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

arXiv:2203.08514

Recursive Variational Quantum Compiling

Stian D. Bilek, Kristian Wold

Published Mar 16, 2022• 2 citations
arXivHTMLPDF

Abstract

Variational quantum compiling (VQC) algorithms aim to approximate deep quantum circuits with shallow parameterized ansatzes, making them more suitable for NISQ hardware. In this article a variant of VQC named the recursive variational quantum compiling (RVQC) algorithm is proposed. Existing VQC algorithms typically require coherently executing the full circuit during compilation. Under the influence of noise, sufficiently deep target circuits make compiling unfeasible using ordinary VQC. Since the compiling is often accomplished using a gradient-based quantum-classical approach, the quantum noise manifest as a noisy gradient during optimization, making convergence hard to obtain. On the other hand, RVQC can compile a circuit by first dividing it into $N$ shorter sub-circuits, then evaluate one sub-circuit at a time. As a result, the circuit depth required to implement RVQC is not dependent on the depth of the target circuit, but on the depth of the sub-circuits. Choosing a high enough $N$ thus ensures sufficiently shallow sub-circuit which can be successfully compiled individually. We show mathematical evidence of this property. RVQC was compared with VQC on a noise model of the IBM Santiago device with the goal of compiling several randomly generated five-qubit circuits of approximately depth 1000. It was shown that VQC was not able to converge within 500 iterations of optimization. On the other hand, RVQC was able to converge to a fidelity of $0.90 \pm 0.05$ within a total of 500 iterations when splitting the target circuits into $N = 5$ parts. We argue that this comes as a result of the mitigation of noise-induced barren plateaus.

DOI
10.48550/arxiv.2203.08514

Related papers

Variational quantum compiling with double Q-learning

Zhimin He, Lvzhou Li, Shenggen Zheng +2 more

Abstract Quantum compiling aims to construct a quantum circuitVby quantum gates drawn from a native gate alphabet, which is functionally equivalent to the target unitaryU. It is a crucial stage for the running of quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. However, the space for structure exploration of quantum circuit is enormous, resulting in the requirement of human expertise, hundreds of experimentations or modifications from existing quantum circuits. In this paper, we propose a variational quantum compiling (VQC) algorithm based on reinforcement learning, in order to automatically design the structure of quantum circuit for VQC with no human intervention. An agent is trained to sequentially select quantum gates from the native gate alphabet and the qubits they act on by doubleQ-learning withϵ-greedy exploration strategy and experience replay. At first, the agent randomly explores a number of quantum circuits with different structures, and then iteratively discovers structures with higher performance on the learning task. Simulation results show that the proposed method can make exact compilations with less quantum gates compared to previous VQC algorithms. It can reduce the errors of quantum algorithms due to decoherence process and gate noise in NISQ devices, and enable quantum algorithms especially for complex algorithms to be executed within coherence time.

arXiv:2103.11611•New Journal of Physics•Mar 1, 2021•44 citations

Quantum Wasserstein Compilation: Unitary Compilation using the Quantum Earth Mover's Distance

Richter, Marvin, Abhishek Y. Dubey, Axel Plinge +3 more

Despite advances in the development of quantum computers, the practical application of quantum algorithms requiring deep circuit depths or high-fidelity transformations remains outside the current range of the so-called noisy intermediate-scale quantum devices. Now and beyond, quantum circuit compilation (QCC) is a crucial component of any quantum algorithm execution. Besides translating a circuit into hardware-specific gates, it can optimize circuit depth and adapt to noise. Variational quantum circuit compilation (VQCC) optimizes the parameters of an ansatz according to the goal of reproducing a given unitary transformation. In this work, we present a VQCC-objective function called the quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1. We show that the QWC cost function upper bounds the average infidelity of two circuits. An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit. We demonstrate the efficacy of the QWC cost function by compiling hardware efficient ansatz (HEA) as both the target and the ansatz and comparing to cost functions such as the Loschmidt echo test (LET) and the Hilbert-Schmidt test (HST). Finally, our experiments demonstrate that QWC as a cost function is the least affected by barren plateaus when compared to LET and HST for deep enough circuits.

