Ramsey Experiments Optimise Detuning and Crosstalk Estimation in Quantum Processors

Maintaining the performance of quantum processors demands precise calibration of individual qubit properties, a task complicated by unwanted interactions known as crosstalk. David Shnaiderov, Matan Ben Dov, and Yoav Woldiger, from Bar-Ilan University, along with colleagues, now present a new strategy for accurately determining both qubit detuning and the extent of crosstalk between them. The team optimises standard Ramsey interference experiments, employing Fisher information and the Cramer-Rao bound to achieve the most precise parameter estimation possible. Their results demonstrate that measuring two qubit quadratures simultaneously offers superior precision and resilience compared to taking multiple measurements of a single quadrature, potentially reducing calibration time by up to 50% without sacrificing accuracy, and the approach has been successfully validated using both nitrogen-vacancy centres and transmons.

Fast, Accurate Qubit Calibration Strategies

Maintaining the performance of quantum computers requires frequent and precise calibration of individual qubits, the fundamental building blocks of these machines. Qubits, unlike classical bits, are susceptible to disturbances that cause them to drift from their intended states, necessitating constant adjustments to control fields. This calibration process is time-consuming and represents a significant bottleneck in quantum computing development. Researchers are now addressing this challenge by developing optimal strategies for qubit calibration that minimize the time required without sacrificing accuracy.

A key difficulty in calibrating qubits arises from unavoidable interactions between them, known as crosstalk. This crosstalk effectively alters the individual detuning, or frequency, of each qubit depending on the states of its neighbors, complicating the calibration process. The team’s work focuses on maximizing the information gained from each measurement, allowing for faster and more efficient calibration of both isolated qubits and those subject to crosstalk. The researchers employ a technique rooted in the principles of statistical inference, specifically using the Fisher information and the Cramér-Rao bound to determine the most effective calibration strategies.

This approach allows them to predict the precision achievable with different measurement protocols. Their analysis reveals that obtaining the highest precision does not necessarily require the most measurements; instead, strategically selecting measurement times and the type of data collected is crucial. The team’s findings demonstrate that by carefully optimizing the calibration protocol, it is possible to reduce the total calibration time by up to 50% without compromising accuracy. This improvement is achieved by maximizing the information extracted from each measurement, allowing for a more efficient use of valuable computing resources. This advancement promises to significantly accelerate the development and scalability of quantum computers by reducing the overhead associated with maintaining qubit stability and control.

Resilience to Parameter Variation Assessed

To account for the fact that optimal calibration times require knowledge of qubit parameters, specifically ω and γ, the research assumes that the detuning and decay rates change slowly over time, allowing estimation of their current values using earlier measurements. Consequently, it becomes necessary to assess the resilience of the different methods to variations in the actual values of ω and γ.

Accurate Qubit Control Reduces Calibration Time

Results predict that this approach yields the highest precision and robustness in both isolated and coupled qubits. The team validates this experimentally using a single nitrogen-vacancy (NV) center and superconducting transmons. This method enables accurate parameter extraction with a reduction of up to 50% in calibration time while maintaining estimation accuracy. Unlike classical bits, qubits cannot rely on friction to preserve a stable state. The most common motion of an idle qubit is a random rotation around the Z axis, corresponding to a progressive randomization of the phase difference between the |0⟩ and |1⟩ states. To counteract this jitteriness, quantum computing providers currently perform time-consuming calibrations on an hourly basis, delivering up-to-date values of the qubits’ rotation frequencies, or detunings, which are then used to tune the control fields used to generate quantum gates.

Ramsey Experiment Validates Parameter Estimation Strategies

Analysis of the single-qubit case concludes with experimental results from a Ramsey interference experiment, fitted using curves of the form X(t) = A cos(ωt + φ)e−γt + B. First, “ground truth” values of all parameters were determined using a long measurement with a large number of measurements and time points. Next, to allow direct comparison between strategies, A, B and φ were fixed to their “true” values, and ω and γ were determined from a random downsampling of the experimental measurements. Alternatively, the Fisher Information could be used to find the optimal strategy to probe all five fitting parameters.

The experimental results confirm theoretical predictions for the comparison between the three strategies. Moving to systems of coupled qubits relevant to quantum computers, the researchers consider a model describing qubit interactions as a static crosstalk term. For simplicity, a one-dimensional chain is considered, which is diagonal in the Z basis and can be solved analytically for any initial state. A naive approach to calibrating this system involves preparing all qubits in the |+⟩ state and performing simultaneous Ramsey interference experiments. While formally correct, this approach is not optimal due to the complex shape of the resulting functions, and generally leads to errors one order of magnitude larger than the optimal ones.

The proposed strategy involves reducing the many-body problem to that of isolated single qubits, performing two pairs of experiments to probe the detunings and the crosstalk couplings. Each experiment involves a Ramsey interference experiment on half of the qubits, for different initial states of the other qubits. Numerical results demonstrate the scalability of this protocol, as the error is essentially independent of the system size. Measuring X and Y simultaneously is optimal in this problem. This approach can be extended to quantum computers with more complex connectivity.

For bipartite lattices with nearest-neighbor couplings, all system parameters can be determined using the same four experiments as in the one-dimensional case. Interestingly, for IBM’s heavy-hex topology, four experiments are sufficient. For more complex topologies, the problem can be formulated as a tiling optimization problem, warranting further investigation. The feasibility of this approach was demonstrated by calibrating the crosstalk coupling between two transmon qubits in the Gilboa superconducting quantum computer. The experimental results demonstrate two regimes: for a small number of total measurements, the curves follow the theoretical modelling, while for larger numbers of measurements, the results saturate to a value different than the one obtained by using all measurement times. This discrepancy indicates that the experiment deviates from the simple theoretical model and can be fixed by considering more realistic models, for example, those affected by quasiparticle fluctuations.