Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Science and Technology

Quantum state preparation using tensor networks

Ar. Melnikov, A. Termanova, Sergey Dolgov, Florian Neukart, Michael Romanovich Perelshtein

Published May 30, 2023• 36 citations
Publisher

Abstract

Abstract Quantum state preparation is a vital routine in many quantum algorithms, including solution of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine learning. However, to date, there is no established framework of encoding classical data into gate-based quantum devices. In this work, we propose a method for the encoding of vectors obtained by sampling analytical functions into quantum circuits that features polynomial runtime with respect to the number of qubits and provides > 99.9 % accuracy, which is better than a state-of-the-art two-qubit gate fidelity. We employ hardware-efficient variational quantum circuits, which are simulated using tensor networks, and matrix product state representation of vectors. In order to tune variational gates, we utilize Riemannian optimization incorporating auto-gradient calculation. Besides, we propose a ‘cut once, measure twice’ method, which allows us to avoid barren plateaus during gates’ update, benchmarking it up to 100-qubit circuits. Remarkably, any vectors that feature low-rank structure—not limited by analytical functions—can be encoded using the presented approach. Our method can be easily implemented on modern quantum hardware, and facilitates the use of the hybrid-quantum computing architectures.

DOI
10.1088/2058-9565/acd9e7

Related papers

Approximate encoding of quantum states using shallow circuits

Matan Ben-Dov, David Shnaiderov, Adi Makmal +1 more

Abstract Quantum algorithms and simulations often require the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of required gates grows exponentially with the number of qubits, becoming unfeasible on near-term quantum devices. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. As a first step, we consider a quantum state that is efficiently represented classically, such as a one-dimensional matrix product state. Using tensor network techniques, we develop and implement an efficient optimization algorithm that approaches the optimal implementation, requiring a polynomial number of iterations. We, next, consider the implementation of the proposed optimization algorithm directly on a quantum computer and overcome inherent barren plateaus by employing a local cost function. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.

arXiv:2207.00028•npj Quantum Information•Jul 2, 2024•26 citations

Efficient quantum state preparation of multivariate functions using tensor networks

Marco Ballarin, Juan José García-Ripoll, David Hayes +1 more

For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.

quant-pharXiv:2511.15674•Nov 20, 2025•0 citations

Efficient Quantum Circuit Simulation by Tensor Network Methods on Modern GPUs

Feng Ping Pan, Hanfeng Gu, Lülin Kuang +2 more

Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector-based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determining the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. First, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Second, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96× reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5× compared to the state-of-the-art CPU-based results and 4.48–6.78× compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.

arXiv:2310.03978•ACM Transactions on Quantum Computing•Sep 23, 2024•10 citations

Approximate State Preparation Using Tensor Network Optimization Techniques

Tomonori Shirakawa, Seiji Yunoki

Converting classical information into a quantum circuit is an inevitable step in utilizing quantum computing. Current quantum computers are referred to as NISQ devices, which have a high level of noise without error correction, imposing strict limitations on the number of qubits and quantum gates. Therefore, when constructing quantum circuits, it becomes crucial to generate shallower circuits. Specifically, when amplitude encoding is employed for classical-quantum information conversion, analytical methods often necessitate an exponential number of quantum gates relative to the number of qubits, rendering them unsuitable for current NISQ devices. Here, we explore a method for constructing an approximately improved circuit for amplitude encoding, considering classical information from an array composed of floating-point numbers. In our method, we optimize the matrix elements of a two-qubit unitary gate using a technique similar to that used in the tensor network method. We then analytically decompose the obtained unitary matrix into a product of elementary unitary gates. Furthermore, using this as an element of the basic optimization technique, we explore a method for selectively adapting better quantum gates. We apply this method to the problem of constructing a circuit that approximately generates the ground state of the quantum spin model. Consequently, we find that better circuits can be automatically constructed without prior knowledge of classical information.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•0 citations