arXiv:2409.05849•Sep 9, 2024•0 citations

Error-Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis

Sharu Theresa Jose, Osvaldo Simeone

Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a parameterized quantum circuit (PQC). The goal is minimizing a cost function that depends on measurement outputs obtained from the PQC. Optimization is typically implemented via stochastic gradient descent (SGD). On NISQ computers, gate noise due to imperfections and decoherence affects the stochastic gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits, but they in turn cause an increase in the variance of the gradient estimates. This work studies the impact of quantum gate noise on the convergence of SGD for the variational eigensolver (VQE), a fundamental instance of VQAs. The main goal is ascertaining conditions under which QEM can enhance the performance of SGD for VQEs. It is shown that quantum gate noise induces a nonzero error-floor on the convergence error of SGD (evaluated with respect to a reference noiseless PQC), which depends on the number of noisy gates, the strength of the noise, as well as the eigenspectrum of the observable being measured and minimized. In contrast, with QEM, any arbitrarily small error can be obtained. Furthermore, for error levels attainable with or without QEM, QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently large, and a sufficiently large number of measurements is allowed at each SGD iteration. Numerical examples for a max-cut problem corroborate the main theoretical findings.

arXiv:2209.11514•IEEE Transactions on Quantum Engineering•Jan 1, 2022•16 citations

Adaptive Quantum Circuit Compilation for Variational Quantum Algorithms

Jincheng Zhang

Variational quantum algorithms (VQAs) hold significant promise for solving complex problems across diverse fields. However, their practical implementation on near-term quantum devices is severely hampered by the pervasive effects of quantum noise. Traditional quantum circuit compilation techniques are largely static, failing to account for the unique noise profiles inherent in individual quantum hardware. This paper introduces a novel adaptive quantum circuit compilation framework designed to mitigate these limitations. The core concept centers around dynamically adjusting the circuit layout and gate decomposition in real-time, leveraging measurements of the quantum hardware's noise characteristics to optimize both the accuracy and circuit depth of the compiled quantum circuit. This approach represents a critical step towards unlocking the full potential of VQAs by enabling them to effectively operate within the constraints of noisy quantum computers. The framework incorporates feedback loops for continuous refinement, adapting to evolving noise conditions. The methodology is described, focusing on the key components: noise profiling, adaptive gate decomposition, and circuit re-optimization. Simulation results demonstrate the effectiveness of the adaptive approach in reducing circuit depth and improving the fidelity of VQA computations compared to static compilation methods. This work lays the foundation for robust and efficient VQA execution on future quantum hardware.

•Sep 2, 2026•0 citations

Universal compilation for quantum state preparation and tomography

Vu Tuan Hai, Le Bin Ho

Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking, quantum error mitigation, and so on. Here, we propose a universal compilation-based variational algorithm for the preparation and tomography of quantum states in low-depth quantum circuits. We apply the Fubini-Study distance to be a trainable cost function under various gradient-based optimizers, including the quantum natural gradient approach. We evaluate the performance of various unitary topologies and the trainability of different optimizers for getting high efficiency. In practice, we address different circuit ansatzes in quantum state preparation, including the linear and graph-based ansatzes for preparing different entanglement target states such as representative GHZ and W states. We also discuss the effect of the circuit depth, barren plateau, readout noise in the model, and the error mitigation solution. We next evaluate the reconstructing efficiency in quantum state tomography via various popular circuit ansatzes and reveal the crucial role of the circuit depth in the robust fidelity. The results are comparable with the shadow tomography method, a similar fashion in the field. Our work expresses the adequate capacity of the universal compilation-based variational algorithm to maximize the efficiency in the quantum state preparation and tomography. Further, it promises applications in quantum metrology and sensing and is applicable in the near-term quantum computers for verification of the circuits fidelity and various quantum computing tasks.

arXiv:2204.11635•Apr 25, 2022•0 citations

Implementation of Quantum Deep Reinforcement Learning Using Variational Quantum Circuits

S Lokes, C. Sakthi Jay Mahenthar, S Parvatha Kumaran +2 more

With the evolution of technology, the need to solve complex computational problems like machine learning and deep learning has shot up. However, even the most powerful classical supercomputers find it difficult to execute these tasks. Advancements in quantum computing are leading researchers and tech-giants who strive for better quantum circuits to do machine learning tasks. Current works on Quantum Machine Learning (QML) ensure less memory consumption and reduced model parameters. However, it is strenuous to simulate the classical deep learning approach on existing quantum computing devices due to the inflexibility of Deep quantum circuits. Consequently, designing viable quantum algorithms for QML for noisy intermediate-scale quantum (NISQ) devices is essential. The proposed work aims to explore Variational Quantum Circuits (VQC) for Deep Q network-based Reinforcement Learning by remodeling the target network and experience replay into a representation of VQC. In addition, to the reduction in model parameters, quantum information encoding schemes are used to achieve better results than classical neural networks. VQCs are employed for policyselection and decision-making reinforcement learning by approximating the deep Q-value function with target network and experience replay.

