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Building an analog simulator of a photonic quantum computer with transparent tape, maple syrup, and cat lasers, and implementing first quantum algorithms in the classroom

Ghislain Lefebvre

Abstract

This work presents the implementation of single-qubit gates, including $R_x$ and $R_z$ gates realized using transparent adhesive tape, and $R_y$ gates obtained with optically active maple and agave solutions. These gates form the native gate set of a simple photonic system and are subsequently used to construct a Hadamard gate. Two forms of two-qubit gates are introduced using a combination of a calcite crystal and transparent tape. The setups employ both the polarization and the path degree of freedom of a photon as qubits, illustrating how readily accessible materials can be used to manipulate and transform the quantum information they convey. Calculations are performed to determine the birefringence of two different types of tape and to quantify the specific rotations introduced by multiple layers of transparent tape. Finally, simple algorithms and exercises are proposed for students. These experimental setups are designed to facilitate hands-on manipulation of quantum effects while lowering the barrier to accessing quantum systems, with total costs kept below \$50 CAD for the single-qubit gates and below \$100 CAD for all experiments combined. The configurations presented serve as an analog simulator of a photonic quantum computer: although the laser beams used can be described classically, all theoretical considerations and experimental procedures remain valid for quantized systems employing single-photon emitters and single-photon detectors.

Building an analog simulator of a photonic quantum computer with transparent tape, maple syrup, and cat lasers, and implementing first quantum algorithms in the classroom

Abstract

This work presents the implementation of single-qubit gates, including and gates realized using transparent adhesive tape, and gates obtained with optically active maple and agave solutions. These gates form the native gate set of a simple photonic system and are subsequently used to construct a Hadamard gate. Two forms of two-qubit gates are introduced using a combination of a calcite crystal and transparent tape. The setups employ both the polarization and the path degree of freedom of a photon as qubits, illustrating how readily accessible materials can be used to manipulate and transform the quantum information they convey. Calculations are performed to determine the birefringence of two different types of tape and to quantify the specific rotations introduced by multiple layers of transparent tape. Finally, simple algorithms and exercises are proposed for students. These experimental setups are designed to facilitate hands-on manipulation of quantum effects while lowering the barrier to accessing quantum systems, with total costs kept below \100 CAD for all experiments combined. The configurations presented serve as an analog simulator of a photonic quantum computer: although the laser beams used can be described classically, all theoretical considerations and experimental procedures remain valid for quantized systems employing single-photon emitters and single-photon detectors.

Paper Structure

This paper contains 37 sections, 13 equations, 43 figures, 1 table.

Table of Contents

  1. Introduction
  2. Encoding information in the polarization of a photon
  3. Linear polarization on the x–z plane of the Bloch sphere
  4. Elliptical polarization on the x–y plane of the Bloch sphere
  5. Physical representation of the phase shift of a photon
  6. Elliptical polarization on the y–z plane of the Bloch sphere
  7. Modifying the polarization of a photon
  8. Rotation of linearly polarized photons by optically active materials
  9. Birefringence
  10. The case of calcite
  11. Materials and method for building an analog simulator of a photonic quantum computer
  12. $R_y$ gates: maple syrup and agave syrup
  13. R_x and R_z gates: transparent films
  14. R_x and R_z implementation
  15. Calibration
  16. ...and 22 more sections

Figures (43)

  • Figure 1: Linear polarization associated to various points in the x-z plane of the Bloch sphere.
  • Figure 2: Polarization of various points on the x-y plane of the Bloch sphere.
  • Figure 3: Decomposition of diagonal polarization into its horizontal and vertical components (blue arrows). The positive horizontal component coincides with the positive vertical component. The two waves are said to be in phase.
  • Figure 4: Decomposition of anti-diagonal polarization into its horizontal and vertical components. The positive horizontal component comes $\frac{\lambda}{2}$ before the positive vertical component. The two waves are said to have a phase of $\phi=\pi$ between them.
  • Figure 5: Decomposition of counterclockwise circular polarization into its horizontal and vertical components. The positive horizontal component comes $\frac{\lambda}{4}$ before the positive vertical component. The two waves are said to have a phase of $\phi=\frac{\pi}{2}$ between the two.
  • ...and 38 more figures