Quantum Physics (quant-ph)

Abstract: Quantum walks (QWs) have the property that classical random walks (RWs) do not possess -- coexistence of linear spreading and localization -- and this property is utilized to implement various kinds of applications. This paper proposes a quantum-walk-based algorithm for multi-armed-bandit (MAB) problems by associating the two operations that make MAB problems difficult -- exploration and exploitation -- with these two behaviors of QWs. We show that this new policy based on the QWs realizes high performance compared with the corresponding RW-based one.

Abstract: The Boltzmann machine is one of the various applications using quantum annealer. We propose an application of the Boltzmann machine to the kernel matrix used in various machine-learning techniques. We focus on the fact that shift-invariant kernel functions can be expressed in terms of the expected value of a spectral distribution by the Fourier transformation. Using this transformation, random Fourier feature (RFF) samples the frequencies and approximates the kernel function. In this paper, furthermore, we propose a method to obtain a spectral distribution suitable for the data using a Boltzmann machine. As a result, we show that the prediction accuracy is comparable to that of the method using the Gaussian distribution. We also show that it is possible to create a spectral distribution that could not be feasible with the Gaussian distribution.

Abstract: Quantum computation has a strong implication for advancing the current limitation of machine learning algorithms to deal with higher data dimensions or reducing the overall training parameters for a deep neural network model. Based on a gate-based quantum computer, a parameterized quantum circuit was designed to solve a model-free reinforcement learning problem with the deep-Q learning method. This research has investigated and evaluated its potential. Therefore, a novel PQC based on the latest Qiskit and PyTorch framework was designed and trained to compare with a full-classical deep neural network with and without integrated PQC. At the end of the research, the research draws its conclusion and prospects on developing deep quantum learning in solving a maze problem or other reinforcement learning problems.

Abstract: Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple sub-fields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation by Reichenbach's principle and enabling causal inference with only the observational data. However, it is still not clear how quantum causal inference can provide operational advantages in general cases. Here, we have devised a photonic setup and experimentally realized an algorithm capable of identifying any two-qubit statistical correlations generated by the two basic causal structures under an observational scenario, thus revealing a universal quantum advantage in causal inference over its classical counterpart. We further demonstrate the explainability and stability of our causal discovery method which is widely sought in data processing algorithms. Employing a fully observational approach, our result paves the way for studying quantum causality in general settings.

Abstract: The paper studies resonant generation of higher-order harmonics in a closed cavity in Euler-Heisenberg electrodynamics from the point of view of pure quantum field theory. We consider quantum states of the electromagnetic field in a rectangular cavity with conducting boundary conditions, and calculate the cross-section for the merging of three quanta of cavity modes into a single one ($3 \to 1$ process) as well as the scattering of two cavity mode quanta ($2 \to 2$ process). We show that the amplitude of the merging process vanishes for a cavity with an arbitrary aspect ratio, and provide an explanation based on plane wave decomposition for cavity modes. Contrary, the scattering amplitude is nonzero for specific cavity aspect ratio. This $2 \to 2$ scattering is a crucial elementary process for the generation of a quantum of a high-order harmonics with frequency $2\omega_1 - \omega_2$ in an interaction of two coherent states of cavity modes with frequencies $\omega_1$ and $\omega_2$. For this process we calculate the mean number of quanta in the final state in a model with dissipation, which supports the previous result of resonant higher-order harmonics generation in an effective field theory approach.

Abstract: Diamond colour centres are promising optically-addressable solid state spins that can be matter-qubits, mediate deterministic interaction between photons and act as single photon emitters. Useful quantum computers will comprise millions of logical qubits. To become useful in constructing quantum computers, spin-photon interfaces must therefore become scalable and be compatible with mass-manufacturable photonics and electronics. Here we demonstrate heterogeneous integration of NV centres in nanodiamond with low-fluorescence silicon nitride photonics from a standard 180 nm CMOS foundry process. Nanodiamonds are positioned over pre-defined sites in a regular array on a waveguide, in a single post-processing step. Using an array of optical fibres, we excite NV centres selectively from an array of six integrated nanodiamond sites, and collect the photoluminescence (PL) in each case into waveguide circuitry on-chip. We verify single photon emission by an on-chip Hanbury Brown and Twiss cross-correlation measurement, which is a key characterisation experiment otherwise typically performed routinely with discrete optics. Our work opens up a simple and effective route to simultaneously address large arrays of individual optically-active spins at scale, without requiring discrete bulk optical setups. This is enabled by the heterogeneous integration of NV centre nanodiamonds with CMOS photonics.

