Seminar

To implement arbitrary quantum interactions in architectures with restricted topologies, one may simulate all-to-all connectivity by routing quantum information. Therefore, it is of natural interest to find optimal protocols and lower bounds for routing. We consider a connectivity graph, G, of 2 regions connected only through an intermediate region of a small number of qubits that form a vertex bottleneck. Existing results only imply a trivial lower bound on the entangling rate and routing time across a vertex bottleneck.

Permutation-invariant quantum error correction codes that are invariant under any permutation of the underlying particles. These codes could have potential applications in quantum sensors and quantum memories. Here I will review the field of permutation-invariant codes, from code constructions to applications.

*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*

Fault tolerance is a notion of fundamental importance to the field of quantum information processing. It is one of the central properties a quantum computer must possess in order to enable the achievement of large scale practical quantum computation. While a widely used, general, and intuitive concept, within the literature the term fault tolerant is often applied to specific procedures in an ad-hoc fashion tailored to details of the context or platform under discussion.

Long-range entangled states of matter encompass a variety of exotic quantum phenomena, ranging from topological orders to quantum criticality. In this talk, I will discuss recent advances in leveraging mid-circuit measurements and unitary feedback to efficiently generate these entangled many-body states.

We present a new method for analyzing and identifying errors in quantum circuits. In our approach, we define the problem using a triple {P}C{Q}, where the task is to determine whether a given set P of quantum states at the input of a circuit C produces a set of quantum states at the output that is equal to, or included in, a set Q. We propose a technique that utilizes tree automata to represent sets of quantum states efficiently, and we develop algorithms to apply the operations of quantum gates within this representation.

Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by use of these formulae. This work provides an improved, rigorous analysis of these techniques for the task of calculating time-evolved expectation values.

We introduce the “hidden cut problem:” given as input which is product across an unknown bipartition, the goal is to learn precisely where the state is unentangled, i.e. to find the hidden cut. We give a polynomial time quantum algorithm for the hidden cut problem, which consumes O(n/ε^2) many copies of the state, and show that this asymptotic is optimal. In the special case of Haar-random states, the circuits involved are of merely constant depth, which could prove relevant to experimental implementations.

In this talk I will describe Decoded Quantum Interferometry (DQI), a quantum algorithm for reducing classical optimization problems to classical decoding problems by exploiting structure in the Fourier spectrum of the objective function. (See: https://arxiv.org/abs/2408.08292.) For a regression problem called optimal polynomial intersection, which has been previously studied in the contexts of coding theory and cryptanalysis, we believe DQI achieves an exponential quantum speedup.

Quantum sensing leverages the principles of quantum mechanics to provide ``quantum-enhanced'' measurement sensitivity, thereby amplifying our ability to observe interesting physical phenomena. It employs a rich arsenal of techniques, including squeezing, photon counting, entanglement assistance, and distributed quantum sensing to achieve unprecedented sensitivity.

Aaronson, Atia, and Susskind established that swapping quantum states |ψ〉 and |ϕ〉 is computationally equivalent to distinguishing their superpositions |ψ〉 ± |ϕ〉. We extend this to a general duality principle: manipulating quantum states in one basis is equivalent to extracting values in a complementary basis. Formally, for any group, implementing a unitary representation is computationally equivalent to Fourier subspace extraction from its irreducible representations.