Seminar

We define a quantum monomer-dimer model on a Penrose tiling (a quasicrystal) in the space of maximal dimer coverings. Monomers are necessarily present because it was shown by F. Flicker et al., PRX 10, 011005 (2020) that there are no perfect dimer coverings of Penrose tilings. Despite the presence of a finite density of monomers, our model has a Rokhsar-Kivelson (RK) point at which the ground state is a uniform superposition of all maximal dimer coverings.

In recent years, the use of Gottesman-Kitaev-Preskill (GKP) Codes to  implement fault-tolerant quantum computation has gained significant traction and evidence for their experimental utility has steadily grown.  But what does it even mean for quantum computation with the GKP code to be fault tolerant?  In this talk, we discuss the structure of logical Clifford gates for the GKP code and how their understanding leads to a classification of the space of all GKP Codes.

In this work we present fast constructions for the quantum Fourier transform and quantum integer multiplication, using few ancilla qubits compared to the size of the input. For the approximate QFT we achieve depth O(log n) using only n + O(n / log n) total qubits, by applying a new technique we call "optimistic quantum circuits." To our knowledge this is the first circuit for the AQFT with space-time product O(n log n), matching a known lower bound.

Reservoir engineering has become valuable for preparing and stabilizing quantum systems. Notably, it has enabled the demonstration of dissipatively stabilized Schrödinger’s cat qubits through engineered two-photon loss which are interesting candidates for bosonic error-corrected quantum computation. Reservoir engineering is however limited to simple operators often derived from weak low-order expansions of some native system Hamiltonians. In this talk, I will introduce a novel reservoir engineering approach for stabilizing multi-component Schrödinger’s cat states.

While the search for quantum advantage typically focuses on speedups in execution time, quantum algorithms also offer the potential for advantage in space complexity. Previous work has shown such advantages for data stream problems, in which elements arrive and must be processed sequentially without random access, but these have been restricted to specially-constructed problems [Le Gall, SPAA `06] or polynomial advantage [Kallaugher, FOCS `21]. We show an exponential quantum space advantage for the maximum directed cut problem.

The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. We expect that the approximate stabilizer rank of n-th tensor power of the “magic” T state scale exponentially in n, otherwise there is a polynomial time classical algorithm to simulate arbitrary polynomial time quantum computations.  Despite this intuition, several attempts using various techniques could not lead to a better than a linear lower bound on the “exact” rank.

We discuss recent progress on entanglement catalysis, including the equivalence between catalytic and asymptotic transformations of quantum states and the impossibility to distill entanglement from states having positive partial transpose, even in the presence of a catalyst. A more general notion of catalysis is the concept of entanglement battery. In this framework, we show that a reversible manipulation of entangled states is possible. This establishes a second law of entanglement manipulation without relying on the generalized quantum Stein's lemma.

Light is quantum. Hence, quantifying and attaining fundamental limits of transmitting, processing and extracting information encoded in light must use quantum analyses. This talk is aimed at elucidating this using principles from information and estimation theories, and quantum modeling of light. We will discuss nuances of “informationally optimal” measurements on so-called Gaussian states of light in the contexts of a few different metrics.

Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, the preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models.

Statistical learning is emerging as a new paradigm in science.

This has ignited interest within our inherently quantum world in exploring quantum machines for their advantages in learning, generating, and predicting various aspects of our universe by processing both quantum and classical data. In parallel, the pursuit of scalable science through physical simulations using both digital and analog quantum computers is rising on the horizon.