Abstract: We study the photophysics of molecular aggregates from a quantum optics perspective, with emphasis on deriving scaling laws for the fast non-radiative relaxation of collective electronic excitations, referred to as Kasha's rule. At deep subwavelength separations, quantum emitter arrays exhibit an energetically broad manifold of collective states with delocalized electronic excitations originating from near field dipole-dipole exchanges between the aggregate's monomers. Photoexcitation with visible light addresses almost exclusively symmetric collective states, which for an arrangement known as H-aggregate, have the highest energies (hypsochromic shift). The extremely fast subsequent non-radiative relaxation via intramolecular vibrational modes then populates lower energy, subradiant states which results in the effective inhibition of fluorescence. Our treatment allows for the derivation of an approximate linear scaling law of this relaxation process with the number of available low energy vibrational modes and reveals its direct proportionality to the dipole-dipole interaction strength between neighbouring monomers.

Abstract: Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization. We find emergent classicality for slow and coarse observables of a non-integrable many-body system and extract a finite size scaling law by varying the Hilbert space dimension over four orders of magnitude. Specifically, we conjecture and observe an exponential suppression of quantum effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many worlds interpretation within a minimal theoretical framework, without relying on environmentally induced decoherence, quantum Darwinism, Markov approxmations or ensemble averages. We discuss the implications of our results for the wave function of the Universe, interpretations of quantum mechanics and the arrow(s) of time.

Abstract: Lines of exceptional points are robust in the 3-dimensional non-Hermitian parameter space without requiring any symmetry. However, when more elaborate exceptional structures are considered, the role of symmetry becomes critical. One such case is the exceptional chain (EC), which is formed by the intersection or osculation of multiple exceptional lines (ELs). In this study, we investigate a non-Hermitian classical mechanical system and reveal that a symmetry intrinsic to second-order dynamical equations, in combination with the source-free principle of ELs, guarantees the emergence of ECs. This symmetry can be understood as a non-Hermitian generalized latent symmetry, which is absent in prevailing formalisms rooted in first-order Schr\"odinger-like equations and has largely been overlooked so far. We experimentally confirm and characterize the ECs using an active mechanical oscillator system. Moreover, by measuring eigenvalue braiding around the ELs meeting at a chain point, we demonstrate the source-free principle of directed ELs that underlies the mechanism for EC formation. Our work not only enriches the diversity of non-Hermitian degeneracies, but also highlights the new potential for non-Hermitian physics in second-order dynamical systems.

Abstract: Quantum annealing has emerged as a powerful platform for simulating and optimizing classical and quantum Ising models. Quantum annealers, like other quantum and/or analog computing devices, are susceptible to nonidealities including crosstalk, device variation, and environmental noise. Compensating for these effects through calibration refinement or "shimming" can significantly improve performance, but often relies on ad-hoc methods that exploit symmetries in both the problem being solved and the quantum annealer itself. In this tutorial we attempt to demystify these methods. We introduce methods for finding exploitable symmetries in Ising models, and discuss how to use these symmetries to suppress unwanted bias. We work through several examples of increasing complexity, and provide complete Python code. We include automated methods for two important tasks: finding copies of small subgraphs in the qubit connectivity graph, and automatically finding symmetries of an Ising model via generalized graph automorphism. Code is available at https://github.com/dwavesystems/shimming-tutorial.

Abstract: Recent research has systematically analyzed the security of a fully passive modulation protocol. Based on this, we utilize the gain-switching technique in combination with the post-selection scheme and perform a proof-of-principle demonstration of a fully passive quantum key distribution with polarization encoding at channel losses of 7.2 dB, 11.6 dB, and 16.7 dB. Our work demonstrates the feasibility of active-modulation-free QKD in polarization-encoded systems.

