arXiv subjects

W. V. Pogosov

Publications and source records attributed to W. V. Pogosov.

At least 19 recordsLinked to original sources

arXiv2026

Spectral theory of energy-selective quantum search with Ising Hamiltonian phase oracles

We develop an exact spectral-response theory for the Grover-type iterate $W_T=D_ξ\exp(-\ii T H)$, in which the evolution generated by a diagonal Ising Hamiltonian is used directly as a continuous phase oracle. An energy-grouped recurrence and its generating-function solution show how the empirical characteristic function determines the position, width, height, and saturation time of an energy-selective resonance. For an annealed Gaussian density of states, a high-density-tail resonance containing $M$ configurations is reached after $Θ(\sqrt{2^n/M})$ oracle calls with success probability $Θ(1)$, giving a quadratic query improvement over independent uniform sampling with classical energy evaluation. For correlated random Ising spectra, overlap-dependent covariances lead to a realization-dependent resonance shift with root-mean-square scale $O(n^{-3})$, parametrically larger than the resonance width, and can also reduce the peak height. The shift is both an algorithmic detuning and a coherent probe of sample-specific spectral fluctuations whose ensemble statistics reflect the Ising overlap structure. Spectral symmetrization and iterative calibration can remove or compensate the resonance-center displacement for prescribed-energy targeting. We also clarify the relation to designed spectral filters and the precision and coherence requirements of this asymptotic primitive.

quant-ph↗

arXiv2026

Hybrid physical/logical zero-noise extrapolation with limited logical executions

Partially error-corrected logical executions are expected to become available before fully fault-tolerant quantum computation, but such executions usually take much longer runtime than physical, unencoded ones. We formulate zero-noise extrapolation in this regime as a statistical resource-allocation problem in which the physical/logical execution mode is itself an extrapolation design variable. In the proposed mixed strategy, one or a few logical circuits provide low-noise anchor points, while cheaper folded physical circuits provide a larger extrapolation lever arm. Within an effective error suppression model $p_L=γp$, we derive Richardson variance prefactors for all-logical and mixed data sets, include folded-circuit runtime accounting, obtain the optimal shot allocation for a prescribed target variance, and state the bias--variance criterion determining when the mixed estimator improves finite-runtime accuracy. We illustrate the mixed-data strategy via simulating dynamics of transverse-field Ising model. For error suppression factor $γ\lesssim 0.1$ the mixed strategy can significantly(orders-of-magnitude) reduce the runtime needed to reach a fixed estimator variance, as well as provide better mean-square-error estimators in reasonable parameter regions.

quant-ph↗

arXiv2026

Noise structuring in fixed-depth Trotter simulation: stationary channels and observable-level depolarization

We analyze fixed-depth Trotter simulation as a method for structuring hardware noise in digital many-body dynamics. The number of layers is chosen using the largest endpoint time and is then kept fixed throughout the time scan, making the total noise dose approximately independent of the endpoint time. For local stochastic faults, we show that, once propagated faults lose memory of their insertion layer, the noisy circuit factorizes into ideal evolution followed by a stationary finite-depth binomial channel. In the dilute-layer limit, this channel reduces to a Poissonian exponential. The memory time of a single fault is related to a Loschmidt echo. An important consequence is observable-level depolarization: for selected macroscopic observables at low to moderate noise levels, the stationary channel can act as an almost time-independent affine contrast correction, even though the full channel need not be depolarizing, which is crusial for error mitigation purposes. At short times, the same protocol produces a digital Zeno-like transient, in which a fixed number of noise opportunities competes with a vanishing coherent angle per layer. Our results also reveal limitations of naive zero-noise extrapolatin strategies based on oversimplified functions.

