Quantum Physics (quant-ph)

Abstract: We present a simple null test of a dimension of a quantum system, using a single repeated operation in the method of delays, assuming that each instance is identical and independent. The test is well-suited to current feasible quantum technologies, with programmed gates. We also analyze weaker versions of the test, assuming unitary or almost unitary operations and derive expressions for the statistical error.

Abstract: Superdeterminism -- where the Measurement-Independence assumption in Bell's Theorem is violated -- is typically treated with derision as it appears to imply contrived conspiratorial correlations between properties $\lambda$ of particles being measured, and nominally accurate measurement settings $x$ and $y$. Based on an analysis of Pearlean interventions needed to determine whether $x$ and $y$ are free variables, we show that whilst conspiracy implies superdeterminism, superdeterminism does not imply conspiracy. In conspiratorial superdeterminism these interventions are consistent with physical theory; in non-conspiratorial superdeterminism they are inconsistent. A non-conspiratorial locally-causal superdeterministic model is developed, based in part on the generic properties of chaotic attractors and in part on an arbitrarily fine discretisation of complex Hilbert Space. Here the required interventions are inconsistent with rational-number constraints on exact measurement settings $X$ and $Y$. In this model, hidden variables $\lambda$ are defined as the information, over and above the freely chosen determinants of $x$ and $y$, which determine $X$ and $Y$. These rationality constraints limit the freedom to vary $x$ and $y$ keeping $\lambda$ fixed. These constraints disappear with any coarse-graining of $\lambda$ and hence $X$. We show how quantum mechanics might be `gloriously explained and derived' as the singular continuum limit of a superdeterministic discretisation of Hilbert Space. We argue that the real message behind Bell's Theorem is the need to develop more holistic theories of fundamental physics -- notably gravitational physics -- some ideas for moving in this direction are discussed.

Abstract: Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime by neural-network protocols and classical shadows, while both methods have limitations: the former is plagued by the predictive uncertainty and the latter lacks the generalization ability. Here we propose a data-centric learning paradigm combining the strength of these two approaches to facilitate diverse quantum system learning (QSL) tasks. Particularly, our paradigm utilizes classical shadows along with other easily obtainable information of quantum systems to create the training dataset, which is then learnt by neural networks to unveil the underlying mapping rule of the explored QSL problem. Capitalizing on the generalization power of neural networks, this paradigm can be trained offline and excel at predicting previously unseen systems at the inference stage, even with few state copies. Besides, it inherits the characteristic of classical shadows, enabling memory-efficient storage and faithful prediction. These features underscore the immense potential of the proposed data-centric approach in discovering novel and large-scale quantum systems. For concreteness, we present the instantiation of our paradigm in quantum state tomography and direct fidelity estimation tasks and conduct numerical analysis up to 60 qubits. Our work showcases the profound prospects of data-centric artificial intelligence to advance QSL in a faithful and generalizable manner.

Abstract: In recent advancements of quantum computing utilizing spin qubits, it has been demonstrated that this platform possesses the potential for implementing two-qubit gates with fidelities exceeding 99.5%. However, as with other qubit platforms, it is not feasible to completely turn qubit couplings off. This study aims to investigate the impact of coherent error matrices in gate set tomography by employing a double quantum dot. We evaluate the infidelity caused by residual exchange between spins and compare various mitigation approaches, including the use of adjusted timing through simple drives, considering different parameter settings in the presence of charge noise. Furthermore, we extend our analysis to larger arrays of exchange-coupled spin qubits to provide an estimation of the expected fidelity. In particular, we demonstrate the influence of residual exchange on a single-qubit $Y$ gate and the native two-qubit SWAP gate in a linear chain. Our findings emphasize the significance of accounting for residual exchange when scaling up spin qubit devices and highlight the tradeoff between the effects of charge noise and residual exchange in mitigation techniques.

Abstract: We investigate quantum key distribution (QKD) in optical multiple-input-multiple-output (MIMO) settings. Such settings can prove useful in dealing with harsh channel conditions as in, e.g., satellite-based QKD. We study a $2\times2$ setting for continuous variable (CV) QKD with Gaussian encoding and heterodyne detection and reverse reconciliation. We present our key rate analysis for this system and compare it with single-mode and multiplexed CV QKD scenarios. We show that we can achieve multiplexing gain using multiple transmitters and receivers even if there is some crosstalk between the two channels. In certain cases, when there is nonzero correlated excess noise in the two received signals, we can even surpass the multiplexing gain.

