Single-shot readout is a key component for scalable quantum information processing. However, many solid-state qubits with favorable properties lack the single-shot readout capability. One solution is to use the repetitive quantum-non-demolition readout technique, where the qubit is correlated with an ancilla, which is subsequently read out. The readout fidelity is therefore limited by the back-action on the qubit from the measurement. Traditionally, a threshold method is taken, where only the total photon count is used to discriminate qubit state, discarding all the information of the back-action hidden in the time trace of repetitive readout measurement. Here we show by using machine learning (ML), one obtains higher readout fidelity by taking advantage of the time trace data. ML is able to identify when back-action happened, and correctly read out the original state. Since the information is already recorded (but usually discarded), this improvement in fidelity does not consume additional experimental time, and could be directly applied to preparation-by-measurement and quantum metrology applications involving repetitive readout.
IntroductionSingle-shot readout is a key component for scalable quantum information processing [1, 2], for its close connection to state initialization and fault-tolerant quantum error correction [3]. Indeed, it is one of the main deciding factors in the selection of potential qubits. Single-shot readout has been achieved in various physical qubit systems, ranging from neutral atoms [4][5][6], to trapped ions [7], superconducting qubit [8], and solid-state defect centers [9][10][11][12][13][14][15][16]. There are however situations where a candidate qubit has favorable coherence properties, but does not naturally come with single-shot readout capabilities. Examples include Al + ions [17,18] and roomtemperature nitrogen-vacancy (NV) centers in diamond [12][13][14][15][16], where a closed optical cycle for readout is either lacking, or experimentally challenging. A solution to this problem is through repetitive quantum-nondemolition (QND) measurements [18].In the repetitive QND protocol, a controlled-NOT (CNOT) gate is applied to correlate the qubit state to an ancilla, which is subsequently read out ( figure 1(a)). If the readout operator commutes with the qubit's intrinsic Hamiltonian, in other words, if the readout is QND, one can repeat the above process multiple times to increase signal-to-noise ratio, until the desired fidelity is reached.This protocol is also known as the repetitive readout technique widely adopted in NV research at roomtemperature, where the nuclear spin state (here the 14 N or a 13 C) is repetitively read out with the help of the NV electronic spin [12,19]. In its implementations so far, the spin state was determined by comparing the total photon number collected through all the repetitive readouts with a previously established threshold ( figure 1(b)). The detected photon count numbers are thus divided into two classes, referred to as bright (dark) state of the...