Symmetries are ubiquitous in physics and play a pivotal role in light-matter interactions, where they determine the selection rules governing allowed atomic transitions and define the associated conserved quantities. For the up-conversion process of high harmonic generation, the symmetries of the driving field determine the allowed frequencies and the polarization properties of the resulting harmonics. As a consequence, it is possible to establish classical selection rules when the process is driven by coherent radiation. In this work, we show that fluctuation-induced symmetry breaking in the driving field leads to the appearance of otherwise forbidden harmonics. This is achieved by considering bicircular quantum light, and demonstrate that the enhanced quantum fluctuations due to squeezing in the driving field break the classical selection rules. To this end, we develop a quantum optical description of the dynamical symmetries in the process of high harmonic generation, revealing corrections to the classical selection rules. Moreover, we show that the new harmonics show squeezing-like signatures in their photon statistics, allowing them to be clearly distinguished from classical thermal fluctuations. less

We provide a recursively defined sequence of flag circuits which will detect logical errors induced by non-fault-tolerant $R_{\overline{Z}}(\fracπ{2^l})$ gates on CSS codes with a fault distance of two. As applications, we give a family of circuits with $O(l)$ gates and ancillae which implement fault-tolerant logical $R_{Z}(\fracπ{2^l})$ or $R_{ZZ}(\fracπ{2^l})$ gates on any $[[k + 2, k, 2]]$ iceberg code and fault-tolerant circuits of size $O(l)$ for preparing $|\fracπ{2^l}\rangle$ resource states in the $[[7,1,3]]$ code, which can be used to perform fault-tolerant $R_{\overline{Z}}(\fracπ{2^l})$ rotations via gate teleportation, allowing for implementations of these gates that bypass the high overheads of gate synthesis when $l$ is small relative to the precision required. We show how the circuits above can be generalized to $π( x_0.x_{1}x_{2}\ldots x_{l}) = \sum_{j}^{l} π\frac{x_j}{2^j}$ rotations with identical overheads in $l$, which could be useful in quantum simulations where time is digitized in binary. Finally, we illustrate two approaches to increase the fault-distance of our construction. We show how to increase the fault distance of a Cliffordized version of the T gate circuit to $3$ in the Steane code and how to increase the fault-distance of the $\fracπ{2}$ iceberg circuit to $4$ through concatenation in two-level iceberg codes. This yields a targeted logical $R_{\overline{Z}}(\fracπ{2})$ gate with fault distance $4$ on any row of logical qubits in an $[[(k_2+2)(k_1+2), k_1k_2, 4]]$ code. less

We construct nested Calderbank-Shor-Steane code pairs with non-vanishing coding rate from Hsu-Anastasopoulos codes and MacKay-Neal codes. In the fixed-degree regime, we prove relative linear distance with high probability. Moreover, for several finite degree settings, we prove Gilbert-Varshamov distance by a rigorous computer-assisted proof. less

Quantum probes that enable enhanced exploration and characterization of complex systems are central to modern science, spanning applications from biology to astrophysics and chemical design. In large many-body quantum systems, interactions delocalize phase information across many degrees of freedom, dispersing it away from accessible measurements and limiting the scalability of quantum metrology. Here we show that experimentally accessible Clifford operations acting jointly on quantum states and observables can refocus this distributed information. These operations implement what we term {\it Clifford lensing}--transformations that coherently localize phase information onto a reduced set of degrees of freedom, mapping optimal measurements onto observables of reduced Pauli weight. We establish a correspondence between quantum error-correcting codes and interferometric constructions that enforce deterministic phase kickback, and generalize this to circuits that concentrate many-body phase information onto a controllable subset of qubits. We further develop partial shadow tomography protocols for estimating subsystem-supported phases. We experimentally demonstrate these principles in liquid-state nuclear magnetic resonance systems of up to fifteen qubits, achieving optimal sensing with constrained resources. Our results establish a scalable route to coherent control of information flow in interacting quantum systems, enabling many-body quantum sensing and multimode interferometry across complex architectures. less