Abstract: We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized compiling, and classical statistics to derive verification circuits. These circuits have the property that (i) they strongly resemble the original circuit and (ii) cannot only be classically efficiently simulated in the ideal, i.e. error free, scenario, but also in the realistic situation where errors are present. In fact, in one of the protocols we apply exactly the same circuit as in the original computation, however, to a slightly modified input state.

Abstract: Entanglement, a fundamental concept in quantum mechanics, plays a crucial role as a valuable resource in quantum technologies. The practical implementation of entangled photon sources encounters obstacles arising from imperfections and defects inherent in physical systems and microchips, resulting in a loss or degradation of entanglement. The topological photonic insulators, however, have emerged as promising candidates, demonstrating an exceptional capability to resist defect-induced scattering, thus enabling the development of robust entangled sources. Despite their inherent advantages, building bright and programmable topologically protected entangled sources remains challenging due to intricate device designs and weak material nonlinearity. Here we present an advancement in entanglement generation achieved through a non-magnetic and tunable resonance-based anomalous Floquet insulator, utilizing an optical spontaneous four-wave mixing process. Our experiment demonstrates a substantial enhancement in entangled photon pair generation compared to devices reliant solely on topological edge states and outperforming trivial photonic devices in spectral resilience. This work marks a step forward in the pursuit of defect-robust and bright entangled sources that can open avenues for the exploration of cascaded quantum devices and the engineering of quantum states. Our result could lead to the development of resilient quantum sources with potential applications in quantum technologies.

Abstract: Hanbury-Brown and Twiss (HBT) effect is the foundation for stellar intensity interferometry. However, it is a phase insensitive two-photon interference effect. In this paper, we extend the HBT interferometer by mixing two phase-coherent input fields with coherent auxiliary fields before intensity correlation measurement and achieve phase sensitive two-photon interference so as to measure the complete complex second-order coherence function of the input fields. This practical scheme paves the way for synthetic aperture imaging for astronomical applications in optical regime. Pulsed input fields is also tested for potential remote sensing and ranging applications. We discuss the condition to implement recently proposed entanglement-based telescopy scheme with the more realistic cw broadband anti-bunched light fields.

Abstract: Adaptive optics (AO) has revolutionized imaging in applications ranging from astronomy to microscopy by enabling the correction of optical aberrations. In label-free microscopes, however, conventional AO methods are limited due to the absence of guidestar and the need to select an optimization metric specific to the type of sample and imaging process being used. Here, we propose a quantum-assisted AO approach that exploits correlations between entangled photons to directly access and correct the point spread function (PSF) of the imaging system. This guidestar-free method is independent of the specimen and imaging modality. We demonstrate the imaging of biological samples in the presence of aberrations using a bright-field imaging setup operating with a source of spatially-entangled photon pairs. We show that our approach performs better than conventional AO in correcting certain types of aberrations, particularly in cases involving significant defocus. Our work improves AO for label-free microscopy, and could play a major role in the development of quantum microscopes, in which optical aberrations can counteract the advantages of using entangled photons and undermine their practical use.

Abstract: We present a comprehensive approach to quantum simulations at both zero and finite temperatures, employing a quantum information theoretic perspective and utilizing the Clifford + $k$Rz transformations. We introduce the "quantum magic ladder", a natural hierarchy formed by systematically augmenting Clifford transformations with the addition of Rz gates. These classically simulable similarity transformations allow us to reduce the quantumness of our system, conserving vital quantum resources. This reduction in quantumness is essential, as it simplifies the Hamiltonian and shortens physical circuit-depth, overcoming constraints imposed by limited error correction. We improve the performance of both digital and analog quantum computers on ground state and finite temperature molecular simulations, not only outperforming the Hartree-Fock solution, but also achieving consistent improvements as we ascend the quantum magic ladder. By facilitating more efficient quantum simulations, our approach enables near-term and early fault-tolerant quantum computers to address novel challenges in quantum chemistry.