arXiv subjects

D. V. Babukhin

Publications and source records attributed to D. V. Babukhin.

7 recordsLinked to original sources

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.

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arXiv2025

Echo-evolution data generation for quantum error mitigation via neural networks

Neural networks provide a prospective tool for error mitigation in quantum simulation of physical systems. However, we need both noisy and noise-free data to train neural networks to mitigate errors in quantum computing results. Here, we propose a physics-motivated method to generate training data for quantum error mitigation via neural networks, which does not require classical simulation and target circuit simplification. In particular, we propose to use the echo evolution of a quantum system to collect noisy and noise-free data for training a neural network. Under this method, the initial state evolves forward and backward in time, returning to the initial state at the end of evolution. When run on a noisy quantum processor, the resulting state will be affected by the quantum noise accumulated during evolution. Having a vector of observable values of the initial (noise-free) state and the resulting (noisy) state allows us to compose training data for a neural network. We demonstrate that a feed-forward fully connected neural network trained on echo-evolution-generated data can correct results of forward-in-time evolution. Our findings can enhance the application of neural networks to error mitigation in quantum computing.

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arXiv2023

Harrow-Hassidim-Lloyd algorithm without ancilla postselection

Harrow-Hassidim-Lloyd algorithm (HHL) allows for the exponentially faster solution of a system of linear equations. However, this algorithm requires the postselection of an ancilla qubit to obtain the solution. This postselection makes the algorithm result probabilistic. Here we show conditions when the HHL algorithm can work without postselection of ancilla qubit. We derive expectation values for an observable $M$ on the HHL outcome state when ancilla qubit is measured in $\ket{0}$ and $\ket{1}$ and show condition for postselection-free HHL running. We provide an explicit example of a practically-interesting input matrix and an observable, which satisfy postselection-free HHL condition. Our work can improve the performance of the HHL-based algorithms.

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arXiv2022

Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings

A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of 1D system with a non-trivial band topology. An interplay of disorder and topological ordering in the SSH model is of a great interest owing to experimental advancements in synthesized quantum simulators. In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random. Using a definition for $\mathbb{Z}_2$-topological invariant $ν\in \{ 0; 1\}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $\langleν\rangle$ averaged by random realizations. This allows to find (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite size fluctuations of $ν$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green function method for a thermodynamic limit.

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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.

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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.

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arXiv2019

Nondestructive classification of quantum states using an algorithmic quantum computer

Methods of processing quantum data become more important as quantum computing devices improve their quality towards fault tolerant universal quantum computers. These methods include discrimination and filtering of quantum states given as an input to the device that may find numerous applications in quantum information technologies. In the present paper, we address a scheme of a classification of input states, which is nondestructive and deterministic for certain inputs, while probabilistic, in general case. This can be achieved by incorporating phase estimation algorithm into the hybrid quantum-classical computation scheme, where quantum block is trained classically. We perform proof-of-principle implementation of this idea using superconducting quantum processor of IBM Quantum Experience. Another aspect we are interested in is a mitigation of errors occurring due to the quantum device imperfections. We apply a series of heuristic tricks at the stage of classical postprocessing in order to improve raw experimental data and to recognize patterns in them. These ideas may find applications in other realization of hybrid quantum-classical computations with noisy quantum machines.

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