Characterizing non-Markovian Quantum Process by Fast Bayesian Tomography
Su, R. Y., J. Y. Huang, Nard Dumoulin Stuyck, M. K. Feng, W. Gilbert, T. J. Evans, Wee Han Lim, Fay E. Hudson, Chan, K. W., Huang, W., Kohei M. Itoh, Robin Harper, Stephen D. Bartlett, C. H. Yang, Arne Laucht, André Saraiva, Tuomo Tanttu, Andrew S. Dzurak
To push gate performance to levels beyond the thresholds for quantum error correction, it is important to characterize the error sources occurring on quantum gates. However, the characterization of non-Markovian error poses a challenge to current quantum process tomography techniques. Fast Bayesian Tomography (FBT) is a self-consistent gate set tomography protocol that can be bootstrapped from earlier characterization knowledge and be updated in real-time with arbitrary gate sequences. Here we demonstrate how FBT allows for the characterization of key non-Markovian error processes. We introduce two experimental protocols for FBT to diagnose the non-Markovian behavior of two-qubit systems on silicon quantum dots. To increase the efficiency and scalability of the experiment-analysis loop, we develop an online FBT software stack. To reduce experiment cost and analysis time, we also introduce a native readout method and warm boot strategy. Our results demonstrate that FBT is a useful tool for probing non-Markovian errors that can be detrimental to the ultimate realization of fault-tolerant operation on quantum computing.
To push gate performance to levels beyond the thresholds for quantum error correction, it is important to characterize the error sources occurring on quantum gates. However, the characterization of non-Markovian error poses a challenge to current quantum process tomography techniques. Fast Bayesian Tomography (FBT) is a self-consistent gate set tomography protocol that can be bootstrapped from earlier characterization knowledge and be updated in real-time with arbitrary gate sequences. Here we demonstrate how FBT allows for the characterization of key non-Markovian error processes. We introduce two experimental protocols for FBT to diagnose the non-Markovian behavior of two-qubit systems on silicon quantum dots. To increase the efficiency and scalability of the experiment-analysis loop, we develop an online FBT software stack. To reduce experiment cost and analysis time, we also introduce a native readout method and warm boot strategy. Our results demonstrate that FBT is a useful tool for probing non-Markovian errors that can be detrimental to the ultimate realization of fault-tolerant operation on quantum computing.
To push gate performance to levels beyond the thresholds for quantum error correction, it is important to characterize the error sources occurring on quantum gates. However, the characterization of non-Markovian error poses a challenge to current quantum process tomography techniques. Fast Bayesian tomography (FBT) is a self-consistent tomographic protocol that can be bootstrapped from earlier characterization knowledge and be updated in real time with arbitrary gate sequences. Here we demonstrate how FBT allows for the characterization of key non-Markovian error processes. We introduce two experimental protocols for FBT to diagnose the non-Markovian behavior of two-qubit systems on silicon quantum dots. To increase the efficiency and scalability of the experiment-analysis loop, we develop a web-based FBT software stack. To reduce experiment cost and analysis time, we also introduce a native readout method and warm boot strategy. Our results demonstrate that FBT is a useful tool for probing non-Markovian errors that can be detrimental to the ultimate realization of fault-tolerant operation on quantum computing.
Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. We develop a data-driven learning protocol for characterizing quantum gates that builds off previous work on learning the Nakajima-Mori-Zwanzig (NMZ) formulation of open system dynamics from time series data, which allows detailed reconstruction of quantum evolution, including non-Markovian dynamics. We demonstrate this learning technique on three different systems: a simulation of a qubit whose dynamics are purely Markovian, a simulation of a driven qubit coupled to stochastic noise produced by an Ornstein-Uhlenbeck process, and trapped-ion experimental data of a driven qubit whose noise environment is not characterized ahead of time. Our technique is able to learn the generators of time evolution, or the NMZ operators, in all three cases and can learn the timescale in which the qubit dynamics can no longer be accurately described by a purely Markovian model. Our technique complements existing quantum gate characterization methods such as gate set tomography by explicitly capturing non-Markovianity in the gate generator, thus allowing for more thorough diagnosis of noise sources.
Complete characterization of the errors that occur in using sets of logic gates is critical to developing the technology of fault-tolerant quantum computing, but current tomography methods are either slow or include unchecked assumptions. This study presents a self-consistent method for process tomography that is both fast and flexible. The technique complements the broad suite of existing characterization tools, and may potentially allow for pulse optimization to further increase gate fidelities.
As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate-set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one- and two-qubit gates can be compressed by 10× and 100× , respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two-qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large arrays of quantum devices with non-Markovian noise. Published by the American Physical Society 2024
Engineering of quantum computers requires reliable characterization of qubits, quantum operations, and even the entire hardware. Quantum tomography is an indispensable framework in quantum characterization, verification, and validation (QCVV), which has been widely accepted by researchers. According to the tomographic target, quantum tomography can be categorized into quantum state tomography (QST), quantum process tomography (QPT), gate set tomography (GST), process tensor tomography (PTT), and instrument set tomography (IST). Standard quantum tomography toolkits generally consist of basic linear inverse methods and statistical maximum likelihood estimation (MLE) based methods. Furthermore, the performance of standard methods, including effectiveness and efficiency, has been further developed by exploiting Bayesian estimation, neural networks, matrix completion techniques, etc. In this review, we introduce the fundamental quantum tomography techniques, including QST, QPT, GST, PTT, and IST. We first introduce the details of basic linear inverse methods. Then, the framework of MLE methods with constraints is summarized. Finally, we briefly introduce recent further research in developing the performance of tomography. This review provides a primary getting-start in developing quantum tomography, which promotes quantum computer development.
Characterizing errors on many-qubit quantum computers remains a key challenge to understanding and improving the performance of these devices. Current characterization methods either don't scale beyond a few qubits, or make simplifying assumptions (such as assuming stochastic Pauli error) that obscure the underlying physical error mechanisms. In this work, we present a scalable extension to gate set tomography-linearized gate set tomography-that enables characterization of many-qubit systems. Linearized gate set tomography relies on sparse error models, a linear approximation to enable efficient data fitting, and data from shallow circuits-so that the systematic error in the linear approximation is small. We demonstrate the accuracy of our technique using simulations of a ten-qubit system with coherent and stochastic errors, including coherent crosstalk, and we demonstrate that it is robust in presence of additional errors that are not included within the sparse error model ansatz.