Abstract: Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions of scenarios, largely benefiting from computational speedups. We develop a novel hybrid quantum-classical algorithm based on polynomial approximation of nonlinear functions and compare different implementation variants. We prove a quadratic quantum speedup, up to polylogarithmic factors, when forms are bilinear and approximating polynomials have second degree, if efficient loading unitaries are available for the input data sets. We also enhance the bidirectional encoding, that allows tuning the balance between circuit depth and width, proposing an improved version that can be exploited for the calculation of inner products. Lastly, we exploit the dynamic circuit capabilities, recently introduced on IBM Quantum devices, to reduce the average depth of the Quantum Hadamard Product circuit. A proof of principle is implemented and validated on IBM Quantum systems.

Abstract: Quantum memories represent one of the main ingredients of future quantum communication networks. Their certification is therefore a key challenge. Here we develop efficient certification methods for quantum memories. Considering a device-independent approach, where no a priori characterisation of sources or measurement devices is required, we develop a robust self-testing method for quantum memories. We then illustrate the practical relevance of our technique in a relaxed scenario by certifying a fidelity of 0.87 in a recent solid-state ensemble quantum memory experiment. More generally, our methods apply for the characterisation of any device implementing a qubit identity quantum channel.

Abstract: A four-stroke quantum Otto engine can outperform when conducted between two thermal reservoirs, one at a positive spin temperature and the other one at an effective negative spin temperature. Along with a magnetic field in the (x,y)-plane, we introduce an additional magnetic field in the z-direction. We demonstrate that the efficiency increases with the increase in the strength of the additional magnetic field although the impact is not monotonic. Specifically, we report a threshold value of the magnetic field, depending on the driving time which exhibits a gain in efficiency. We argue that this benefit may result from the system being more coherent with driving time, which we assess using the l1-norm coherence measure. Moreover, we find that the increment obtained in efficiency with an additional magnetic field endures even in presence of disorder in parameter space.

Abstract: While long-lived singlet states (LLS) of nuclear spin pairs in the isotropic phase have been extensively studied and utilized in the liquid state NMR, there are hardly any reports of LLS in anisotropic phases. Here we report observing LLS in a pair of nuclear spins partially oriented in the nematic phase of a liquid crystal solvent. The spins are strongly interacting via the residual dipole-dipole coupling. We observe LLS in the oriented phase living up to three times longer than the usual spin-lattice relaxation time constant ($T_1$). Upon heating, the system undergoes a phase transition from nematic into isotropic phase, wherein the LLS is up to five times longer lived than the corresponding $T_1$. Interestingly, we find that the LLS prepared in the oriented phase can survive the phase transition from the nematic to the isotropic phase. As an application of LLS in the oriented phase, we utilize its longer life to measure the small translational diffusion coefficient of solute molecules in the liquid crystal solvent. Finally, we propose utilizing the phase transition to lock or unlock access to LLS.

Abstract: Discrete-time quantum walks with position-dependent coin operators have numerous applications. For a position dependence that is sufficiently smooth, it has been provided in Ref. [1] an approximate quantum-circuit implementation of the coin operator that is efficient. If we want the quantum-circuit implementation to be exact (e.g., either, in the case of a smooth position dependence, to have a perfect precision, or in order to treat a non-smooth position dependence), but the depth of the circuit not to scale exponentially, then we can use the linear-depth circuit of Ref. [1], which achieves a depth that is linear at the cost of introducing an exponential number of ancillas. In this paper, we provide an adjustable-depth quantum circuit for the exact implementation of the position-dependent coin operator. This adjustable-depth circuit consists in (i) applying in parallel, with a linear-depth circuit, only certain packs of coin operators (rather than all of them as in the original linear-depth circuit [1]), each pack contributing linearly to the depth, and in (ii) applying sequentially these packs, which contributes exponentially to the depth.

Abstract: We define creation and annihilation operators for any 2D non-abelian anyon theory by studying the algebraic structure from the anyon diagrammatic formalism. We construct the creation operators for Fibonacci anyons explicitly. We obtain that a single creation operator per particle type is not enough; we need an extra creation operator for every alternative fusion channel. We express any physically allowed observable in terms of these creation and annihilation operators. Finally, we express the 2D Fibonacci Hubbard Hamiltonian in terms of the Fibonacci creation and annihilation operators, and we comment on developing methods for simulation based on these creation and annihilation operators.