Scalable Tensor Ring Methods for Variational Quantum Algorithms

Dheeraj Peddireddy

Variational quantum algorithms (VQAs) have emerged as a promising candidate for realizing quantum advantage in machine learning and optimization tasks on noisy intermediate-scale quantum (NISQ) devices. Despite significant theoretical promise, the practical impact of VQAs is constrained by the exponential growth in computational resources required for classical simulation, the onset of barren plateaus in parameterized landscapes, and the inherent difficulties of scaling classical optimization routines to circuits with many qubits and layers. Addressing these intertwined challenges is essential for both advancing quantum algorithm development and extracting actionable physical insights from modern quantum hardware.This dissertation develops, analyzes, and validates an efficient framework based on approximate tensor ring decompositions for the classical simulation, training, and benchmarking of variational quantum circuits and eigensolvers. The first component of this work formalizes the representation of quantum states and gates within a cyclic tensor ring structure, enabling the compression of parameterized quantum circuits to linear scaling in both qubit number and circuit depth, while preserving essential quantum correlations and entanglement structure. Gate operations are efficiently approximated via truncated singular value decomposition, and novel algorithms for forward propagation and gradient-based training in the tensor ring domain are developed. These methodological advances are systematically benchmarked on standard supervised learning tasks, including Iris and MNIST datasets, and compared to conventional statevector and matrix product state baselines, resulting in competitive accuracy and orders-of-magnitude reductions in simulation cost. Extending this framework, the dissertation also introduces a scalable method for gradient evaluation in variational quantum eigensolvers (VQE) using the approximate tensor ring representation. This approach enables the simulation and training of large circuits for combinatorial optimization problems, supporting practical qubit counts and circuit depths inaccessible to traditional simulation methods. Detailed experiments on the Maximum-Cut optimization problem demonstrate both the computational efficiency and robustness of the tensor ring framework in nontrivial optimization landscapes.Collectively, the results establish approximate tensor ring decomposition as a versatile and powerful framework for advancing quantum machine learning and discrete optimization, supporting both pre-deployment benchmarking on classical hardware and algorithm design for next-generation quantum devices. This work provides a foundation for the further exploration of scalable quantum-classical hybrid algorithms, with implications for quantum simulation, optimization, and beyond.

•Jan 20, 2026•0 citations

Pre-optimization of quantum circuits, barren plateaus and classical simulability: tensor networks to unlock the variational quantum eigensolver

Baptiste Anselme Martin, Thomas Ayral

Variational quantum algorithms are practical approaches to prepare ground states, but their potential for quantum advantage remains unclear. Here, we use differentiable 2D tensor networks (TN) to optimize parameterized quantum circuits that prepare the ground state of the transverse field Ising model (TFIM). Our method enables the preparation of states with high energy accuracy, even for large systems beyond 1D. We show that TN pre-optimization can mitigate the barren plateau issue by giving access to enhanced gradient zones that do not shrink exponentially with system size. We evaluate the classical simulation cost evaluating energies at these warm-starts, and identify regimes where quantum hardware offers better scaling than TN simulations.

