Is the Hilbert Space Language Too Rich?

Marian Kupczyński

Stephen Bruce Sontz

Qin Zhao, Chenguang Hou, Ruifeng Xu

Aiming at classifying the polarities over aspects, aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. The vector representations of current models are generally constrained to real values. Based on mathematical formulations of quantum theory, quantum language models have drawn increasing attention. Words in such models can be projected as physical particles in quantum systems, and naturally represented by representation-rich complex-valued vectors in a Hilbert Space, rather than real-valued ones. In this paper, the Hilbert Space representation for ABSA models is investigated and the complexification of three strong real-valued baselines are constructed. Experimental results demonstrate the effectiveness of complexification and the outperformance of our complex-valued models, illustrating that the complex-valued embedding can carry additional information beyond the real embedding. Especially, a complex-valued RoBERTa model outperforms or approaches the previous state-of-the-art on three standard benchmarking datasets.

Songbo Xie

Bojja Sreedhar, Saroja Pathapati, Satyapriya Krishna +3 more

Quantum Natural language processing (QNLP) is the new technology that incorporates the theory of quantum computing with the linguistic theory to make more effective and transparent models of comprehending natural language. The paper proposes QNLP model of type combining the vector space semantics and the graphical ZX-calculus, applicable to quantum computing to describe, process, and interpret the sentences structure as a quantum circuit. Its approach includes a sentence parsing with a categorial grammar, a mapping of the semantic constituents to products of high dimensional Hilbert spaces and a representation of their interaction with the so-called ZX-diagrams. Such circuits are compiled into quantum instructions and emulated on quantum devices such as Qiskit. The model was compared in terms of the accuracy of parse, preservation of semantics, diagrammatic effectiveness, quantum fidelity and sentence reprehensibility. This has been demonstrated to match the outputs of classical and quantum semantics, by 86 percent on parsing accuracy and above 96% on quantum circuit fidelity. The paper shows ZX-calculus is a potentially powerful and understandable framework to construct large-scale and semantically rich QNLP systems, given near-term quantum hardware.

Boldizsár Poór, Razin Abdulrauf Shaikh, Quanlong Wang

The ZX-calculus is a graphical language for reasoning about quantum computing and quantum information theory.As a complete graphical language, it incorporates a set of axioms rich enough to derive any equation of the underlying formalism.While completeness of the ZX-calculus has been established for qubits and the Clifford fragment of prime-dimensional qudits, universal completeness beyond two-level systems has remained unproven until now.In this paper, we present a proof establishing the completeness of finite-dimensional ZX-calculus, incorporating only the mixeddimensional Z-spider and the qudit X-spider as generators.Our approach builds on the completeness of another graphical language, the finite-dimensional ZW-calculus, with direct translations between these two calculi.By proving its completeness, we lay a solid foundation for the ZX-calculus as a versatile tool not only for quantum computation but also for various fields within finite-dimensional quantum theory.