Fast High-Fidelity Readout of a Single Trapped-Ion Qubit via Machine-Learning Methods

In this work, we introduce machine-learning (ML) methods to implement fast and high-fidelity readout of a trapped-ion qubit on a hardware module, which is based on field-programmable gate arrays (FPGAs) and an ARM (Advanced RISC Machines) processor. An average readout fidelity of 99.5% (with ${10}^5$ magnitude trials) within $171\mu \mathrm{s}$ is achieved in experiments. Different ML architectures including convolutional neural networks and fully connected neural networks are implemented to compare with traditional methods, demonstrating higher fidelity and more robust readout results in a relatively short time with the proposed methods. Our hardware implementation of the proposed ML methods with FPGAs improves the readout efficiency to a higher level, through reducing the communication time between the trapped-ion system and central processing units (CPUs) in general personal computer (PCs) and the hardware can be devolved to a functional module, which is compatible with the real-time readout and feedback control of qubit states.

Figure 1

The energy levels and single-qubit readout on the ${}^{171}{\mathrm{Yb}}^{+}$ trapped-ion system. A laser of 369.53 nm is used to excite the bright state ${}^2{S}_{1/2}\left|F=1\right.⟩$, so as to spontaneously radiate fluorescence, which can be collected via a $\mathrm{NA}=0.4$ lens and detected by the following photomultiplier tube (PMT). The output of the PMT is processed to be the photon-counting numbers for the purpose of ion-state (also called a qubit) discrimination.

Figure 2

The single-qubit dark-state and bright-state readout on the ${}^{171}{\mathrm{Yb}}^{+}$ trapped-ion system. The diagram shows the readout experiment, carried out ten times, for both dark-state (0–9) and bright-state (10–19) sequences, each with photon counts in 100 sub-bins.

Figure 3

The architecture of the CNN for single-qubit readout in a test. For the two units of the output layer, $y_1$ and $y_2$, if $y_1>y_2$, the state is inferred to be a bright state; otherwise, it is a dark state.

Figure 4

The infidelity of single-qubit readout with different numbers of sub-bins in a test. The proposed CNN method can achieve 99% accuracy within 43 sub-bins (approximately $129\mu \mathrm{s}$), while the threshold and maximum-likelihood methods need more than 80 sub-bins. And the CNN method has the more robust readout performance.

Figure 5

The fast qubit readout system as used in the experiment. (a) The scheme of the overall system. The inputs of our proposed embedded-qubit readout system are TTL signals from the PMT, which are acquired through detection of the bright-state fluorescence in the ion-trap system. The gate signal is an enable-disable signal to control the counting process. A frequency divider and a counter are implemented on a FPGA and the implementation of a feedforward neural network is programmed into the ARM processor. Every time the counter counts a photon number in a sub-bin time, the PL triggers an interrupt to stop the loop of the software program in the PS and sends the number through the registers to the PS. The parameters for the weights and the bias of the neural network are pretrained on a CPU or GPU and loaded on the Zynq development board. Whenever the PS receives a signal that denotes the end of a bin time, it automatically starts the inference process and outputs the state of the ion to the pin. (b) The waveform-sequence diagram of the controlling signals in an experiment. The 33.3-kHz clock is generated from the 100-MHz system clock and serves as the controlling signals of the counter. The extraneous 1.67-kHz gate signal sets the time window ($300\mu \mathrm{s}$ high-level voltage for the detection time) of the single-sample photon counting and it is the controlling signals of both the counter and the frequency divider. Each rising edge of the PMT signals is detected to be one photon count within a one-sub-bin time $30\mu \mathrm{s}$, which is in accordance with the period of the generated 33.3-kHz clock.

Figure 6

Detection signals measured by an oscilloscope. (a) The experimental readout of a cross-fade bright and/or dark state sequence, with seven states in scope and five detection sub-bins for each state. (b),(c) Enlarged images of signals of a dark state and a bright state, respectively. The yellow rectangular wave represents the high-level gate signals of $160\mu \mathrm{s}$ ($>30\times 5$, to ensure five detection bins) and the red $1\mu \mathrm{s}$ pulse inside the gate signal is the sampling clock sign for each sub-bin. The green triple pulse right after the high-level gate signal in (b) is the signal for a bright state; its absence indicates a dark state.

Figure 7

A comparison of the different methods for single-qubit readout with incident laser powers of $2.95\mu \mathrm{W}$ and $5.90\mu \mathrm{W}$.