arXiv subjects

Daniil Rabinovich

Publications and source records attributed to Daniil Rabinovich.

9 recordsLinked to original sources

arXiv2026

Role of overparametrization in quantum approximate optimization

Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. While they have demonstrated considerable promise in solving problems of practical interest, efficiently determining the minimal quantum resources necessary to obtain such a solution remains an open question. In this work, inspired by concepts from classical machine learning, we investigate the impact of overparameterization on the performance of variational algorithms. Our study focuses on the quantum approximate optimization algorithm (QAOA) -- a prominent variational quantum algorithm designed to solve combinatorial optimization problems. We investigate if circuit overparametrization is necessary and sufficient to solve such problems in QAOA, considering two representative problems -- MAX-CUT and MAX-2-SAT. For MAX-CUT we observe that overparametriation is both sufficient and (statistically) necessary for attaining exact solutions, as confirmed numerically for up to $20$ qubits. In fact, for MAX-CUT on 2-regular graphs we show the necessity to be exact, based on the analytically found optimal depth. In sharp contrast, for MAX-2-SAT, underparametrized circuits suffice to solve most instances. This result highlights the potential of QAOA in the underparametrized regime, supporting its utility for current noisy devices.

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arXiv2026

Zero-Noise Extrapolation via Cyclic Permutations of Quantum Circuit Layouts

Increasing the utility of currently available Noisy Intermediate-Scale Quantum (NISQ) devices requires developing efficient methods to mitigate hardware errors. In this work we propose a novel Cyclic Layout Permutations-based Zero-Noise Extrapolation (CLP-ZNE) protocol for such a task. The method leverages the inherent non-uniformity of gate errors in NISQ hardware to extrapolate the expectation value, averaged over cyclic circuit layout permutations, to the level of zero noise. In contrast to the previous layout permutation based approaches, for an $n$-qubit circuit CLP-ZNE requires execution of only $O(n)$ and at most $O(n^2)$ different circuit layouts for circuits of one-dimensional and arbitrary connectivity, respectively. When benchmarked against noise channels modeling the IBM Torino quantum computer, the method reduces a typical error in expectation values of $n=12$ qubit circuits by an order of magnitude, outperforming standard unitary folding ZNE. By demonstrating the ability to mitigate noise of real hardware specifications, including both depolarizing and $T_1/T_2$ relaxation processes, these results give evidence for the applicability of CLP-ZNE to present-day NISQ processors.

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arXiv2026

Machine Learning-based Quantum Error Mitigation for Variational Algorithms

Machine Learning-based quantum error mitigation (ML-QEM) has emerged as a promising approach for improving the performance of noisy quantum algorithms. However, existing ML-QEM methods often have restricted applicability to variational circuits and rely on inaccessible noiseless training data. In this work, we propose a practical ML-QEM protocol tailored to variational quantum algorithms, which generates training data by simulating (near-)Clifford circuits. This data is used for model selection and training, producing a mitigation model that can correct variational circuits with arbitrary parameters and transfer across different target Hamiltonians of similar structure. We benchmark the proposed method on the Variational Quantum Eigensolver (VQE) task for the Sherrington-Kirkpatrick Hamiltonian of up to $n=12$ qubits under various noise models, analyzing its effect on trainability and comparing its performance against standard Zero-Noise Extrapolation (ZNE). The results demonstrate consistent several-fold error suppression across all tested settings and superior performance over ZNE in the high-noise regime, providing evidence for the applicability of the proposed protocol to present-day NISQ processors.

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arXiv2026

Problem specific ion native ansatz for combinatorial optimization

Variational quantum algorithms have become a standard approach for solving a wide range of problems on near-term quantum computers. Identifying an appropriate ansatz configuration for variational algorithms, however, remains a challenging task, especially when taking into account restrictions imposed by real quantum platforms. This motivated the development of digital-analog quantum circuits, where sequences of quantum gates are alternated with natural Hamiltonian evolutions. A prominent example is the use of the controllable long-range Ising interaction induced in ion-based quantum computers. This interaction has recently been applied to develop an algorithm similar to the quantum approximate optimization algorithm (QAOA), but native to the ion hardware. The performance of this algorithm has demonstrated a strong dependence on the strengths of the individual ion-ion interactions, which serve as ansatz hyperparameters. In this work, we propose a heuristic for identifying a problem-specific ansatz configuration, which enhances the trainability of the ion native digital-analog circuit. The proposed approach is systematically applied to random instances of the Sherrington-Kirkpatrick Hamiltonian for up to 15 qubits, providing favorable cost landscapes. As the result, the developed approach identifies a well-trainable ion native ansatz, which requires a lower circuit depth to solve specific problems as compared to standard QAOA. This brings the algorithm one step closer to its large scale practical implementation.

