# High-Precision Voltage Measurement for Optical Quantum Computation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Quantum Description of Optical Phenomena

#### 2.2. Experimental Setup

## 3. Results

#### 3.1. Experimental Setup for QCoSamp

- The optical path for a given nonlinear unit is extended by the Mach–Zehnder interferometer;
- The light phase is calibrated using the adjustable phase shifter until both outputs from the interferometer have the same intensity.

#### 3.2. Implementation of the QCoSamp Component Using the MSO

## 4. Discussion and Conclusions

- The detection of the temporal correlation of four or more photons in two polarization states. Our setup requires a specific detector for the ququartits’ states. For example, the state |00〉 must be detected by observing the remainder of the system. However, states with two photons on the same rail with the same polarization, such as |20〉, were rejected, as they are not required for computations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Knill, E.; Laflamme, R.; Milburn, G.J. A scheme for efficient quantum computation with linear optics. Nature
**2001**, 409, 46–52. [Google Scholar] [CrossRef] [PubMed] - Bourassa, J.E.; Alexander, R.N.; Vasmer, M.; Patil, A.; Tzitrin, I.; Matsuura, T.; Su, D.; Baragiola, B.Q.; Guha, S.; Dauphinais, G.; et al. Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer. Quantum
**2021**, 5, 392. [Google Scholar] [CrossRef] - Mirrahimi, M.; Leghtas, Z.; Albert, V.V.; Touzard, S.; Schoelkopf, R.J.; Jiang, L.; Devoret, M.H. Dynamically protected cat-qubits: A new paradigm for universal quantum computation. New J. Phys.
**2014**, 16, 045014. [Google Scholar] [CrossRef] - Wereszczyński, K.; Michalczuk, A.; Pęszor, D.; Paszkuta, M.; Cyran, K.; Polański, A. Cosine series quantum sampling method with applications in signal and image processing. arXiv
**2020**, arXiv:2011.12738. [Google Scholar] - Bruzewicz, C.D.; Chiaverini, J.; McConnell, R.; Sage, J.M. Trapped-ion quantum computing: Progress and challenges. Appl. Phys. Rev.
**2019**, 6, 021314. [Google Scholar] [CrossRef][Green Version] - Huang, H.L.; Wu, D.; Fan, D.; Zhu, X. Superconducting Quantum Computing: A Review. arXiv
**2020**, arXiv:2006.10433. [Google Scholar] [CrossRef] - Benhelm, J.; Kirchmair, G.; Rapol, U.; Körber, T.; Roos, C.F.; Blatt, R. Measurement of the hyperfine structure of the S
_{1/2}–D_{5/2}transition in^{43}Ca^{+}. Phys. Rev.**2007**, 75, 032506. [Google Scholar] [CrossRef][Green Version] - Okamoto, R.; O’Brien, J.L.; Hofmann, H.F.; Takeuchi, S. Realization of a Knill-Laflamme-Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities. Proc. Natl. Acad. Sci. USA
**2011**, 108, 10067–10071. [Google Scholar] [CrossRef][Green Version] - Okoth, C.; Cavanna, A.; Santiago-Cruz, T.; Chekhova, M. Microscale Generation of Entangled Photons without Momentum Conservation. Phys. Rev. Lett.
**2019**, 123, 263602. [Google Scholar] [CrossRef][Green Version] - Santiago-Cruz, T.; Sultanov, V.; Zhang, H.; Krivitsky, L.A.; Chekhova, M.V. Entangled photons from subwavelength nonlinear films. Opt. Lett.
**2021**, 46, 653. [Google Scholar] [CrossRef] - Borregaard, J.; Pichler, H.; Schröder, T.; Lukin, M.D.; Lodahl, P.; Sørensen, A.S. One-Way Quantum Repeater Based on Near-Deterministic Photon-Emitter Interfaces. Phys. Rev. X
**2020**, 10, 021071. [Google Scholar] [CrossRef] - Schimpf, C.; Reindl, M.; Basso Basset, F.; Jöns, K.D.; Trotta, R.; Rastelli, A. Quantum dots as potential sources of strongly entangled photons: Perspectives and challenges for applications in quantum networks. Appl. Phys. Lett.
**2021**, 118, 100502. [Google Scholar] [CrossRef] - Wang, J.; Long, Y. On-chip silicon photonic signaling and processing: A review. Sci. Bull.
**2018**, 63, 1267–1310. [Google Scholar] [CrossRef][Green Version] - Killoran, N.; Izaac, J.; Quesada, N.; Bergholm, V.; Amy, M.; Weedbrook, C. Strawberry Fields: A Software Platform for Photonic Quantum Computing. Quantum
**2019**, 3, 129. [Google Scholar] [CrossRef][Green Version] - Ruiz-Perez, L.; Garcia-Escartin, J.C. Quantum arithmetic with the quantum Fourier transform. Quantum Inf. Process.
**2017**, 16, 1–14. [Google Scholar] [CrossRef] - Grover, L.K. A fast quantum mechanical algorithm for database search. In Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing—STOC ’96, Philadelphia, PA, USA, 22–24 May 1996; ACM Press: Philadelphia, PA, USA, 1996; pp. 212–219. [Google Scholar] [CrossRef][Green Version]
- Brassard, G.; Hoyer, P. An Exact Quantum Polynomial-Time Algorithm for Simon’s Problem. In Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems, Ramat-Gan, Israel, 17–19 June 1997; pp. 12–23. [Google Scholar] [CrossRef][Green Version]
- Viola, P.; Jones, M. Rapid object detection using a boosted cascade of simple features. In Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2001, Kauai, HI, USA, 8–14 December 2001; Volume 1, pp. I-511–I-518. [Google Scholar] [CrossRef]
- Buhrman, H.; Cleve, R.; Watrous, J.; de Wolf, R. Quantum Fingerprinting. Phys. Rev. Lett.
**2001**, 87, 167902. [Google Scholar] [CrossRef][Green Version] - Kok, P.; Munro, W.J.; Nemoto, K.; Ralph, T.C.; Dowling, J.P.; Milburn, G.J. Review article: Linear optical quantum computing. Rev. Mod. Phys.
**2007**, 79, 135–174. [Google Scholar] [CrossRef][Green Version] - Hong, C.K.; Ou, Z.Y.; Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett.
**1987**, 59, 2044–2046. [Google Scholar] [CrossRef][Green Version] - Magnitskiy, S.; Frolovtsev, D.; Firsov, V.; Gostev, P.; Protsenko, I.; Saygin, M. A SPDC-Based Source of Entangled Photons and its Characterization. J. Russ. Laser Res.
**2015**, 36, 618–629. [Google Scholar] [CrossRef] - Wang, X.L.; Chen, L.K.; Li, W.; Huang, H.L.; Liu, C.; Chen, C.; Luo, Y.H.; Su, Z.E.; Wu, D.; Li, Z.D.; et al. Experimental Ten-Photon Entanglement. Phys. Rev. Lett.
**2016**, 117, 210502. [Google Scholar] [CrossRef] - Zhong, H.S.; Li, Y.; Li, W.; Peng, L.C.; Su, Z.E.; Hu, Y.; He, Y.M.; Ding, X.; Zhang, W.; Li, H.; et al. 12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion. Phys. Rev. Lett.
**2018**, 121, 250505. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ji, Y.; Chung, Y.; Sprinzak, D.; Heiblum, M.; Mahalu, D.; Shtrikman, H. An electronic Mach–Zehnder interferometer. Nature
**2003**, 422, 415–418. [Google Scholar] [CrossRef] [PubMed][Green Version] - Rarity, J.; Tapster, P.; Jakeman, E.; Larchuk, T.; Campos, R.; Teich, M.; Saleh, B. Two-photon interference in a Mach-Zehnder interferometer. Phys. Rev. Lett.
**1990**, 65, 1348–1351. [Google Scholar] [CrossRef] [PubMed] - Guo, X.; Meng, Z.; Li, J.; Yang, J.Z.; Aili, M.; Zhang, A.N. The interference properties of single-photon vortex beams in Mach–Zehnder interferometer. Appl. Phys. Lett.
**2021**, 119, 011103. [Google Scholar] [CrossRef] - Heinrich, S.; Novak, E. On a problem in quantum summation. J. Complex.
**2003**, 19, 1–18. [Google Scholar] [CrossRef][Green Version] - Harrow, A.W.; Hassidim, A.; Lloyd, S. Quantum Algorithm for Linear Systems of Equations. Phys. Rev. Lett.
**2009**, 103, 150502. [Google Scholar] [CrossRef]

