Quantum Information

In this talk, I will discuss quantum diagonalization methods, based on subspaces obtained from quantum computers, which overcome the scaling limitations of variational algorithms and enabled realistic chemistry computations of up to 77 qubits on a quantum centric supercomputing architecture, using a Heron quantum processor and the RIKEN supercomputer Fugaku. Merging these ideas with Krylov quantum subspaces, I will present a ground state algorithm with convergence similar to phase estimation and robustness to noise, which led to an experimental demonstration for lattice ground state problems obtained with Heron processors and the supercomputer Frontier.

Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. We present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in  d  different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error correction. Here, we introduce the concept of topological quantum spin glass (TQSG) order which marries these two notions, exhibiting both the complex energy landscapes of spin glasses, and the quantum memory and long-range entanglement characteristic of topologically ordered systems. Using techniques from coding theory and a quantum generalization of Gibbs state decompositions, we show that TQSG order is the low-temperature phase of various quantum LDPC codes on expander graphs, including hypergraph and balanced product codes. Our work introduces a topological analog of spin glasses that preserves quantum information, opening new avenues for both statistical mechanics and quantum computer science.

Quantum computing and sensing represent two distinct frontiers of quantum information science. Here, we harness quantum computing to solve a fundamental and practically important sensing problem: the detection of weak oscillating fields with unknown strength and frequency. We present a quantum computing enhanced sensing protocol, that we dub quantum search sensing, outperforming all existing approaches. Furthermore, we prove our approach is optimal by establishing the Grover-Heisenberg limit -- a fundamental lower bound on the minimum sensing time. The key idea is to robustly digitize the continuous, analog signal into a discrete operation, which is then integrated into a quantumalgorithm. Our metrological gain originates from quantum computation, distinguishing our protocol from conventional sensing approaches. Indeed, we prove that broad classes of protocols based on quantum Fisher information, finite-lifetime quantum memory, or classical signal processing are strictly less powerful. We propose and analyze a proof-of-principle experiment using nitrogen-vacancy centers, where meaningful improvements are achievable using current technology. This work establishes quantum computation as a powerful new resource for advancing sensing capabilities.