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arXiv2025

Distributed quantum architecture search using multi-agent reinforcement learning

Quantum architecture search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms. The framework finds a well-suited problem-specific structure of a variational ansatz. Among possible implementations of QAS the reinforcement learning (RL) stands out as one of the most promising. Current RL approaches are single-agent-based and show poor scalability with a number of qubits due to the increase of the action space dimension and the computational cost. We propose a novel multi-agent RL algorithm for QAS with each agent acting separately on its own block of a quantum circuit. This procedure allows to significantly accelerate the convergence of the RL-based QAS and reduce its computational cost. We benchmark the proposed algorithm on MaxCut problem on 3-regular graphs and on ground energy estimation for the Schwinger Hamiltonian. In addition, the proposed multi-agent approach naturally fits into the set-up of distributed quantum computing, favoring its implementation on modern intermediate scale quantum devices.

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arXiv2024

Depth scaling of unstructured search via quantum approximate optimization

Variational quantum algorithms have become the de facto model for current quantum computations. A prominent example of such algorithms -- the quantum approximate optimization algorithm (QAOA) -- was originally designed for combinatorial optimization tasks, but has been shown to be successful for a variety of other problems. However, for most of these problems the optimal circuit depth remains unknown. One such problem is unstructured search which consists on finding a particular bit string, or equivalently, preparing a state of high overlap with a target state. To bound the optimal QAOA depth for such problem we build on its known solution in a continuous time quantum walk (CTQW). We trotterize a CTQW to recover a QAOA sequence, and employ recent advances on the theory of Trotter formulas to bound the query complexity (circuit depth) needed to prepare a state of almost perfect overlap with the target state. The obtained complexity exceeds the Grover's algorithm complexity $O\left(N^\frac{1}{2}\right)$, but remains smaller than $O \left(N^{\frac{1}{2}+c}\right)$ for any $c>0$, which shows quantum advantage of QAOA over classical solutions. We verify our analytical predictions by numerical simulations of up to 68 qubits, which demonstrate that our result overestimates the number of QAOA layers resulting from a trotterized CTQW by at most a polynomial factor.

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arXiv2024

Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation

Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline in performance due to the presence of stochastic errors and limited coherence time. In this work, we develop a recipe for mitigating quantum gate errors for variational algorithms using zero-noise extrapolation. We introduce an experimentally amenable method to control error strength in the circuit. We utilize the fact that gate errors in a physical quantum device are distributed inhomogeneously over different qubits and qubit pairs. As a result, one can achieve different circuit error sums based on the manner in which abstract qubits in the circuit are mapped to a physical device. We find that the estimated energy in the variational approach is approximately linear with respect to the circuit error sum (CES). Consequently, a linear fit through the energy-CES data, when extrapolated to zero CES, can approximate the energy estimated by a noiseless variational algorithm. We demonstrate this numerically and investigate the applicability range of the technique.

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arXiv2024

Robustness of Variational Quantum Algorithms against stochastic parameter perturbation

Variational quantum algorithms are tailored to perform within the constraints of current quantum devices, yet they are limited by performance-degrading errors. In this study, we consider a noise model that reflects realistic gate errors inherent to variational quantum algorithms. We investigate the decoherence of a variationally prepared quantum state due to this noise model, which causes a deviation from the energy estimation in the variational approach. By performing a perturbative analysis of optimized circuits, we determine the noise threshold at which the criteria set by the stability lemma is met. We assess our findings against the variational quantum eigensolver and quantum approximate optimization algorithm for various problems with up to 14 qubits. Moreover, we show that certain gate errors have a significantly smaller impact on the coherence of the state, allowing us to reduce the execution time without compromising performance.

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arXiv2022

Ion native variational ansatz for quantum approximate optimization

Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm. Realization of this algorithm on any modern quantum processor requires either embedding a problem instance into a Hamiltonian or emulating the corresponding propagator by a gate sequence. For a vast range of problem instances this is impossible due to current circuit depth and hardware limitations. Hence we adapt the variational approach -- using ion native Hamiltonians -- to create ansatze families that can prepare the ground states of more general problem Hamiltonians. We analytically determine symmetry protected classes that make certain problem instances inaccessible unless this symmetry is broken. We exhaustively search over six qubits and consider upto twenty circuit layers, demonstrating that symmetry can be broken to solve all problem instances of the Sherrington-Kirkpatrick Hamiltonian. Going further, we numerically demonstrate training convergence and level-wise improvement for up to twenty qubits. Specifically these findings widen the class problem instances which might be solved by ion based quantum processors. Generally these results serve as a test-bed for quantum approximate optimization approaches based on system native Hamiltonians and symmetry protection.

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