Exploring the promise of quantum computing

ACM Computing Prize recipient Scott Aaronson discusses his work in quantum complexity.

How smooth is quantum complexity?

The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational complexity, it has since been argued to hold a fundamental significance in its own right, as a physical quantity analogous to the thermodynamic entropy. In this paper, we present a unified perspective on various notions of quantum complexity, viewed as functions on the space of unitary operators. One striking feature of these functions is that they can exhibit non-smooth and even fractal behaviour. We use ideas from Diophantine approximation theory and sub-Riemannian geometry to rigorously quantify this lack of smoothness. Implications for the physical meaning of quantum complexity are discussed.

Self-testing of a single quantum device under computational assumptions

Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.

Dialogs of a hybrid world

The article is based on reports and discussions held during three online events organized by the Russian Research Center for the Internet of Things together with the Department of Philosophy and Sociology of South-West State University during 2021: an open discussion with the famous transhumanist philosopher David Pearce dedicated to the birthday of Jeremiah Bentham on February 15, a round table dedicated to the World Internet of Things Day on April 9, and a session within the first IoT Hot Spots conference on June 16.The main topics for discussion this year were the consideration of the following philosophical and socio-cultural problems and concepts in the light of the development of cyberphysical systems: anthropological differences between the «posthuman» and «metahuman» projects, epistemological aspects of bio- and cybersemiotics in modern hybrid techno-social networks, the cultural dimension of remote proximity in the digital age, the ontology of the quantum complexity of the digital multiverse, the ethical dimensions of the digital economy in the post-covid period, the aesthetics of metamodernism in the smart city, the anthropocene effects of silicon addiction and the race of computing, socio-philosophical problems of management in situations of high uncertainty, political strategies for sustainable development.

Size and momentum of an infalling particle in the black hole interior

The future interior of black holes in AdS/CFT can be described in terms of a quantum circuit. We investigate boundary quantities detecting properties of this quantum circuit. We discuss relations between operator size, quantum complexity, and the momentum of an infalling particle in the black hole interior. We argue that the trajectory of the infalling particle in the interior close to the horizon is related to the growth of operator size. The notion of size here differs slightly from the size which has previously been related to momentum of exterior particles and provides an interesting generalization. The fact that both exterior and interior momentum are related to operator size growth is a manifestation of complementarity.

The power of quantum complexity

A theorem about computations that exploit quantum mechanics challenges longstanding ideas in mathematics and physics.