**Figure 1.**Experimental setup for six-photon entanglement. Firstly, two pairs of photons are generated by nonlinear units (NUs) in series. Following this, one photon from each pair reconnects with the remaining section of the system via the polarization beam splitter. From the reconnection points, entanglement propagates throughout the entire system, generating the GHZ state.

**Figure 2.**Experimental setup, showing (

**left**) the main optical setup (MOS) and (

**right**) the Fock state interpretation. The SPDC implemented by the nonlinear unit (NU), the beam splitter (BS), and the phase shifter (PS) are all indicated. The signal and output rails of the first NU are highlighted in red (1) and orange (2), respectively. The signal and output rails of the second NU are highlighted in dark blue (3) and light blue (4), respectively. The number of each output rail is shown, circled. The crossing of lines depicted in the setup should not occur in the actual experiment. The signal and output rails of each NU contain the stream of entangled photon pairs in the state $\frac{|HV\rangle +{e}^{i\delta}|VH\rangle}{\sqrt{2}}$ [22]. Each pair of photons then passes through a 50:50 beam splitter. Due to the Hong–Ou–Mandel effect, the photons group in one of the beam splitter outputs, and so, the output produces |20〉 or |02〉 states. The final state is the tensor product of these two states, giving |2000〉, |0200〉, |0020〉, or |0002〉. However, this description of the state is insufficient: the entanglement within the polarization domain generated by the cross-Kerr nonlinearities is not covered here. Therefore, we propose the state notation presented on the right. The ket has two slots for each mode: one for horizontal polarisation, one for vertical polarization. We will henceforth refer to this as rail-polarization (RP) notation.

**Figure 4.**Diagram showing (

**left**) the optical path and (

**right**) the tables of coefficients for the two states corresponding to the path.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wereszczyński, K.; Michalczuk, A.; Paszkuta, M.; Gumiela, J.
High-Precision Voltage Measurement for Optical Quantum Computation. *Energies* **2022**, *15*, 4205.
https://doi.org/10.3390/en15124205

**AMA Style**

Wereszczyński K, Michalczuk A, Paszkuta M, Gumiela J.
High-Precision Voltage Measurement for Optical Quantum Computation. *Energies*. 2022; 15(12):4205.
https://doi.org/10.3390/en15124205

**Chicago/Turabian Style**

Wereszczyński, Kamil, Agnieszka Michalczuk, Marcin Paszkuta, and Jacek Gumiela.
2022. "High-Precision Voltage Measurement for Optical Quantum Computation" *Energies* 15, no. 12: 4205.
https://doi.org/10.3390/en15124205