QuICS Special Seminar

In this seminar, we look at how one can use certain properties of quantum physics to bypass the fair-sampling assumption commonly used in most practical Bell experiments. Our approach is based on an alternative nonlocality framework called “semi-quantum nonlocality”, where measurement instructions are represented by quantum inputs instead of classical inputs. A key feature of this framework is that all “entangled states are nonlocal”, in the sense that for any entangled state there is always a semi-quantum Bell inequality with which violation can be achieved.

Topological quantum computation is a fault tolerant protocol for quantum computing using non-abelian topological phases of matter. Information is encoded in states of multi-quasiparticle excitations(anyons), and quantum gates are realized by braiding of anyons. The mathematical foundation of anyon systems is described by unitary modular tensor categories.

In the study of Markovian processes, one of the principal achievements is the equivalence between the Φ-Sobolev inequalities and an exponential decrease of the Φ-entropies. In this work, we develop a framework of Markov semigroups on matrix-valued functions and generalize the above equivalence to the exponential decay of matrix Φ-entropies. This result also specializes to spectral gap inequalities and modified logarithmic Sobolev inequalities in the random matrix setting.

The discovery of postquantum nonlocality, i.e. the existence of nonlocal correlations stronger than any quantum correlations but nevertheless consistent with the no-signaling principle, has deepened our understanding of the foundations quantum theory. In this work, we investigate whether the phenomenon of Einstein-Podolsky-Rosen steering, a different form of quantum nonlocality, can also be generalized beyond quantum theory. While postquantum steering does not exist in the bipartite case, we prove its existence in the case of three observers.

Cellular automata (CA) are computational structures spaciously and temporally discrete which were originally proposed by John von Neumann in the late 1940’s. They have the same computational power of Turing machines.This tool enables us to simulate a large number of different problems in distinct areas.

We present an algorithm for efficiently approximating qubit unitaries over gate sets derived from totally definite quaternion algebras. The algorithm achieves ε-approximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T and a few other gate sets. Moreover, the algorithm to compile the efficient approximation is efficient as well: its running time is polynomial in O(log(1/ε)), conditional on a number-theoretic conjecture.

I will show how to use basic facts from representation theory to derive a unitary version of Cayley's theorem (it allows embedding any finite group in a continuous subgroup of the unitary group). When applied to the symmetric group, this can be used to permute quantum systems in a continuous fashion. I will illustrate how this works for a small number of systems and conclude with some interesting open questions. My talk is loosely based on arXiv:1508.00860.

Estimation of the minimum eigenvalue of a quantum Hamiltonian can be formalised as the Local Hamiltonian problem. In one natural special case of the Local Hamiltonian problem, the same 2-local interaction, with differing weights, is applied across each pair of qubits. I will talk about some recent work classifying the computational complexity of this problem when some additional physically motivated restrictions are made to these weights.

Linear optics quantum computing is a promising candidate for the implementation of scalable quantum computing. However, it remains extremely technically challenging owing to the large number of optical elements that would be required for a large-scale device, potentially requiring millions of discrete elements. I present a substantially simplified scheme based on time-bin encoding, whereby only three optical elements are required, independent of the size of the computation.