This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
Walgate and Scott have determined the maximum number of generic pure quantum states in multipartite space that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we determine this number in a more general setting in which the local parties have access to pre-shared entanglement in the form of a resource state. We find that, for an arbitrary pure resource state, this number is equal to the Krull dimension of (the closure of) the set of pure states obtainable from the resource state by SLOCC.
In this talk, I argue that the question of whether a physical system can be simulated on a computer is important not just from a practical perspective but also a fundamental one. We consider the complexity of simulating Hamiltonians with respect to both dynamics and equilibrium properties. This gives us a classification and a phase diagram of the complexity. I will cover recent results in this topic, such as a dynamical complexity phase diagram for a long-range bosonic Hamiltonian and a complexity classification of the local Hamiltonian problem in the presence of a spectral gap.
Relativistic quantum tasks are quantum computations which have inputs and outputs that occur at designated spacetime locations.
Understanding which tasks are possible to complete, and what resources are required to complete them, captures spacetime-specific aspects of quantum information. In this talk we explore the connections between such tasks and quantum gravity, specifically in the context of the AdS/CFT correspondence. We find that tasks reveal a novel connection between causal features of bulk geometry and boundary entanglement.
Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities.
In this talk, I will discuss two problems: quantum data compression
and quantum causal order discovery, both for multipartite quantum
systems. For data compression, we model finitely correlated states as
tensor networks, and design quantum compression algorithms. We first
establish an upper bound on the amount of memory needed to store an
arbitrary state from a given state family. The bound is determined by
the minimum cut of a suitable flow network, and is related to the flow
In a quantum measurement process, classical information about the measured system spreads through the environment. In contrast, quantum information about the system becomes inaccessible to local observers. In this talk, I will present a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e.
"Analogue" Hamiltonian simulation involves engineering a Hamiltonian of
interest in the laboratory and studying its properties experimentally.
Large-scale Hamiltonian simulation experiments have been carried out in
optical lattices, ion traps and other systems for two decades. Despite
this, the theoretical basis for Hamiltonian simulation is surprisingly
sparse. Even a precise definition of what it means to simulate a
Hamiltonian was lacking.
The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. In this talk, I will discuss recent work which carried out a detailed analysis and optimisation of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including extensive numerical experiments for systems with up to 12 sites.
I will review work by myself and others in recent years on the use of randomization in quantum circuit optimization. I will present general results showing that any deterministic compiler for an approximate synthesis problem can be lifted to a better random compiler. I will discuss the subtle issue of what "better" means and how it is sensitive to the metric and computation task at hand. I will then review specific randomized algorithms for quantum simulations, including randomized Trotter (Su & Childs) and my group's work on the qDRIFT and SPARSTO algorithms. The qDRIFT algorithm i
Discriminating between unknown objects in a given set is a fundamental task in experimental science. Suppose you are given a quantum system which is in one of two given states with equal probability. Determining the actual state of the system amounts to doing a measurement on it which would allow you to discriminate between the two possible states. It is known that unless the two states are mutually orthogonal, perfect discrimination is possible only if you are given arbitrarily many identical copies of the state.