quant-ph↗

arXiv2026

Sideband fingerprints of antibunched light in cascaded quantum wave mixing

Quantum wave mixing on a single superconducting qubit produces a hierarchy of coherent side peaks associated with elastic multiphoton scattering pathways. In a cascaded source--probe geometry these pathways become sensitive to the photon statistics of the radiation emitted by the source qubit. We develop an analytical theory of this effect starting from the cascaded master equation in the weak-driving regime. In the coherent-filtering limit $γ_{\rm s}\ggγ_{\rm pr}$, the standard coherent--coherent wave-mixing hierarchy is recovered. In the opposite limit $γ_{\rm pr}\ggγ_{\rm s}$, side peaks associated with multiphoton absorption from the antibunched source field are parametrically suppressed. Numerical solutions confirm the analytical scaling laws. The resulting sideband hierarchy provides a frequency-domain fingerprint of antibunched itinerant microwave light.

quant-ph↗

arXiv2026

Photon pairs, squeezed light and the quantum wave mixing effect in a cascaded qubit system

We develop a theoretical description of quantum wave mixing (QWM) in a cascaded waveguide-QED system of two superconducting qubits, where the probe is driven by an external coherent tone and by the resonance fluorescence of a strongly driven source qubit. Starting from the field correlation functions of the source emission, we derive an effective master-equation treatment for the probe and identify the regime in which the incident fluorescence is characterized by anomalous correlations. When the coherent Rayleigh component of the source spectrum is suppressed, the probe equations of motion become equivalent to those for a qubit driven by a coherent tone and broadband squeezed light. This equivalence implies a selection rule for the peaks of the QWM spectrum, with a strong suppression of sidebands associated with processes involving an odd number of photons taken from the source field. Numerical simulations of the full cascaded two-qubit model for different ratios of radiative decay rates unambiguously confirm the participation of correlated photon pairs in QWM processes. The current research illustrates that the analysis of peak amplitudes can be used to probe photon statistics in the incident nonclassical field.

quant-ph↗

arXiv2024

Optimal-order Trotter-Suzuki decomposition for quantum simulation on noisy quantum computers

The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transverse-field Ising model and the XY model, it is demonstrated that when the gate error is decreased by approximately an order of magnitude relative to typical modern values, higher-order Trotterization becomes advantageous. This form of Trotterization yields a global minimum of the overall simulation error, comprising both the mathematical error of Trotterization and the physical error arising from gate execution.

quant-ph↗

arXiv2024

Direct experimental observation of sub-poissonian photon statistics by means of multi-photon scattering on a two-level system

A cascade of two-level superconducting artificial atoms -- a source and a probe -- strongly coupled to a semi-infinite waveguide is a promising tool for observing nontrivial phenomena in quantum nonlinear optics. The probe atom can scatter an antibunched radiation emitted from the source, thereby generating a field with specific properties. We experimentally demonstrate wave mixing between nonclassical light from the coherently cw-pumped source and another coherent wave acting on the probe. We observe unique features in the wave mixing stationary spectrum which differs from mixing spectrum of two classical waves on the probe. These features are well described by adapting the theory for a strongly coupled cascaded system of two atoms. We further analyze the theory to predict non-classical mixing spectra for various ratios of atoms' radiative constants. Both experimental and numerical results confirm the domination of multi-photon scattering process with only a single photon from the source. We evaluate entanglement of atoms in the quasistationary state and illustrate the connection between the expected second-order correlation function of source's field and wave mixing side peaks corresponding to a certain number of scattered photons.

quant-ph↗

arXiv2024

Measurement induced phase transition in the central spin model: second Rényi entropy in dual space approach

We conduct a numerical investigation of the dynamics of the central spin model in the presence of measurement processes. This model holds promise for experimental exploration due to its topology, which facilitates the natural distinction of a central particle and the quantum bath as different subsystems, allowing for the examination of entanglement phase transitions. To characterize the measurement-induced phase transition in this system, we employ a recently developed method based on second Rényi entropy in dual space. Our simulations account for decoherence, energy relaxation, and gate errors. We determine critical measurement rates and demonstrate that they significantly differ from those predicted by a simple approach based on mutual entropy.

