Entropic property of randomized QAOA circuits

Quantum approximate optimization algorithm (QAOA) aims to minimize some binary objective function by sampling bitstrings using a parameterized quantum circuit. In contrast to common optimization-based methods for searching circuit parameters (angles), here we consider choosing them at random. Despite the fact that this approach does not outperform classical algorithms for quadratic unconstrained spin optimization (QUSO) problems, including Max-Cut, it surprisingly provides an advantage over the classical random search. Investigation of this effect has led us to the following conjecture: given the probability distribution of obtaining distinct objective values, random parameters QAOA for QUSO problems always gives a higher entropy of this distribution than the classical random search. We also provide an analytical expressions for the distribution

The study of amplitude and phase relaxation impact on the quality of quantum information technologies

The influence of amplitude and phase relaxation on evolution of quantum states within the formalism of quantum operations is considered. The model of polarizing qubits where noises are determined by the existence of spectral degree of freedom that shows up during the light propagation inside anisotropic mediums with dispersion is studied. Approximate analytic model for calculation of phase plate impact on polarizing state with dispersion influence taken into consideration is suggested.Comment: 7 pages, 4 figures, report for the International Symposium "Quantum Informatics-2014" (QI-2014), Zvenigorod, Moscow region, October 06-10, 201

Fast reconstruction of programmable interferometers with intensity-only measurements

Programmable linear optical interferometers are promising for classical and quantum applications. Their integrated design makes it possible to create more scalable and stable devices. To use them in practice, one has to reconstruct the whole device model taking the manufacturing errors into account. The inability to address individual interferometer elements complicates the reconstruction problem. A naive approach is to train the model via some complex optimization procedure. A faster optimization-free algorithm has been recently proposed [Opt. Express 31, 16729 (2023)]. However, it requires the full transfer matrix tomography while a more practical setup measures only the fields intensities at the interferometer output. In this paper, we propose the modification of the fast algorithm, which uses additional set of interferometer configurations in order to reconstruct the model in the case of intensity-only measurements. We show that it performs slightly worse than the original fast algorithm but it is more practical and still does not require intensive numerical optimization

Fast reconstruction of programmable integrated interferometers

Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing optical interferometers that could implement arbitrary transformations of input fields even in the case of high manufacturing errors. The building of detailed models of such devices drastically increases the efficiency of their practical use. The integral design of interferometers complicates its reconstruction since the internal elements are hard to address. This problem can be approached by using optimization algorithms [Opt. Express 29, 38429 (2021)]. In this paper, we present a novel efficient algorithm based on linear algebra only, which does not use computationally expensive optimization procedures. We show that this approach makes it possible to perform fast and accurate characterization of high-dimensional programmable integrated interferometers. Moreover, the method provides access to the physical characteristics of individual interferometer layers

Numerical and analytical research of the impact of decoherence on quantum circuits

Three different levels of noisy quantum schemes modeling are considered: vectors, density matrices and Choi-Jamiolkowski related states. The implementations for personal computers and supercomputers are described, and the corresponding results are shown. For the level of density matrices, we present the technique of the fixed rank approximation and show some analytical estimates of the fidelity level.Comment: 11 pages, 9 figures, report for the International Symposium "Quantum Informatics-2014" (QI-2014), Zvenigorod, Moscow region, October 06-10, 201

High-precision tomography of ion qubits based on registration of fluorescent photons

We develop a new method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of its logical states. It is not always possible to achieve low error rates during the readout of the quantum states of ion qubits due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture, etc. However, the model of fuzzy quantum measurements makes it possible to ensure precise tomography of quantum states. To do this, we developed a fuzzy measurement model based on counting the number of fluorescent photons. A statistically adequate algorithm for the reconstruction of quantum states of ion qubit registers based on fuzzy measurement operators is proposed. The algorithm uses the complete information available in the experiment and makes it possible to account for systematic measurement errors associated with the limited distinguishability of the logical states of ion qubits. We show that the developed model, although computationally more complex, contains significantly more information about the state of the qubit and provides a higher accuracy of state reconstruction compared to the model based on the threshold algorithm.Comment: 9 pages, 4 figure

Quantum tomography based on principles of completeness, adequacy and fidelity

In this report we present a general approach for estimating quantum circuits by means of measurements. We apply the developed general approach for estimating the quality of superconducting and optical quantum chips. Using the methods of quantum states and processes tomography developed in our previous works, we have defined the adequate models of the states and processes under consideration.Comment: 9 pages, 7 figure