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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2022.3185287