Chapter 2 serves as a primer on quantum mechanics tailored for quantum computing. It reviews essential concepts such as quantum states, operators, superposition, entanglement, and the probabilistic nature of quantum measurements. This chapter focuses on two-level quantum systems (i.e. qubits). Mathematical formulations that are specific to quantum mechanics are introduced, such as Dirac (bra–ket) notation, the Bloch sphere, density matrices, and Kraus operators. This provides the reader with the necessary tools to understand quantum algorithms and the behaviour of quantum systems. The chapter concludes with a review of the quantum harmonic oscillator, a model to describe quantum systems that are complementary to qubits and used in some quantum computer implementations.

In this chapter, we describe a tensor network (TN) based common language established between machine learning and many-body physics, which allows for bidirectional contributions. By showing that many-body wave functions are structurally equivalent to mappings of convolutional and recurrent networks, we bring forth quantum entanglement measures as natural quantifiers of dependencies modeled by such networks. Accordingly, we propose a novel entanglement-based deep learning design scheme that sheds light on the success of popular architectural choices made by deep learning practitioners and suggests new practical prescriptions. In the other direction, we construct TNs corresponding to deep recurrent and convolutional networks. This allows us to theoretically demonstrate that these architectures are powerful enough to represent highly entangled quantum systems polynomially more efficiently than previously employed architectures. We thus provide theoretical motivation to shift neural-network-based wave function representations closer to state-of-the-art deep learning architectures.

From questions posed by Wilfred Owen at a Craiglockhart War Hospital talk ‘Do Plants Think?’ and Alan Turing’s rhetorical echo ‘Can Machines Think?’ to Dipesh Chakrabarty’s query ‘Who is the we?’ in a postcolonial Anthropocene, times of crisis goad us into recognising wider sentience and reimagining collective agency. This essay considers how a collective comprised of humans, intelligent botanical or zoological life, and AI might respond to climate crisis using two literary case studies. Richard Powers’ The Overstory and Vandana Singh’s ‘Entanglement’ use contemporary tree science and quantum entanglement, respectively, as innovative, interdisciplinary narrative models. These models also dictate the resolutions of their stories – eventualities of collectivity that may still be evolving, but gesture toward potential climate-changed futures. As this essay argues, these two works offer contrasting visions based on how they deploy AI design potentials, the emotional responses of hope and despair, and the spectre of uncertainty as either a creative space for solutions or a reminder of impossible choices. These stories also pose important questions about corporate power, empathy, and social justice, reminding us that reckoning with human cultural diversity is still the soil from which any more-than-human climate collective must grow.