Seminar

Learning properties of unknown quantum systems or processes is of fundamental importance to the development of quantum technologies. While many learning algorithms require access to external ancillary qubits (referred to as quantum memory), the statistical complexity and experimental costs for these algorithms vary considerably due to different sizes of quantum memory. Here, we investigate the transitions for statistical complexity required for learning quantum data with bounded quantum memory.

Quantum computers in the NISQ era are prone to noise. A range of quantum error mitigation techniques has been proposed to address this issue. Zero-noise extrapolation (ZNE) stands out as a promising one. ZNE involves increasing the noise levels in a circuit and then using extrapolation to infer the zero noise case from the noisy results obtained. This paper presents a novel ZNE approach that does not require circuit folding or noise scaling to mitigate depolarizing and/or decoherence noise.

The Quantum PCP Conjecture (QPCP) claims that estimating ground-state energies of local Hamiltonians to constant precision is hard for quantum computers. If true, QPCP implies the existence of local Hamiltonians with non-trivial low-energy space properties, and a recent trend has been to construct (or conjecture) such Hamiltonians independently of QPCP. This proposal will focus on topics surrounding QPCP and one such implication, the No Low-energy Sampleable States (NLSS) Conjecture.

Demonstrations of quantum advantage for random circuit and boson sampling over the past few years have generated considerable excitement for the future of quantum computing and has further spurred the development of a wide range of gate-based digital quantum computers, which represent quantum programs as a sequence of quantum gates acting on one and two qubits.

There is a rich connection between classical and quantum codes and holographic correspondence connecting 2d CFTs and abelian 3d Chern-Simons theories. In the 3d language the codes emerge as a way to parametrize condensable anyons. Upon condensation 3d topological field theory gives rise to 2d CFT at the boundary. This provides a way to construct 2d CFTs from codes - the so called "code CFTs." This construction of code CFT has a natural interpretation in terms of a CSS quantum code (defined in terms of the original classical code, defining the CFT).

I will discuss recent advances in improving and costing quantum algorithms for linear differential equations. I will introduce a stability-based analysis of Berry et al.’s 2017 algorithm that greatly extends its scope and leads to complexities sublinear in time in a broad range of settings – Hamiltonian simulation being a boundary case that prevents this kind of broad fast-forwarding. I illustrate these gains via toy examples such as the linearized Vlasov-Possion equation, networks of coupled, damped, forced harmonic oscillators and quadratic nonlinear systems of ODEs.

I will review the concept of Floquet quantum error-correcting codes, and, more generally, dynamic codes. These codes are defined through sequences of low-weight measurements that change the instantaneous code in time and enable error correction.  I will explain a few viewpoints on these codes, including state teleportation and anyon condensation, and will explain how to implement gates purely by adjusting the sequences of low-weight measurement.

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems.

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties (time evolution up to short times t). In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a 16-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device.