Population in the leakage states builds up as operations are applied, which increases the error of subsequent operations and even causes other nearby qubits to leak as well - resulting in a particularly challenging source of correlated error. We use the higher energy states ( |2 ⟩, |3 ⟩ and higher) to help achieve high-fidelity entangling operations, but these entangling operations can sometimes allow the qubit to “leak” into these higher states, earning them the name leakage states. We use the two lowest energy states to encode our qubit with information to be used for computation (we call these the computational states). While a qubit needs only two energy states, which are usually labeled |0 ⟩ and |1 ⟩, our devices feature a ladder of energy states, |0 ⟩, |1 ⟩, |2 ⟩, |3 ⟩, and so on. However, one key challenge stems from how we make qubits out of superconducting circuits. When the measured parities change between rounds, we’ve detected an error. We repeat this process over and over in rounds that last only one microsecond. It does so by entangling each pair of data qubits with their shared measure qubit in a way that tells us whether those data qubit states are the same or different (i.e., their parity) without telling us the states themselves. The goal of the repetition code is to detect errors on the data qubits without measuring their states directly. Layout of the repetition code (21 qubits, 1D chain) and distance-2 surface code (7 qubits) on the Sycamore device. Then, in “ Exponential suppression of bit or phase flip errors with repetitive error correction”, published in Nature, we show that the logical errors of these repetition codes are exponentially suppressed as we add more and more physical qubits, consistent with expectations from QEC theory. In “ Removing leakage-induced correlated errors in superconducting quantum error correction”, published in Nature Communications, we use these repetition codes to demonstrate a new technique for reducing the amount of correlated errors in our physical qubits. While these repetition codes can only correct for one kind of quantum error at a time 1, they contain all of the same ingredients as more sophisticated error correction codes and require fewer physical qubits per logical qubit, allowing us to better explore how logical errors decrease as logical qubit size grows. These codes consist of one-dimensional chains of qubits that alternate between data qubits, which encode the logical qubit, and measure qubits, which we use to detect errors in the logical state. Our team has recently implemented the ideas of QEC in our Sycamore architecture using quantum repetition codes. Such correlated errors produce more complex patterns of error detections that are more difficult to correct and more easily cause logical errors. In particular, it’s important to suppress correlated errors, where one physical error simultaneously affects many qubits at once or persists over many cycles of error correction. This exponential scaling behavior relies on physical qubit errors being sufficiently rare and independent. While logical errors may still occur if a series of physical qubits experience an error together, this error rate should exponentially decrease with the addition of more physical qubits (more physical qubits need to be involved to cause a logical error). When a physical error occurs, one can detect it by repeatedly checking certain properties of the qubits, allowing it to be corrected, preventing any error from occurring on the logical qubit state. The core idea of QEC is to make a logical qubit by distributing its quantum state across many physical data qubits. Bridging this tremendous gap in error rates will require more than just making better qubits - quantum computers of the future will have to use quantum error correction (QEC). However, current generation quantum processors still have high operational error rates - in the range of 10 -3 per operation, compared to the 10 -12 believed to be necessary for a variety of useful algorithms. The Google Quantum AI team has been building quantum processors made of superconducting quantum bits ( qubits) that have achieved the first beyond-classical computation, as well as the largest quantum chemical simulations to date. Posted by Jimmy Chen, Quantum Research Scientist and Matt McEwen, Student Researcher, Google Quantum AI
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