Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy quantum and classical correlations at the level of the circuit. The relevant spatiotemporal effects are difficult enough to understand, let alone combat. There is presently a lack of either scalable or complete methods to address the phenomena responsible for scrambling and loss of quantum information. Here, we make deep strides to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, assumes no parameters values, and is written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing also for easy modularisation and simplification based on the expected physics of the system. This is then demonstrated through both extensive numerical studies and implementations on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. Finally, we conclude our analysis with applications thereof to the efficacy of control techniques to counteract these effects -- including noise-aware circuit compilation and optimised dynamical decoupling. We find significant improvements are possible in the diamond norm and average gate fidelity of arbitrary $SU(4)$ operations, as well as related decoupling improvements in contrast to off-the-shelf schemes.

Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the temporal domain to explore multi-time phenomena. This enables us to efficiently learn the features of multi-time processes such as correlated error rates, multi-time non-Markovianity, and temporal entanglement. We test the efficacy of these tools on a noisy quantum processor to characterise its noise features. Implementing these tools requires mid-circuit instruments, typically slow or unavailable in current quantum hardware. We devise a protocol to achieve fast and reliable instruments such that these multi-time distributions can be learned to a high accuracy. This enables a compact matrix product operator representation of large processes allowing us to showcase a reconstructed 20-step process (whose naive dimensionality is that of a 42-qubit state). Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of noisy intermediate-scale quantum devices.

We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a 1D bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the non-interacting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spin-like for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection we find that these edge excitations are quasiparticle-like as long as they remain within the bulk gap. Above a critical interaction strength of $U_c\approx 5 t$ these quasiparticles on the boundary loose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the non-trivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.

The reliable, deterministic production of trustworthy high-quality single photons is a critical component of discrete variable, optical quantum technology. For single-photon based fully error-corrected quantum computing systems, it is estimated that photon sources will be required to produce a reliable stream of photons at rates exceeding 1 GHz [1]. Photon multiplexing, where low probability sources are combined with switching networks to route successful production events to an output, are a potential solution but requires extremely fast single photon switching with ultra-low loss rates. In this paper we examine the specific properties of the switching elements and present a new design that exploits the general one-way properties of common switching elements such as thermal pads. By introducing multiple switches to a basic, temporal multiplexing device, we are able to use slow switching elements in a multiplexed source being pumped at much faster rates. We model this design under multiple error channels and show that anticipated performance is now limited by the intrinsic loss rate of the optical waveguides within integrated photonic chipsets.

Strain is extensively used to controllably tailor the electronic properties of materials. In the context of indirect band-gap semiconductors such as silicon, strain lifts the valley degeneracy of the six conduction band minima, and by extension the valley states of electrons bound to phosphorus donors. Here, single phosphorus atoms are embedded in an engineered thin layer of silicon strained to 0.8% and their wave function imaged using spatially resolved spectroscopy. A prevalence of the out-of-plane valleys is confirmed from the real-space images, and a combination of theoretical modelling tools is used to assess how this valley repopulation effect can yield isotropic exchange and tunnel interactions in the $xy$-plane relevant for atomically precise donor qubit devices. Finally, the residual presence of in-plane valleys is evidenced by a Fourier analysis of both experimental and theoretical images, and atomistic calculations highlight the importance of higher orbital excited states to obtain a precise relationship between valley population and strain. Controlling the valley degree of freedom in engineered strained epilayers provides a new competitive asset for the development of donor-based quantum technologies in silicon.