QuICS seminar

Characterising quantum processes is a key task in the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency.

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. To date, all proposed schemes for implementing a universal logical gate set, such as magic state distillation or code switching, require a substantial space-time overhead, including a time overhead that necessarily diverges in the limit of vanishing logical error rate.

Soon, quantum computing researchers can expect to have access to a quantum computer consisting of 50 to 100 qubits. While fault-tolerant quantum computer promises great speedups over a range of important problems, these devices will not be reliable enough to fulfill these promises. An outstanding challenge then is to come up with an application that can reliably carry out a nontrivial task of interest. Can we do anything that is practically useful?

Quantum computing is at an inflection point, where 79-qubit (quantum bit) machines are being tested, 100-qubit machines are just around the corner, and even 1000-qubit machines are perhaps only a few years away.  These machines have the potential to fundamentally change our concept of what is computable and demonstrate practical applications in areas such as quantum chemistry, optimization, and quantum simulation.
 

An outstanding open question in quantum information theory concerns the computational complexity of nonlocal games. in a nonlocal game, a classical verifier interacts with multiple players that cannot communicate, but are allowed to share entanglement. In a recent breakthrough result, Slofstra showed that the following problem is undecidable: given a nonlocal game, is there a quantum strategy for the players to win with probability 1?
 

The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos. In this talk, we will address the question of scrambling and operator complexity in continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: 1) scrambling in the phase space of a single mode and 2) scrambling across multiple modes of a many-body system.

I will give an overview of the range of algorithms for simulating Hamiltonian evolution on a quantum computer.  These include Lie-Trotter-Suzuki product formulae, quantum walks, linear combinations of unitaries, Taylor series, Dyson series, quantum signal processing and qubitisation.  I will discuss the relations between these approaches, as well as how they can be applied to quantum chemistry.  The talk will also cover a new log-depth technique for antisymmetrising states to use for quantum chemistry.

In this work, we show that for local Hamiltonians in 1D with translationally invariant nearest neighbour interactions, deciding whether or not the system is gapped or gapless, is undecidable. In order to prove this, we need to go beyond the already-known 2D case, and replace a fractal Robinson tiling---only possible in more than one dimension---with a specific Hamiltonian that has a type of attractive force in its ground state.

I will present a study of continuum limits of Matrix Product States (MPS). We show that an MPS has a continuum limit if and only if its transfer matrix is an infinitely divisible channel. To prove this result, we first need to define the irreducible form of an MPS, which is a generalization of the canonical form. This result also implies that the continuum limit of an MPS can generally not be described by a continuous MPS -- I will mention a possible generalization of the latter class.

Our first result concerns an old question in quantum information theory: how much quantum communication is required to approximately convert one pure bipartite entangled state into another? We give a simple and efficiently computable bound in terms of the earth mover or Wasserstein distance. We show that the communication cost of converting between two pure states is bounded (up to a constant factor) by the Absolute Earth Mover distance between the distributions given by the negative logarithm of the Schmidt coefficients of each state.