arXiv subjects

M. R. Perelshtein

Publications and source records attributed to M. R. Perelshtein.

9 recordsLinked to original sources

arXiv2025

Qubit-efficient quantum local search for combinatorial optimization

An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate neighbors. The size $l$ of this set is limited due to the computational costs required to run the method on classical processing units. We present a qubit-efficient variational quantum algorithm that implements a quantum version of local search with only $\lceil \log_2 l \rceil$ qubits and, therefore, can potentially work with classically intractable neighborhood sizes when realized on near-term quantum computers. Increasing the amount of quantum resources employed in the algorithm allows for a larger neighborhood size, improving the quality of obtained solutions. This trade-off is crucial for present and near-term quantum devices characterized by a limited number of logical qubits. Numerically simulating our algorithm, we successfully solved the largest graph coloring instance that was tackled by a quantum method. This achievement highlights the algorithm's potential for solving large-scale combinatorial optimization problems on near-term quantum devices.

quant-ph↗

arXiv2024

Tensor networks based quantum optimization algorithm

In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an eigenvalue/eigenvector search, this algorithm features wide applicability. Operationally, power iterations consist of performing repeated matrix-to-vector multiplications (or MatVec) followed by a renormilization step in order to converge to the dominant eigenvalue/eigenvector. However, classical realizations, including novel tensor network based approaches, necessitate an exponential scaling for the algorithm's run-time. In this paper, we propose a quantum realiziation to circumvent this pitfall. Our methodology involves casting low-rank representations; Matrix Product Operators (MPO) for matrices and Matrix Product States (MPS) for vectors, into quantum circuits. Specifically, we recover a unitary approximation by variationally minimizing the Frobenius distance between a target MPO and an MPO ansatz wherein the tensor cores are constrained to unitaries. Such an unitary MPO can easily be implemented as a quantum circuit with the addition of ancillary qubits. Thereafter, with appropriate initialization and post-selection on the ancillary space, we realize a single iteration of the classical algorithm. With our proposed methodology, power iterations can be realized entirely on a quantum computer via repeated, static circuit blocks; therefore, a run-time advantage can indeed be guaranteed. Moreover, by exploiting Riemannian optimization and cross-approximation techniques, our methodology becomes instance agnostic and thus allows one to address black-box optimization within the framework of quantum computing.

quant-ph↗

arXiv2023

NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum algorithms training, the shape of their cost landscape, the accuracy of their output, and their ability to scale to large-size problems. Here, we present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms. We employ numerical simulations to test it on MaxCut problems with complete weighted graphs with thousands of nodes and run the algorithm on a superconducting quantum processor. We find that for unconstrained MaxCut problems with more than 1000 nodes, the hybrid approach combining our algorithm with a classical solver called CPLEX can find a better solution than CPLEX alone. This demonstrates that hybrid optimization is one of the leading use cases for modern quantum devices.

quant-ph↗

arXiv2023

Generation and structuring of multipartite entanglement in Josephson parametric system

Quantum correlations are a vital resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for the generation of multipartite quantum entanglement. In this work, we achieve generation of genuine tripartite entangled state and its control by the use of the phase difference between two continuous pump tones. We demonstrate control of the subspaces of the covariance matrix for tripartite bisqueezed state. Furthermore, by optimizing the phase relationships in a three-tone pumping scheme we explore genuine quadripartite entanglement of a \textit{generalized} H-graph state ($\mathscr{\tilde{H}}$-graph). Our scheme provides a comprehensive control toolbox for the entanglement structure and allows us to demonstrate, for first time to our knowledge, genuine quadripartite entanglement of microwave modes. All experimental results are verified with numerical simulations of the nonlinear quantum Langevin equation. We envision that quantum resources facilitated by multi-pump configurations offer enhanced prospects for quantum data processing using parametric microwave cavities.

quant-ph↗

arXiv2022

Solving workflow scheduling problems with QUBO modeling

In this paper we investigate the workflow scheduling problem, a known NP-hard class of scheduling problems. We derive problem instances from an industrial use case and compare against several quantum, classical, and hybrid quantum-classical algorithms. We develop a novel QUBO to represent our scheduling problem and show how the QUBO complexity depends on the input problem. We derive and present a decomposition method for this specific application to mitigate this complexity and demonstrate the effectiveness of the approach.

quant-ph↗

arXiv2021

Large-scale quantum hybrid solution for linear systems of equations

State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are restricted to exploring specific simplified protocols, whereas the implementation of full-scale quantum algorithms aimed at solving concrete large scale problems arising in data analysis and numerical modelling remains a challenge. Here we introduce and implement a hybrid quantum algorithm for solving linear systems of equations with exponential speedup, utilizing quantum phase estimation, one of the exemplary core protocols for quantum computing. We introduce theoretically classes of linear systems that are suitable for current generation quantum machines and solve experimentally a $2^{17}$-dimensional problem on superconducting IBMQ devices, a record for linear system solution on quantum computers. The considered large-scale algorithm shows superiority over conventional solutions, demonstrates advantages of quantum data processing via phase estimation and holds high promise for meeting practically relevant challenges.

quant-ph↗

arXiv2021

Linear Ascending Metrological Algorithm

The ubiquitous presence of shot noise sets a fundamental limit to the measurement precision in classical metrology. Recent advances in quantum devices and novel quantum algorithms utilizing interference effects are opening new routes for overcoming the detrimental noise tyranny. However, further progress is limited by the restricted capability of existing algorithms to account for the decoherence pervading experimental implementations. Here, adopting a systematic approach to the evaluation of effectiveness of metrological procedures, we devise the Linear Ascending Metrological Algorithm (LAMA), which offers a remarkable increase in precision in the demanding situation where a decohering quantum system is used to measure a continuously distributed variable. We introduce our protocol in the context of magnetic field measurements, assuming superconducting transmon devices as sensors operated in a qudit mode. Our findings demonstrate a quantum-metrological procedure capable of mitigating detrimental dephasing and relaxation effects.

quant-ph↗

arXiv2020

Phase estimation algorithm for the multibeam optical metrology

Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can be translated into the classical linear optical framework. The developed setup made of beam splitters, mirrors and phase shifters demonstrates how the classical coherence, similarly to the quantum coherence, poses a resource for obtaining information about the measurable physical quantities. Our study opens route to the reliable implementation of the small-scale unitary algorithms on path-encoded qudits, thus establishing an easily accessible platform for unitary computation.

quant-ph↗

arXiv2018

Broadband lumped-element Josephson parametric amplifier with single-step lithography

We present a lumped-element Josephson parametric amplifier (JPA) utilizing a straightforward fabrication process involving a single electron beam lithography step followed by double-angle evaporation of aluminum and in-situ oxidation. The Josephson junctions forming the SQUID are fabricated using bridgeless shadow evaporation technique, which enables reliable fabrication of relatively large ($\sim9~\mathrm{μm^2}$) junctions. Our strongly coupled flux-pumped JPA achieves 20~dB gain with 95~MHz bandwidth around 5~GHz, while the center frequency is tunable by more than 1~GHz, with the additional possibility for rapid tuning by varying the pump frequency alone. Analytical calculations based on the input-output theory reproduce our measurement results closely.

cond-mat.mes-hall↗