Quantum encoder for fixed Hamming-weight subspaces

• URL: http://arxiv.org/abs/2405.20408v2
• Date: Thu, 5 Sep 2024 11:50:39 GMT
• Title: Quantum encoder for fixed Hamming-weight subspaces
• Authors: Renato M. S. Farias, Thiago O. Maciel, Giancarlo Camilo, Ruge Lin, Sergi Ramos-Calderer, Leandro Aolita,
• Abstract summary: We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-principle data vectors of $d=binomnk$ provided in analytical form. We also perform an experimental proof-of-principle demonstration of our scheme on a commercial trapped-ion quantum computer.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression. The circuit is optimal in that it expresses an arbitrary data vector using only $d-1$ (controlled) Reconfigurable Beam Splitter (RBS) gates and is constructed by an efficient classical algorithm that sequentially generates all bitstrings of weight $k$ and identifies all gate parameters. An explicit compilation into CNOTs and single-qubit gates is presented, with the total CNOT-gate count of $\mathcal{O}(k\, d)$ provided in analytical form. In addition, we show how to load data in the binary basis by sequentially stacking encoders of different Hamming weights using $\mathcal{O}(d\,\log(d))$ CNOT gates. Moreover, using generalized RBS gates that mix states of different Hamming weights, we extend the construction to efficiently encode arbitrary sparse vectors. Finally, we perform an experimental proof-of-principle demonstration of our scheme on a commercial trapped-ion quantum computer. We successfully upload a $q$-Gaussian probability distribution in the non-log-concave regime with $n = 6$ and $k = 2$. We also showcase how the effect of hardware noise can be alleviated by quantum error mitigation. Our results constitute a versatile framework for quantum data compression with various potential applications in fields such as quantum chemistry, quantum machine learning, and constrained combinatorial optimizations.

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