Abstract: Can a sender non-interactively transmit one of two strings to a receiver without knowing which string was received? Does there exist minimally-interactive secure multiparty computation that only makes (black-box) use of symmetric-key primitives? We provide affirmative answers to these questions in a model where parties have access to shared EPR pairs, thus demonstrating the cryptographic power of this resource. First, we construct a one-shot (i.e., single message) string oblivious transfer (OT) protocol with random receiver bit in the shared EPR pairs model, assuming the (sub-exponential) hardness of LWE. Building on this, we show that {\em secure teleportation through quantum channels} is possible. Specifically, given the description of any quantum operation $Q$, a sender with (quantum) input $\rho$ can send a single classical message that securely transmits $Q(\rho)$ to a receiver. That is, we realize an ideal quantum channel that takes input $\rho$ from the sender and provably delivers $Q(\rho)$ to the receiver without revealing any other information. This immediately gives a number of applications in the shared EPR pairs model: (1) non-interactive secure computation of unidirectional \emph{classical} randomized functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness assumptions, and (3) a non-interactive \emph{zero-knowledge} state synthesis protocol. Next, we construct a two-round (round-optimal) secure multiparty computation protocol for classical functionalities in the shared EPR pairs model that is \emph{unconditionally-secure} in the (quantum-accessible) random oracle model.

Abstract: Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.

Abstract: Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates the develop of accurate, but approximate, ways to parametrize the wavefunction, including methods like couple cluster theory and correlator product states (CPS). Recently, there has been interest in approaches based on machine learning both direct applications of neural network architecture and the combinations of conventional wavefunction parametrizations with various Boltzmann machines. While all these methods can be exact in principle, they are usually applied with only a polynomial number of parameters, limiting their applicability. This research's objective is to present a fresh approach to wavefunction parametrization that is size-consistent, rapidly convergent, and robust numerically. Specifically, we propose a hierarchical ansatz that converges rapidly (with respect to the number of least-squares optimization). The general utility of this approach is verified by applying it to uncorrelated, weakly-correlated, and strongly-correlated systems, including small molecules and the one-dimensional Hubbard model.

Abstract: The Number Partitioning Problem (NPP) is one of the NP-complete computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $\sqrt{N}$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $N$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time-dependence of the physical parameters or the choice of the annealing protocol.

Abstract: Self-imaging in near-field diffraction is a practical application of coherent manipulation of matter waves in Talbot interferometry. In this work, near-field diffraction of protons by a nanostructured metallic grating under the influence of (a) uniform, (b) spatially modulated, and (c) temporally modulated electric fields are investigated. Time-domain simulations of two-dimensional Gaussian wave packets for protons are performed by solving the time-dependent Schr\"odinger's equation using the generalized finite difference time domain (GFDTD-Q) method for quantum systems. Effects of strength ($E_0$) and orientation ($\theta$) of the uniform electric field on the diffraction properties, such as fringe pattern, intensity of the peaks, fringe shift, and visibility, are investigated. The results show that the Talbot fringes shift significantly in the transverse direction even for a small change in the applied electric field ($\Delta E_0$ $=0.1$ V/m) and its orientation ($\Delta \theta$ $=0.1^o$). The potential barriers arising from a spatially modulated electric field are observed to cause significant distortions in the Talbot patterns when the modulation length ($\lambda'$) is equal to the de Broglie wavelength ($\lambda_{dB}$). Sidebands are observed in the Talbot pattern due to the efficient transfer of energy from the oscillating field to the wave packet when the frequency of oscillation ($\omega$) is of the order of $\omega_0$ ($=2\pi/T_0$), where $T_0$ is the interaction time. This study will be helpful in uniform electric field-controlled precision metrology, developing a highly sensitive electric field sensor based on Talbot interference, and precisely aligning the matter wave optical setup. Furthermore, the sidebands in the Talbot fringe can be used as a precise tool as momentum splitter in matter wave interferometry.

Abstract: We introduce modifications to Monte Carlo simulations of the Feynman path integral that improve sampling of localised interactions. The new algorithms generate trajectories in simple background potentials designed to concentrate them about the interaction region, reminiscent of importance sampling. This improves statistical sampling of the system and overcomes a long-time "undersampling problem" caused by the spatial diffusion inherent in Brownian motion. We prove the validity of our approach using previous analytic work on the distribution of values of the Wilson line over path integral trajectories and illustrate the improvements on some simple quantum mechanical systems