Quantum Physics (quant-ph)

Abstract: Quantum chemistry is envisioned as an early and disruptive application where quantum computers would provide a genuine advantage with respect to purely classical approaches. In this work, we propose two criteria for evaluating the potential of the two leading quantum approaches for this class of problems. The first criterion applies to the Variational Quantum Eigensolver (VQE) algorithm and sets an upper bound to the level of noise that can be tolerated in quantum hardware as a function of the target precision and problem size. We find a crippling effect of noise with an overall scaling of the precision that is generically less favourable than in the corresponding classical algorithms. This is due to the studied molecule being unrelated to the hardware dynamics, hence its noise; conversely the hardware noise populates states of arbitrary energy of the studied molecule. The second criterion applies to the Quantum Phase Estimation (QPE) algorithm that is often presented as the go-to replacement of VQE upon availability of (noiseless) fault-tolerant quantum computers. QPE suffers from the phenomenon known as the orthogonality catastrophe that generically leads to an exponentially small success probability when the size of the problem grows. Our criterion allows one to estimate quantitatively the importance of this phenomenon from the knowledge of the variance of the energy of the input state used in the calculation.

Abstract: The dynamics of a single quantum state embedded in one or several (quasi-)continua is one of the most studied phenomena in quantum mechanics. In this work we investigate its discrete analogue and consider short and long time dynamics based on numerical and analytical solutions of the Schr\"odinger equation. In addition to derivation of explicit conditions for initial exponential decay, it is shown that a recent model of this class [Phys. Rev. A 95, 053821, (2017)], describing a qubit coupled to a phonon reservoir with energy dependent coupling parameters is identical to a qubit interacting with a finite number of parallel regularly spaced band of states via constant couplings. As a consequence, the characteristic near periodic initial state revivals can be viewed as a transition of probability between different continua via the reviving initial state. Furthermore, the observation of polynomial decay of the reviving peaks is present in any system with constant and sufficiently strong coupling.

Abstract: Beam splitters are optical elements widely used in modern technological applications to split the initial light beam into a required number of beams and they play a very promising role for generating entangled optical states. Here, a potential scheme is proposed to generate Bell coherent-states superpositions through the action of a beam splitter when a Glauber coherent state is injected on one input mode and vacuum state is incident on the other one. Different quantifiers are used to measure the quantumness in the output state such as concurrence entanglement, entropic quantum discord, quantum coherence, geometric measure of quantum discord, local quantum uncertainty (LQU) and local quantum Fisher information. Thereby, we derive their analytical formulas and focus more on the behavior and bounds of each measure. Besides, we have introduced the notion of "weak measurement-induced LQU" captured by weak measurements as the generalization of normal LQU defined for standard projective measurement, and we investigate the effect of the measurement strength on the estimated phase enhancement if the generated Bell cat states are the probe states in quantum metrology. Our results suggest that the sensitivity of the interferometric phase estimation depends on how strongly one perturbs the probe state and that a weak measurement does not necessarily capture more quantumness in composite system.

Abstract: In the quantum theory, it has been shown that one can see if a process has the time reversal symmetry by applying the matrix transposition and examine if it remains physical. However, recent discoveries regarding the indefinite causal order of quantum processes suggest that there may be other, more general symmetry transformations of time besides the complete reversal. In this work, we introduce an expanded concept of matrix transposition, the generalized transposition, that takes into account general bipartite unitary transformations of a quantum operation's future and past Hilbert spaces, allowing for making the time axis definitely lie in a superposed direction, which generalizes the previously studied `indefinite direction of time', i.e., superposition of the forward and the backward time evolution. This framework may have applications in approaches that treat time and space equally like quantum gravity, where the spatio-temporal structure is explained to emerge from quantum mechanics. We apply this generalized transposition to investigate a continuous generalization of perfect tensors, a dynamic version of tracing out a subsystem, and the compatibility of multiple time axes in bipartite quantum interactions. Notably, we demonstrate that when a bipartite interaction is consistent with more distinct local temporal axes, there is a reduced allowance for information exchange between the two parties in order to prevent causality violations.