International Conference on Trends in Quantum Computing and Emerging Business Technologies (TQCEBT)•Oct 13, 2022•19 citations
Variational quantum compiling (VQC) algorithms aim to approximate deep quantum circuits with shallow parameterized ansatzes, making them more suitable for NISQ hardware. In this article a variant of VQC named the recursive variational quantum compiling (RVQC) algorithm is proposed. Existing VQC algorithms typically require coherently executing the full circuit during compilation. Under the influence of noise, sufficiently deep target circuits make compiling unfeasible using ordinary VQC. Since the compiling is often accomplished using a gradient-based quantum-classical approach, the quantum noise manifest as a noisy gradient during optimization, making convergence hard to obtain. On the other hand, RVQC can compile a circuit by first dividing it into NNN shorter sub-circuits, then evaluate one sub-circuit at a time. As a result, the circuit depth required to implement RVQC is not dependent on the depth of the target circuit, but on the depth of the sub-circuits. Choosing a high enough NNN thus ensures sufficiently shallow sub-circuit which can be successfully compiled individually. We show mathematical evidence of this property. RVQC was compared with VQC on a noise model of the IBM Santiago device with the goal of compiling several randomly generated five-qubit circuits of approximately depth 1000. It was shown that VQC was not able to converge within 500 iterations of optimization. On the other hand, RVQC was able to converge to a fidelity of 0.90±0.050.90 \pm 0.050.90±0.05 within a total of 500 iterations when splitting the target circuits into N=5N = 5N=5 parts. We argue that this comes as a result of the mitigation of noise-induced barren plateaus.
Abstract Quantum compiling aims to construct a quantum circuitVby quantum gates drawn from a native gate alphabet, which is functionally equivalent to the target unitaryU. It is a crucial stage for the running of quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. However, the space for structure exploration of quantum circuit is enormous, resulting in the requirement of human expertise, hundreds of experimentations or modifications from existing quantum circuits. In this paper, we propose a variational quantum compiling (VQC) algorithm based on reinforcement learning, in order to automatically design the structure of quantum circuit for VQC with no human intervention. An agent is trained to sequentially select quantum gates from the native gate alphabet and the qubits they act on by doubleQ-learning withϵ-greedy exploration strategy and experience replay. At first, the agent randomly explores a number of quantum circuits with different structures, and then iteratively discovers structures with higher performance on the learning task. Simulation results show that the proposed method can make exact compilations with less quantum gates compared to previous VQC algorithms. It can reduce the errors of quantum algorithms due to decoherence process and gate noise in NISQ devices, and enable quantum algorithms especially for complex algorithms to be executed within coherence time.
Despite advances in the development of quantum computers, the practical application of quantum algorithms requiring deep circuit depths or high-fidelity transformations remains outside the current range of the so-called noisy intermediate-scale quantum devices. Now and beyond, quantum circuit compilation (QCC) is a crucial component of any quantum algorithm execution. Besides translating a circuit into hardware-specific gates, it can optimize circuit depth and adapt to noise. Variational quantum circuit compilation (VQCC) optimizes the parameters of an ansatz according to the goal of reproducing a given unitary transformation. In this work, we present a VQCC-objective function called the quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1. We show that the QWC cost function upper bounds the average infidelity of two circuits. An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit. We demonstrate the efficacy of the QWC cost function by compiling hardware efficient ansatz (HEA) as both the target and the ansatz and comparing to cost functions such as the Loschmidt echo test (LET) and the Hilbert-Schmidt test (HST). Finally, our experiments demonstrate that QWC as a cost function is the least affected by barren plateaus when compared to LET and HST for deep enough circuits.
Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy intermediate-scale quantum (NISQ) processors. Such systems leverage classical optimization to tune the parameters of a parameterized quantum circuit (PQC). The goal is minimizing a cost function that depends on measurement outputs obtained from the PQC. Optimization is typically implemented via stochastic gradient descent (SGD). On NISQ computers, gate noise due to imperfections and decoherence affects the stochastic gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits, but they in turn cause an increase in the variance of the gradient estimates. This work studies the impact of quantum gate noise on the convergence of SGD for the variational eigensolver (VQE), a fundamental instance of VQAs. The main goal is ascertaining conditions under which QEM can enhance the performance of SGD for VQEs. It is shown that quantum gate noise induces a nonzero error-floor on the convergence error of SGD (evaluated with respect to a reference noiseless PQC), which depends on the number of noisy gates, the strength of the noise, as well as the eigenspectrum of the observable being measured and minimized. In contrast, with QEM, any arbitrarily small error can be obtained. Furthermore, for error levels attainable with or without QEM, QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently large, and a sufficiently large number of measurements is allowed at each SGD iteration. Numerical examples for a max-cut problem corroborate the main theoretical findings.
Variational quantum algorithms (VQAs) hold significant promise for solving complex problems across diverse fields. However, their practical implementation on near-term quantum devices is severely hampered by the pervasive effects of quantum noise. Traditional quantum circuit compilation techniques are largely static, failing to account for the unique noise profiles inherent in individual quantum hardware. This paper introduces a novel adaptive quantum circuit compilation framework designed to mitigate these limitations. The core concept centers around dynamically adjusting the circuit layout and gate decomposition in real-time, leveraging measurements of the quantum hardware's noise characteristics to optimize both the accuracy and circuit depth of the compiled quantum circuit. This approach represents a critical step towards unlocking the full potential of VQAs by enabling them to effectively operate within the constraints of noisy quantum computers. The framework incorporates feedback loops for continuous refinement, adapting to evolving noise conditions. The methodology is described, focusing on the key components: noise profiling, adaptive gate decomposition, and circuit re-optimization. Simulation results demonstrate the effectiveness of the adaptive approach in reducing circuit depth and improving the fidelity of VQA computations compared to static compilation methods. This work lays the foundation for robust and efficient VQA execution on future quantum hardware.
Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking, quantum error mitigation, and so on. Here, we propose a universal compilation-based variational algorithm for the preparation and tomography of quantum states in low-depth quantum circuits. We apply the Fubini-Study distance to be a trainable cost function under various gradient-based optimizers, including the quantum natural gradient approach. We evaluate the performance of various unitary topologies and the trainability of different optimizers for getting high efficiency. In practice, we address different circuit ansatzes in quantum state preparation, including the linear and graph-based ansatzes for preparing different entanglement target states such as representative GHZ and W states. We also discuss the effect of the circuit depth, barren plateau, readout noise in the model, and the error mitigation solution. We next evaluate the reconstructing efficiency in quantum state tomography via various popular circuit ansatzes and reveal the crucial role of the circuit depth in the robust fidelity. The results are comparable with the shadow tomography method, a similar fashion in the field. Our work expresses the adequate capacity of the universal compilation-based variational algorithm to maximize the efficiency in the quantum state preparation and tomography. Further, it promises applications in quantum metrology and sensing and is applicable in the near-term quantum computers for verification of the circuits fidelity and various quantum computing tasks.
With the evolution of technology, the need to solve complex computational problems like machine learning and deep learning has shot up. However, even the most powerful classical supercomputers find it difficult to execute these tasks. Advancements in quantum computing are leading researchers and tech-giants who strive for better quantum circuits to do machine learning tasks. Current works on Quantum Machine Learning (QML) ensure less memory consumption and reduced model parameters. However, it is strenuous to simulate the classical deep learning approach on existing quantum computing devices due to the inflexibility of Deep quantum circuits. Consequently, designing viable quantum algorithms for QML for noisy intermediate-scale quantum (NISQ) devices is essential. The proposed work aims to explore Variational Quantum Circuits (VQC) for Deep Q network-based Reinforcement Learning by remodeling the target network and experience replay into a representation of VQC. In addition, to the reduction in model parameters, quantum information encoding schemes are used to achieve better results than classical neural networks. VQCs are employed for policyselection and decision-making reinforcement learning by approximating the deep Q-value function with target network and experience replay.