quant-pharXiv:2602.04676•Feb 5, 2026•0 citations
Abstract Quantum state preparation is a vital routine in many quantum algorithms, including solution of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine learning. However, to date, there is no established framework of encoding classical data into gate-based quantum devices. In this work, we propose a method for the encoding of vectors obtained by sampling analytical functions into quantum circuits that features polynomial runtime with respect to the number of qubits and provides > 99.9 % accuracy, which is better than a state-of-the-art two-qubit gate fidelity. We employ hardware-efficient variational quantum circuits, which are simulated using tensor networks, and matrix product state representation of vectors. In order to tune variational gates, we utilize Riemannian optimization incorporating auto-gradient calculation. Besides, we propose a ‘cut once, measure twice’ method, which allows us to avoid barren plateaus during gates’ update, benchmarking it up to 100-qubit circuits. Remarkably, any vectors that feature low-rank structure—not limited by analytical functions—can be encoded using the presented approach. Our method can be easily implemented on modern quantum hardware, and facilitates the use of the hybrid-quantum computing architectures.
Abstract Quantum algorithms and simulations often require the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of required gates grows exponentially with the number of qubits, becoming unfeasible on near-term quantum devices. Here, we aim at creating an approximate encoding of the target state using a limited number of gates. As a first step, we consider a quantum state that is efficiently represented classically, such as a one-dimensional matrix product state. Using tensor network techniques, we develop and implement an efficient optimization algorithm that approaches the optimal implementation, requiring a polynomial number of iterations. We, next, consider the implementation of the proposed optimization algorithm directly on a quantum computer and overcome inherent barren plateaus by employing a local cost function. Our work offers a universal method to prepare target states using local gates and represents a significant improvement over known strategies.
For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.
Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector-based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determining the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. First, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Second, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96× reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5× compared to the state-of-the-art CPU-based results and 4.48–6.78× compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.
Converting classical information into a quantum circuit is an inevitable step in utilizing quantum computing. Current quantum computers are referred to as NISQ devices, which have a high level of noise without error correction, imposing strict limitations on the number of qubits and quantum gates. Therefore, when constructing quantum circuits, it becomes crucial to generate shallower circuits. Specifically, when amplitude encoding is employed for classical-quantum information conversion, analytical methods often necessitate an exponential number of quantum gates relative to the number of qubits, rendering them unsuitable for current NISQ devices. Here, we explore a method for constructing an approximately improved circuit for amplitude encoding, considering classical information from an array composed of floating-point numbers. In our method, we optimize the matrix elements of a two-qubit unitary gate using a technique similar to that used in the tensor network method. We then analytically decompose the obtained unitary matrix into a product of elementary unitary gates. Furthermore, using this as an element of the basic optimization technique, we explore a method for selectively adapting better quantum gates. We apply this method to the problem of constructing a circuit that approximately generates the ground state of the quantum spin model. Consequently, we find that better circuits can be automatically constructed without prior knowledge of classical information.
Variational quantum algorithms (VQAs) have emerged as a promising candidate for realizing quantum advantage in machine learning and optimization tasks on noisy intermediate-scale quantum (NISQ) devices. Despite significant theoretical promise, the practical impact of VQAs is constrained by the exponential growth in computational resources required for classical simulation, the onset of barren plateaus in parameterized landscapes, and the inherent difficulties of scaling classical optimization routines to circuits with many qubits and layers. Addressing these intertwined challenges is essential for both advancing quantum algorithm development and extracting actionable physical insights from modern quantum hardware.This dissertation develops, analyzes, and validates an efficient framework based on approximate tensor ring decompositions for the classical simulation, training, and benchmarking of variational quantum circuits and eigensolvers. The first component of this work formalizes the representation of quantum states and gates within a cyclic tensor ring structure, enabling the compression of parameterized quantum circuits to linear scaling in both qubit number and circuit depth, while preserving essential quantum correlations and entanglement structure. Gate operations are efficiently approximated via truncated singular value decomposition, and novel algorithms for forward propagation and gradient-based training in the tensor ring domain are developed. These methodological advances are systematically benchmarked on standard supervised learning tasks, including Iris and MNIST datasets, and compared to conventional statevector and matrix product state baselines, resulting in competitive accuracy and orders-of-magnitude reductions in simulation cost. Extending this framework, the dissertation also introduces a scalable method for gradient evaluation in variational quantum eigensolvers (VQE) using the approximate tensor ring representation. This approach enables the simulation and training of large circuits for combinatorial optimization problems, supporting practical qubit counts and circuit depths inaccessible to traditional simulation methods. Detailed experiments on the Maximum-Cut optimization problem demonstrate both the computational efficiency and robustness of the tensor ring framework in nontrivial optimization landscapes.Collectively, the results establish approximate tensor ring decomposition as a versatile and powerful framework for advancing quantum machine learning and discrete optimization, supporting both pre-deployment benchmarking on classical hardware and algorithm design for next-generation quantum devices. This work provides a foundation for the further exploration of scalable quantum-classical hybrid algorithms, with implications for quantum simulation, optimization, and beyond.
Variational quantum algorithms are practical approaches to prepare ground states, but their potential for quantum advantage remains unclear. Here, we use differentiable 2D tensor networks (TN) to optimize parameterized quantum circuits that prepare the ground state of the transverse field Ising model (TFIM). Our method enables the preparation of states with high energy accuracy, even for large systems beyond 1D. We show that TN pre-optimization can mitigate the barren plateau issue by giving access to enhanced gradient zones that do not shrink exponentially with system size. We evaluate the classical simulation cost evaluating energies at these warm-starts, and identify regimes where quantum hardware offers better scaling than TN simulations.