quant-ph↗

arXiv2024

Dynamical quantum Ansatz tree approach for the heat equation

Quantum computers can be used for the solution of various problems of mathematical physics. In the present paper, we consider a discretized version of the heat equation and address its solution on quantum computer using variational Anzats tree approach (ATA). We extend this method originally proposed for the system of linear equations to tackle full time dependent heat equation. The key ingredients of our method are (i) special probabilistic quantum circuit in order to add heat sources to temperature distribution, (ii) limiting auxiliary register in the preparation of quantum state, (iii) utilizing a robust cluster of repetitive nodes in the anzats tree structure. We suggest that our procedure provides an exponential speedup compared to the classical algorithms in the case of time dependent heat equation.

quant-ph↗

arXiv2024

Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics

We address a learning-based quantum error mitigation method, which utilizes deep neural network applied at the postprocessing stage, and study its performance in presence of different types of quantum noises. We concentrate on the simulation of Trotterized dynamics of 2D spin lattice in the regime of high noise, when expectation values of bounded traceless observables are strongly suppressed. By using numerical simulations, we demonstrate a dramatic improvement of data quality for both local weight-1 and weight-2 observables for the depolarizing and inhomogeneous Pauli channels. At the same time, the effect of coherent $ZZ$ crosstalks is not mitigated, so that in practise crosstalks should be at first converted into incoherent errors by randomized compiling.

quant-ph↗

arXiv2023

Quantum theory of wave mixing on a two-level system

We apply the scattering matrix formalism to wave mixing on a quantum two-level system. We carry out the fermionization of the two-level system degrees of freedom using the Popov-Fedotov semions, calculate n-particle Green's function, and apply the Lehmann-Symanzik-Zimmermannn reduction procedure. Using the developed approach, we provide a consistent quantum explanation of the appearance of coherent side peaks observed in an experiment on the scattering of bichromatic radiation on a two-level artificial atom \cite{dmitriev2019probing}. We show that the spectrum observed in the experiment is the result of bosonic stimulated scattering of photons from one mode of the bichromatic drive to another and vice versa.

quant-ph↗

arXiv2023

Depth analysis of variational quantum algorithms for heat equation

Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider three approaches to solve the heat equation on a quantum computer. Using the direct variational method we minimize the expectation value of a Hamiltonian with its ground state being the solution of the problem under study. Typically, an exponential number of Pauli products in the Hamiltonian decomposition does not allow for the quantum speed up to be achieved. The Hadamard test based approach solves this problem, however, the performed simulations do not evidently prove that the ansatz circuit has a polynomial depth with respect to the number of qubits. The ansatz tree approach exploits an explicit form of the matrix what makes it possible to achieve an advantage over classical algorithms. In our numerical simulations with up to $n=11$ qubits, this method reveals the exponential speed up.

quant-ph↗

arXiv2022

Quantum error reduction with deep neural network applied at the post-processing stage

Deep neural networks (DNN) can be applied at the post-processing stage for the improvement of the results of quantum computations on noisy intermediate-scale quantum (NISQ) processors. Here, we propose a method based on this idea, which is most suitable for digital quantum simulation characterized by the periodic structure of quantum circuits consisting of Trotter steps. A key ingredient of our approach is that it does not require any data from a classical simulator at the training stage. The network is trained to transform data obtained from quantum hardware with artificially increased Trotter steps number (noise level) towards the data obtained without such an increase. The additional Trotter steps are fictitious, i.e., they contain negligibly small rotations and, in the absence of hardware imperfections, reduce essentially to the identity gates. This preserves, at the training stage, information about relevant quantum circuit features. Two particular examples are considered that are the dynamics of the transverse-field Ising chain and XY spin chain, which were implemented on two real five-qubit IBM Q processors. A significant error reduction is demonstrated as a result of the DNN application that allows us to effectively increase quantum circuit depth in terms of Trotter steps.

