Posted by Kevin Miao and Matt McEwen, Research Scientists, Quantum AI Team
The qubits used in Google’s quantum devices are fragile and prone to errors. To build a useful quantum computer, we need to incorporate error correction procedures that can identify and account for these errors. The two most common types of errors are bit-flip errors, where the energy state of the qubit changes, and phase-flip errors, where the phase of the encoded quantum information changes. Quantum error correction (QEC) aims to address and mitigate these errors. However, there are other error mechanisms that pose challenges to the effectiveness of QEC.
While we would like qubits to behave as ideal two-level systems without any loss mechanisms, this is not the case in reality. We use the lowest two energy levels of our qubit, labeled |0⟩ (“ket zero”) and |1⟩ (“ket one”), as the computational basis for our computations. However, our qubits also have higher levels called leakage states, which can become occupied. These leakage states are labeled |2⟩, |3⟩, |4⟩, and so on, indicating the number of excitations in the qubit.
In our publication “Overcoming leakage in quantum error correction” in Nature Physics, we investigate how our qubits leak energy to higher states and how these leaked states can corrupt neighboring qubits during our two-qubit gate operations. We propose and implement a strategy to remove leakage and convert it into an error that can be efficiently fixed by QEC. Our results show improved performance and stability of the QEC process, which is crucial considering that additional operations often lead to more errors.
Our quantum processors are built from superconducting qubits called transmons. Unlike ideal qubits with only two computational levels, transmon qubits have additional states with higher energy. These higher leakage states are useful for certain operations that generate entanglement, a necessary resource in quantum algorithms, and also help prevent the qubits from becoming too non-linear and difficult to operate. However, the transmon qubits can unintentionally be excited into leakage states due to imperfections in control pulses or residual heat in the cryogenic refrigerator. This transition from computational states to leakage states is collectively referred to as leakage.
One of the key operations we use in our QEC experiments is the CZ gate, which operates on two qubits. When both qubits are in the |1⟩ level, the CZ gate causes the excitations to briefly “bunch” together in one qubit, forming the |2⟩ state, while the other qubit becomes the |0⟩ state, before returning to the original configuration where both qubits are in the |1⟩ state. This bunching is what enables the CZ gate to entangle the qubits. However, there is a small probability of error where the excitations do not return to their original configuration, leaving one qubit in the |2⟩ leakage state. With multiple CZ gates, this small leakage error probability accumulates. The transmon qubits support many leakage states beyond the computational basis, and when a qubit enters these leakage states, it disrupts the normal operation of our qubits. A single leakage event can cause many individual errors, preventing correct execution of the algorithm. Furthermore, CZ gates applied to a qubit in a leakage state can cause the neighboring qubit to leak as well.
Leakage poses challenges to our QEC strategies, which aim to mitigate qubit errors by applying operations to a collection of imperfect physical qubits to form a logical qubit with properties closer to an ideal qubit. QEC assumes that errors occur independently for each operation, but leakage can persist over many operations and cause a correlated pattern of errors. Leakage also spreads between different qubits through CZ gates, resulting in space- and time-correlated errors that are difficult to diagnose and correct using QEC algorithms.
In our previous work, we developed a method called multi-level reset (MLR) to remove leakage from measure qubits. However, MLR cannot be used with data qubits because they hold important quantum information. Therefore, we introduce a new operation called data qubit leakage removal (DQLR) that targets leakage states in data qubits and converts them into computational states in the data qubit and a neighboring measure qubit. DQLR consists of a two-qubit gate called Leakage iSWAP, similar to the CZ gate, followed by a rapid reset of the measure qubit to remove errors. DQLR effectively reduces the average population of leakage states in all qubits to about 0.1%, compared to nearly 1% without it. This approach minimally disturbs the computational basis states of the data qubits.
Overall, our research focuses on identifying and addressing leakage in quantum error correction to improve the performance and stability of our quantum processors. By understanding how leakage occurs and interacts with our operations, we can develop strategies to mitigate its effects and enhance the reliability of quantum computations.
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