QuICS seminar

In recent years Gottesman-Kitaev-Preskill (GKP) codes have witnessed an increasing amount of interest for both their theoretically interesting features and as a possible route towards scalable hardware-efficient error correction.

Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output is not known. We introduce quantum majority vote as the following task: given a product state ∣ψ_1〉⊗⋯⊗∣ψ_n〉 where each qubit ∣ψ_i〉 is in one of two orthogonal states ∣ψ〉 or ∣ψ^⊥〉, output the majority state. We show that an optimal algorithm for this problem achieves worst-case fidelity of 1/2 + Θ(1/n).

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE states such as preparing the toric code from measuring a sublattice of a 2D cluster state.

Monitored random quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations.

In this talk, I will introduce a new security property of a cryptographic hash function that is useful for quantum cryptography. This property (1) suffices to construct pseudorandom quantum states, (2) holds for a random oracle, and thus plausibly holds for existing hash functions like SHA3, and (3) is independent of the P vs. NP question in the black box setting. This offers further evidence that one-way functions are not necessary for computationally-secure quantum cryptography. Our proof builds on recent work of Aaronson, Ingram, and Kretschmer (2022).

We study the stellar representation of quantum computations, based on holomorphic functions, which delineates the boundary between discrete- and continuous-variable quantum information theory.

In this talk, I'll motivate studying the complexity of quantum states and transformations. I'll discuss how this general study is related to a seminal theoretical computer science concept: search vs. decision. I'll show how to construct a form of search-to-decision reductions for QMA problems and show why it is unlikely that we can do (much) better. I'll conclude by discussing a parametrized notion of QMA and the notion of QMA solutions in this context.

Several tasks in quantum-information processing involve quantum learning. For example, quantum sensing, quantum machine learning and quantum-computer calibration involve learning and estimating unknown parameters from measurements of many copies of a quantum state that depends on those parameters. This type of metrological information is described by the quantum Fisher information matrix, which bounds the average amount of information learnt about the parameters per measurement of the state.

In this talk I want to introduce shadow sequence estimation. This is a protocol for learning noise in (random) quantum circuits in a flexible and scalable manner. It arises essentially as a combination of randomised shadow estimation (in the Huang-Kueng-Preskill sense) and randomised benchmarking, a time-honoured gate-fidelity estimation protocol.

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently this concept has found applications beyond quantum computing---in the classification of topological phases of matter and in the description of chaotic many-body systems. Furthermore, within the context of the AdS/CFT correspondence, it has been postulated that the complexity of a specific time-evolved many-body quantum state is sensitive to the long-time properties of AdS-black hole interiors.