Abstract: $k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for $k$-clustering in $\mathbb{R}^d$ with $\tilde{O}(\sqrt{nk}d^{3/2})$ query complexity. Our coreset reduces the input size from $n$ to $\mathrm{poly}(k\epsilon^{-1}d)$, so that existing $\alpha$-approximation algorithms for clustering can run on top of it and yield $(1 + \epsilon)\alpha$-approximation. This eventually yields a quadratic speedup for various $k$-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make $\Omega(\sqrt{nk})$ queries in order to achieve even $O(1)$-approximation for $k$-clustering.

Abstract: Quantum computing devices have been rapidly developed in the past decade. Tremendous efforts have been devoted to finding quantum advantages for useful but classically intractable problems via current noisy quantum devices without error correction. It is important to know the fundamental limitations of noisy quantum devices with the help of classical computers. For computation with general classical processing, we show that noisy quantum devices with a circuit depth of more than $O(\log n)$ provide no advantages in any quantum algorithms. This rigorously rules out the possibility of implementing well-known quantum algorithms, including Shor's, Grover's, Harrow-Hassidim-Lloyd, and linear-depth variational algorithms. Then, we study the maximal entanglement that noisy quantum devices can produce under one- and two-dimensional qubit connections. In particular, for a one-dimensional qubit chain, we show an upper bound of $O(\log n)$. This finding highlights the restraints for quantum simulation and scalability regarding entanglement growth. Additionally, our result sheds light on the classical simulatability in practical cases.

Abstract: The long-lived electronic spin of the nitrogen-vacancy (NV) center in diamond is a promising quantum sensor for detecting nanoscopic magnetic and electric fields in a variety of experimental conditions. Nevertheless, an outstanding challenge in improving measurement sensitivity is the poor signal-to-noise ratio (SNR) of prevalent optical spin-readout techniques. Here, we address this limitation by coupling individual NV centers to optimized diamond nanopillar structures, thereby improving optical collection efficiency of fluorescence. First, we optimize the structure in simulation, observing an increase in collection efficiency for tall ($\geq$ 5 $\mu$m) pillars with tapered sidewalls. We subsequently verify these predictions by fabricating and characterizing a representative set of structures using a reliable and reproducible nanofabrication process. An optimized device yields increased SNR, owing to improvements in collimation and directionality of emission. Promisingly, these devices are compatible with low-numerical-aperture, long-working-distance collection optics, as well as reduced tip radius, facilitating improved spatial resolution for scanning applications.

Abstract: We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress towards the realisation of programmable hybrid analogue-digital quantum simulators.

Abstract: Protecting a quantum object against irreversible accidental measurements from its surroundings is necessary for controlled quantum operations. This becomes especially challenging or unfeasible if one must simultaneously measure or reset a nearby object's quantum state, such as in quantum error correction. In atomic systems - among the most established quantum information processing platforms - current attempts to preserve qubits against resonant laser-driven adjacent measurements waste valuable experimental resources such as coherence time or extra qubits and introduce additional errors. Here, we demonstrate high-fidelity preservation of an `asset' ion qubit while a neighboring `process' qubit is reset or measured at a few microns distance. We achieve $< 1\times 10^{-3}$ probability of accidental measurement of the asset qubit while the process qubit is reset, and $< 4\times 10^{-3}$ probability while applying a detection beam on the same neighbor for experimentally demonstrated fast detection times, at a distance of $6\ \rm{\mu m}$ or four times the addressing Gaussian beam waist. These low probabilities correspond to the preservation of the quantum state of the asset qubit with fidelities above $99.9\%$ (state reset) and $99.6\%$ (state measurement). Our results are enabled by precise wavefront control of the addressing optical beams while utilizing a single ion as a quantum sensor of optical aberrations. Our work demonstrates the feasibility of in-situ state reset and measurement operations, building towards enhancements in the speed and capabilities of quantum processors, such as in simulating measurement-driven quantum phases and realizing quantum error correction.

Abstract: Dirac's conjecture, that secondary first-class constraints generate transformations that do not change the physical system's state, has various counterexamples. Since no matching gauge conditions can be imposed, the Dirac bracket cannot be defined, and restricting the phase space first and then quantizing is an inconsistent procedure. The latter observation has discouraged the study of systems of this kind more profoundly, while Dirac's conjecture is assumed generally valid. We point out, however, that secondary first-class constraints are just initial conditions that do not imply Poisson's bracket modification, and we carry out the quantization successfully by imposing these constraints on the initial state of the wave function. We apply the method to two Dirac's conjecture counterexamples, including Cawley's iconical system.