Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider th...

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Veröffentlicht in:	IEEE transactions on communications Jg. 70; H. 8; S. 5386 - 5400
Hauptverfasser:	Cui, Jingjing, Xiong, Yifeng, Ng, Soon Xin, Hanzo, Lajos
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.08.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Bit error rate bit error rate (BER) Circuits Complexity Computers Detectors Eigenvalues Error detection Evolution maximum likelihood (ML) detection Optimization Optimization algorithms quantum approximation optimization algorithm (QAOA) Quantum computing Quantum technology Quantum theory Qubit Sensors Stationary state Symbols
ISSN:	0090-6778, 1558-0857
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Abstract	Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> QAOA circuit having <inline-formula> <tex-math notation="LaTeX">2p </tex-math></inline-formula> variational parameters, which can be optimized by classical optimizers. This level-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector.
AbstractList	Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> QAOA circuit having <inline-formula> <tex-math notation="LaTeX">2p </tex-math></inline-formula> variational parameters, which can be optimized by classical optimizers. This level-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector. Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-[Formula Omitted] QAOA circuit having [Formula Omitted] variational parameters, which can be optimized by classical optimizers. This level-[Formula Omitted] QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in [Formula Omitted] consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector.
Author	Xiong, Yifeng Ng, Soon Xin Hanzo, Lajos Cui, Jingjing
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SubjectTerms	Algorithms Bit error rate bit error rate (BER) Circuits Complexity Computers Detectors Eigenvalues Error detection Evolution maximum likelihood (ML) detection Optimization Optimization algorithms quantum approximation optimization algorithm (QAOA) Quantum computing Quantum technology Quantum theory Qubit Sensors Stationary state Symbols
Title	Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection
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