# Arbitrary Configurable 20-Channel Coincidence Counting Unit for Multi-Qubit Quantum Experiment

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{3}. In Figure 5, 20 input ports and a USB port for data transmission are placed at front and back sides, respectively, of the packaged box. For experiments demanding more than 20 inputs, the function of the CCU could be made affordable by exchanging the upper version of an FPGA. In fact, 20 channels of the CCU consumed only 10% of the LEs with the Stratix family FPGA. Additionally, the CCU could be developed with an Artix, Kintex, or Virtex family FPGA from different vendors because it only used less than 20,000 conventional logic elements and not special elements.

## 3. Experiments

_{C}using the following equation:

_{C}= R

_{AB}/(R

_{A}· R

_{B})

_{A}, R

_{B}, and R

_{AB}are single counts of channels A and B and their accidental coincidence counts, respectively. Figure 7b shows the experimental results (dots) and the fitting data (lines). The coincidence windows with pulse reshaping steps of 2, 6, and 10 were set to 0.3 ns, 1.3 ns, and 2.8 ns, respectively. There were some negligible errors of the coincidence time window with the experimental results of Figure 7a,b, which resulted due to different shapes of the input pulses. We used a square wave for the experiment shown in Figure 7a, but Gaussian pulses were applied as inputs for the experiment shown in Figure 7b.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Overall architecture of the coincidence counting unit (CCU). All the required functional blocks are implemented in a low-end field-programmable gate array (FPGA). The processor controls all the functional blocks and transfers data to a personal computer via a USB connection. All the parameters can be controlled with the graphical user interface (GUI) software.

**Figure 2.**(

**a**) Schematic of the pulse-reshaping block and timing diagram for (

**b**) shortening the pulse width, (

**c**) widening the pulse width, and (

**d**) a malfunction case.

**Figure 3.**Schematic of the coincidence signal generator. It consists of 20 input AND gates and multiplexers (MUXs). Each AND gate generates a coincidence signal, and the MUXs determine the combination of inputs for the coincidence output.

**Figure 7.**(

**a**) Coincidence probability versus the time interval between two input pulses with three coincidence time windows (T

_{C}). (

**b**) Accidental coincidence counting rates of the different coincidence time windows versus the average input count rates.

**Figure 8.**(

**a**) Four arbitrary generated inputs and (

**b**) its 4 single and 20 coincidence counts displayed on the GUI program.

**Figure 9.**Twentyfold coincidence probability versus the time delay between one input and the other inputs.

Resource | Utilization/Available |
---|---|

Total logic elements | 17,476/22,320 (78%) |

Registers | 4101/22,320 (18%) |

Pins | 27/154 (18%) |

Memory | 279,552/608,256 (46%) |

PLL | 1/4 (25%) |

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**MDPI and ACS Style**

Park, B.K.; Kim, Y.-S.; Cho, Y.-W.; Moon, S.; Han, S.-W. Arbitrary Configurable 20-Channel Coincidence Counting Unit for Multi-Qubit Quantum Experiment. *Electronics* **2021**, *10*, 569.
https://doi.org/10.3390/electronics10050569

**AMA Style**

Park BK, Kim Y-S, Cho Y-W, Moon S, Han S-W. Arbitrary Configurable 20-Channel Coincidence Counting Unit for Multi-Qubit Quantum Experiment. *Electronics*. 2021; 10(5):569.
https://doi.org/10.3390/electronics10050569

**Chicago/Turabian Style**

Park, Byung Kwon, Yong-Su Kim, Young-Wook Cho, Sung Moon, and Sang-Wook Han. 2021. "Arbitrary Configurable 20-Channel Coincidence Counting Unit for Multi-Qubit Quantum Experiment" *Electronics* 10, no. 5: 569.
https://doi.org/10.3390/electronics10050569