mitigation schemes. Our scheme removes biases in the readout errors, allowing a general error model to be built with far fewer calibration measurements. Specifically, for reading out n-qubits, we show a factor of 2n reduction in the number of calibration measurements without sacrificing the ability to compensate for correlated errors. Our approach can be combined with, and simplify, other mitigation methods, allowing tractable mitigation even for large numbers of qubits.

Electron shelving of a superconducting artificial atom

Interfacing long-lived qubits with propagating photons is a fundamental challenge in quantum technology. Cavity and circuit quantum electrodynamics (cQED) architectures rely on an off-resonant cavity, which blocks the qubit emission and enables a quantum non-demolition (QND) dispersive readout. However, no such buffer mode is necessary for controlling a large class of three-level systems that combine a metastable qubit transition with a bright cycling transition, using the electron shelving effect. Here we demonstrate shelving of a circuit atom, fluxonium, placed inside a microwave waveguide. With no cavity modes in the setup, the qubit coherence time exceeds 50 μs, and the cycling transition’s radiative lifetime is under 100 ns. By detecting a homodyne fluorescence signal from the cycling transition, we implement a QND readout of the qubit and account for readout errors using a minimal optical pumping model. Our result establishes a resource-efficient (cavityless) alternative to cQED for controlling superconducting qubits.

Generation and verification of 27-qubit Greenberger-Horne-Zeilinger states in a superconducting quantum computer

Generating and detecting genuine multipartite entanglement (GME) of sizeable quantum states prepared on physical devices is an important benchmark for highlighting the progress of near-term quantum computers. A common approach to certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure a GHZ fidelity of at least 0.5. We measure the fidelities using multiple quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum ibmq_montreal device. Combinations of quantum readout error mitigation (QREM) and parity verification error detection are applied to the states. A fidelity of 0.546 ± 0.017 was recorded for a 27-qubit GHZ state when QREM was used, demonstrating GME across the full device with a confidence level of 98.6%. We benchmarked the effect of parity verification on GHZ fidelity for two GHZ state preparation embeddings on the heavy-hexagon architecture. The results show that the effect of parity verification, while relatively modest, led to a detectable improvement of GHZ fidelity.

Mitigating Crosstalk-Induced Qubit Readout Error with Shallow-Neural-Network Discrimination

Measurement for qubits plays a key role in quantum computation. Current methods for classifying states of single qubit in a superconducting multi-qubit system produce fidelities lower than expected due to the existence of crosstalk, especially in case of frequency crowding. Here, We make the digital signal processing (DSP) system used in measurement into a shallow neural network and train it to be an optimal classifier to reduce the impact of crosstalk. The experiment result shows the crosstalk-induced readout error deceased by 100% after a 3-second optimization applied on the 6-qubit superconducting quantum chip.

Accurately computing the electronic properties of a quantum ring.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform1-4. However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10-4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation5,6 and paves the way to study new quantum materials with superconducting qubits.

Quantum Nondemolition Dispersive Readout of a Superconducting Artificial Atom Using Large Photon Numbers

Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating photon number $\bar{n}$ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing $\bar{n}$ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a function of $\bar{n}$, up to $\bar{n}\approx200$. Despite the fact that we observe the expected decrease of the dispersive shift with increasing readout power, the signal-to-noise ratio continuously improves with increasing $\bar{n}$. Even without the use of a parametric amplifier, at $\bar{n}=74$, we measure fidelities of 99% and 93% for feedback-assisted ground and excited state preparation, respectively.

The hybrid topological longitudinal transmon qubit

We introduce a new hybrid qubit consisting of a Majorana qubit interacting with a transmon longitudinally coupled to a resonator. To do so, we equip the longitudinal transmon qubit with topological quasiparticles, supported by an array of heterostructure nanowires, and derive charge- and phase-based interactions between the Majorana qubit and the resonator and transmon degrees of freedom. Inspecting the charge coupling, we demonstrate that the Majorana self-charging can be eliminated by a judicious choice of charge offset, thereby maintaining the Majorana degeneracy regardless of the quasiparticles spatial arrangement and parity configuration. We perform analytic and numerical calculations to derive the effective qubit–qubit interaction elements and discuss their potential utility for state readout and quantum error correction. Further, we find that select interactions depend strongly on the overall superconducting parity, which may provide a direct mechanism to characterize deleterious quasiparticle poisoning processes.