quant-ph↗

arXiv2021

The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors

Quantum walks are an analog of classical random walks in quantum systems. Quantum walks have smaller hitting times compared to classical random walks on certain types of graphs, leading to a quantum advantage of quantum-walks-based algorithms. An important feature of quantum walks is that they are accompanied by the excitation transfer from one site to another, and a moment of hitting the destination site is characterized by the maximum probability amplitude of observing the excitation on this site. It is therefore prospective to consider such problems as candidates for quantum advantage demonstration, since gate errors can smear out a peak in the transfer probability as a function of time, nevertheless leaving it distinguishable. We investigate the influence of quantum noise on hitting time and fidelity of a typical quantum walk problem - a perfect state transfer (PST) over a qubit chain. We simulate dynamics of a single excitation over the chain of qubits in the presence of typical noises of a quantum processor (homogeneous and inhomogeneous Pauli noise, crosstalk noise, thermal relaxation, and dephasing noise). We find that Pauli noise mostly smears out a peak in the fidelity of excitation transfer, while crosstalks between qubits mostly affect the hitting time. Knowledge about these noise patterns allows us to propose an error mitigation procedure, which we use to refine the results of running the PST on a simulator of a noisy quantum processor.

quant-ph↗

arXiv2021

Effects of photon statistics in wave mixing on a single qubit

We theoretically consider wave mixing under the irradiation of a single qubit by two photon fields. The first signal is a classical monochromatic drive, while the second one is a nonclassical light. Particularly, we address two examples of a nonclassical light: (i) a broadband squeezed light and (ii) a periodically excited quantum superposition of Fock states with 0 and 1 photons. The mixing of classical and nonclassical photon fields gives rise to side peaks due to the elastic multiphoton scattering. We show that side peaks structure is distinct from the situation when two classical fields are mixed. The most striking feature is that some peaks are absent. The analysis of peak amplitudes can be used to probe photon statistics in the nonclassical mode.

quant-ph↗

arXiv2021

Universal fluctuations and squeezing in generalized Dicke model near the superradiant phase transition

In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model, we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete $\mathbb{Z}_2$ symmetry), and that of (anti-) and Tavis-Cummings $U(1)$ models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of photon number take universal values. We also find a temperature scales below which one approaches zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss Bethe ansatz solution for integrable $U(1)$ limits.

cond-mat.mes-hall↗

arXiv2020

Photon transport in a Bose-Hubbard chain of superconducting artificial atoms

We demonstrate non-equilibrium steady-state photon transport through a chain of five coupled artificial atoms simulating the driven-dissipative Bose-Hubbard model. Using transmission spectroscopy, we show that the system retains many-particle coherence despite being coupled strongly to two open spaces. We show that system energy bands may be visualized with high contrast using cross-Kerr interaction. For vanishing disorder, we observe the transition of the system from the linear to the nonlinear regime of photon blockade in excellent agreement with the input-output theory. Finally, we show how controllable disorder introduced to the system suppresses this non-local photon transmission. We argue that proposed architecture may be applied to analog simulation of many-body Floquet dynamics with even larger arrays of artificial atoms paving an alternative way to demonstration of quantum supremacy

quant-ph↗

arXiv2020

Hybrid digital-analog simulation of many-body dynamics with superconducting qubits

In recent years, there has been a significant progress in the development of digital quantum processors. The state-of-the-art quantum devices are imperfect, and fully-algorithmic fault-tolerant quantum computing is a matter of future. Until technology develops to the state with practical error correction, computational approaches other than the standard digital one can be used to avoid execution of the most noisy quantum operations. We demonstrate how a hybrid digital-analog approach allows simulating dynamics of a transverse-field Ising model without standard two-qubit gates, which are currently one of the most problematic building blocks of quantum circuits. We use qubit-qubit crosstalks (couplings) of IBM superconducting quantum processors to simulate Trotterized dynamics of spin clusters and then we compare the obtained results with the results of conventional digital computation based on two-qubit gates from the universal set. The comparison shows that digital-analog approach significantly outperforms standard digital approach for this simulation problem, despite of the fact that crosstalks in IBM quantum processors are small. We argue that the efficiency of digital-analog quantum computing can be improved with the help of more specialized processors, so that they can be used to efficiently implement other quantum algorithms. This indicates the prospect of a digital-to-analog strategy for near-term noisy intermediate-scale quantum computers.

quant-ph↗