Gleb Struchalin. Adaptive Methods in Quantum Tomography (2024)

The given thesis subject is quantum tomography protocols for states and processes. The goal is to experimentally validate and develop adaptive tomography protocols to improve the reconstruction accuracy of unknown quantum states or processes compared to existing approaches. Spontaneous parametric down conversion in nonlinear crystals was used to prepare quantum states. The thesis results can be applied in the practical implementation of quantum computing devices and their debugging. This thesis demonstrated experimentally that the adaptive Bayesian tomography method has a higher accuracy in reconstructing unknown quantum states and processes compared to a random measurement strategy. Also, this adaptive method is less susceptible to hardware errors. A high-dimensional two-component system tomography algorithm was developed and experimentally validated, and a shadow tomography method was also investigated.

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Ivan Bobrov. Spatial Correlations in Biphotonic and Classical Fields (2017)

This thesis is devoted to studying the spatial correlation properties of spontaneous parametric down-conversion. The thesis also proposes an original method for spatial-mode-detector tomography and examines quantum interference in a Young scheme.

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Konstantin Katamadze. Controlling the Biphoton Field Frequency-Angular Spectrum (2013)

This thesis is devoted to the new methods development for controlling the frequency-angular spectrum of a biphoton field, an experimental and theoretical study of these methods capabilities, and a comparison with the existing methods.

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Stanislav Straupe. Correlation Properties of High-Dimensional Quantum States Based on Biphoton Fields (2011)

This thesis is devoted to the experimental study of multilevel quantum systems implemented using various biphoton-field degrees of freedom. Issues related to quantum state preparation and measurement are considered in their possible use context in various quantum information protocols.

Alexey Moiseevskiy. Analysis of Randomized Algorithms for Realistic Quantum Computer Models (2020)

The thesis examines the methods for determining practical quantum supremacy boundaries. This task is designed to demonstrate the existence of supremacy for specific cases. The original part involves implementation of a cold-atom quantum computer emulator, developing a realistic noise model, and conducting mathematical modeling to determine the supremacy boundary for promising quantum computers of this type. The dynamics of the quantum register state under the influence of various types of errors is also studied. As a result, it was demonstrated that quantum supremacy for quantum computers with this type of hardware architecture is achievable with only a few dozen qubits in the register. These values ​​are realistic and quite feasible in practice.

Sergey Samoylenko. Quantum Registers with Individual Addressing Based on Single Neutral Atoms in Optical Microtraps (2018)

The following objectives were stated in this graduate thesis:

1. Phase masks generation for a spatial phase light modulator using various methods:
   • Using the Gerchberg–Saxton algorithm
   • Pixel-by-pixel mixing of Fourier planes
2. Single atoms visualization in dipole traps using various methods:
   • Using a scanning mirror
   • Using a CCD camera
3. Single atom arrays reconfiguration by creating dynamic phase holograms

The thesis goal was to develop a method for creation of ordered single-atom arrays with arbitrary configuration.

Ivan Pogorelov. Optical Mode Transformation Using Reconfigurable Integrated Optical Interferometers (2018)

The thesis examines the methods for creating and characterizing linear optical converters based on integrated photonics. An integrated photonic device capable of converting photonic states is studied theoretically and experimentally, the device's capabilities are tested, and methods for efficient control are developed.

Ivan Pogorelov. Adaptive Bayesian Tomography in High-Dimensional Systems (2016)

The thesis examines the application of Bayesian statistical methods for the problem of quantum process tomography. The goal was to implement an adaptive Bayesian process tomography algorithm with subsequent application for experimental tomography of polarization transformation in integrated optical chips.

Egor Kovlakov. Controlling the Spatial Modes Spectrum of a Biphoton Field (2014)

The thesis presents a review of articles devoted to controlling the angular spectrum of SPDC biphotons by generating a pump beam in spatial transverse Hermite—Gauss and Laguerre—Gauss modes. Special attention is given to focusing the pump beam into the crystal and its influence on the number of modes generated in spontaneous parametric down conversion. The original part discusses the experiment to study cross-correlations between the spatial modes of signal and idler photons in the Hermite—Gauss basis, including the transformation of the pump mode into lower Hermite—Gauss modes with subsequent generation of Bell states based on the photon's spatial degrees of freedom.

Struchalin Gleb. Adaptive Bayesian Tomography of Polarization Ququart States (2014)

The thesis is devoted to the experimental implementation of an adaptive Bayesian tomography protocol. The algorithm allows tomography of high-dimensional states. The experimental implementation was conducted for four-dimensional systems (ququarts). The ququart is the polarization state of a photon pair produced during spontaneous parametric down conversion (SPDC) in two nonlinear crystals with mutually perpendicular axes.

Dyakonov Ivan. Controlling the Frequency-Angular Spectrum of a Biphoton Field via Angular Dispersion (2013)

One of the fundamental problems in modern physics is control of quantum system parameters. There are many quantum systems of diverse natures, one of which is a biphoton field generated during spontaneous parametric down conversion. The problems involving a biphoton field require precise control of its spectral characteristics, the task of finding a method for controlling the frequency spectrum of a biphoton field arises. In the review part, the main methods for broadening the frequency spectrum of a biphoton field are presented, as well as the main tasks requiring the use of a biphoton field with a broad spectrum. In the original thesis section, a new method for creating a biphoton field with a broad frequency spectrum concentrated in a single angular mode is proposed.

Konstantin Katamadze. Biphoton Field Spectrum Control by Non-Uniform Crystal Heating(2009)

The thesis reviews and systematizes currently existing methods for controlling the biphoton spectrum, as well as it explores the spectrum broadening possibilities by the crystal nonuniform heating where biphotons are generated through SPDC. In conclusion, the thesis demonstrates the advantages and disadvantages of the given method compared to the previously implemented ones.

Stanislav Straupe. Two-mode Biphoton Polarization States: Preparation, Transformation, and Application in Quantum Information Protocols (2008)

The thesis goal is to develop methods for experimental preparation of arbitrary four-level quantum systems states (ququarts). Two-mode biphoton polarization states were used to realize ququarts experimentally. The proposed methods have found their application in the deterministic quantum key distribution protocol implementation.

Struchalin G. I. Flat-top beams (2025)

The tutorial considers beams with flat intensity and phase profiles. The flat-top beams are constructed as a superposition of the lowest-order Hermite—Gauss modes (rectangular shape) or Laguerre—Gauss modes (circular shape). Explicit expressions for the beam complex amplitude and the superposition coefficients are presented. Also, the Fourier transform of the obtained profiles is calculated. The lower bound on power losses is derived when the beam is formed by phase-only holograms.