Recent work has demonstrated a new route to discrete time crystal physics in quantum spin chains by periodically driving nearest-neighbor exchange interactions in gate-defined quantum dot arrays [arXiv:2006.10913]. Here, we present a detailed analysis of exchange-driven Floquet physics in small arrays of GaAs quantum dots, including phase diagrams and additional diagnostics. We also show that emergent time-crystalline behavior can benefit the protection and manipulation of multi-spin states. For typical levels of nuclear spin noise in GaAs, the combination of driving and interactions protects spin-singlet states beyond what is possible in the absence of exchange interactions. We further show how to construct a time-crystal-inspired CZ gate between singlet-triplet qubits with high fidelity. These results show that periodically driving exchange couplings can enhance the performance of quantum dot spin systems for quantum information applications.

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further novel cases.

A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg's and others' uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.

We study the symmetry resolved entanglement entropies in one-dimensional systems with boundaries. We provide some general results for conformal invariant theories and then move to a semi-infinite chain of free fermions. We consider both an interval starting from the boundary and away from it. We derive exact formulas for the charged and symmetry resolved entropies based on theorems and conjectures about the spectra of Toeplitz+Hankel matrices. En route to characterise the interval away from the boundary, we prove a general relation between the eigenvalues of Toeplitz+Hankel matrices and block Toeplitz ones. An important aspect is that the saddle-point approximation from charged to symmetry resolved entropies introduces algebraic corrections to the scaling that are much more severe than in systems without boundaries.

The eigenstate decoherence hypothesis (EDH) asserts that each individual eigenstate of a large closed system is locally classical-like. We test this hypothesis for a heavy particle interacting with a gas of light particles. This system is paradigmatic for studies of the quantum-to-classical transition: The reduced state of the heavy particle is widely believed to rapidly loose any nonclassical features due to the interaction with the gas. Yet, we find numerical evidence that the EDH is violated: certain eigenstates of this model are manifestly non-classical. Only the weak version of EDH referring to the majority (instead of the totality) of eigenstates holds.

As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key bottlenecks in near-term quantum computers: bandwidth restrictions arising from data transfer between central processing units (CPUs) and quantum processing units (QPUs), latency delays in the hardware for round-trip communication, and timing restrictions driven by high error rates. In each case we consider a near-term quantum algorithm to highlight the bottleneck: randomised benchmarking to showcase bandwidth limitations, adaptive noisy, intermediate scale quantum (NISQ)-era algorithms for the latency bottleneck and quantum error correction techniques to highlight the restrictions imposed by qubit error rates. In all three cases we discuss how these bottlenecks arise in the current paradigm of executing all the classical computation on the CPU, and how these can be mitigated by providing access to local classical computational resources in the QPU.

As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimental atom-photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.

In this paper, we critically revisit the Horowitz-Maldacena proposal and its generalization of Lloyd. In the original proposal, as well as in Lloyd's generalization, Hawking radiation involves a pair of maximally entangled quantum states in which the ingoing partner state and the collapsed matter form either a maximally entangled pair or a Schmidt decomposed state near the singularity. However, this cannot be the most generic state if there is an interaction between the collapsing matter and the incoming Hawking radiation. In opposition to Lloyd's conclusion such that information can almost certainly escape from a black hole, we analytically and numerically confirm that information will almost certainly be lost because the fidelity will approach zero as the degrees of freedom increase.

We propose a high-rate generation method of optical Schr\"{o}dinger's cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of arbitrary two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\alpha| \ge 2)$ can exceed megacounts per second, about $10^3$ to $10^6$ times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. Ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalable computing platforms have been demonstrated but preparation of non-Gaussian states of light remains as a challenging task. Our proposal reduces the difficulty of the state preparation and open a way for practical applications in quantum optics.

Bell state analyzer (BSA) is one of the most crucial apparatus in photonic quantum information processing. While linear optics provide a practical way to implement BSA, it provides unavoidable errors when inputs are not ideal single-photon states. Here, we propose a simple method to deduce the BSA for single-photon inputs using weak coherent pulses. By applying the method to Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution, we experimentally verify the feasibility and effectiveness of the method.

We revisit the uniaxially strained graphene immersed in a uniform homogeneous magnetic field orthogonal to the layer in order to describe the time evolution of coherent states build from a semi-classical model. We consider the symmetric gauge vector potential to render the magnetic field, and we encode the tensile and compression deformations on an anisotropy parameter $\zeta$. After solving the Dirac-like equation with an anisotropic Fermi velocity, we define a set of matrix ladder operators and construct electron coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. Through the corresponding probability density, we are able to study the anisotropy effects on these states on the $xy$-plane as well as their time evolution. Our results show clearly that the quasi-period of electron coherent states is affected by the uniaxial strain.

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave-packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave-packets that can excite a given superposition of these bound states. As specific examples, we study bound state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

We study the collective radiation properties of cold, trapped ensembles of atoms. We consider the high density regime with the mean interatomic distance being comparable to, or smaller than, the wavelength of the resonant optical radiation emitted by the atoms. We find that the emission rate of a photon from an excited atomic ensemble is strongly enhanced for an elongated cloud. We analyze collective single-excitation eigenstates of the atomic ensemble and find that the absorption/emission spectrum is broadened and shifted to lower frequencies as compared to the non-interacting (low density) or single atom spectrum. We also analyze the spatial and temporal profile of the emitted radiation. Finally, we explore how to efficiently excite the collective super-radiant states of the atomic ensemble from a long-lived storage state in order to implement matter-light interfaces for quantum computation and communication applications.

We present an experimental and theoretical energy- and angle-resolved study on the photoionization dynamics of non-resonant one-color two-photon single valence ionization of neutral N$_2$ molecules. Using 9.3 eV photons produced via high harmonic generation and a 3-D momentum imaging spectrometer, we detect the photoelectrons and ions produced from one-color two-photon ionization in coincidence. Photoionization of N$_2$ populates the X $^2\Sigma^+_g$, A $^2\Pi_u$, and B $^2\Sigma^+_u$ ionic states of N$_2^+$, where the photoelectron angular distributions associated with the X $^2\Sigma^+_g$ and A $^2\Pi_u$ states both vary with changes in photoelectron kinetic energy of only a few hundred meV. We attribute the rapid evolution in the photoelectron angular distributions to the excitation and decay of dipole-forbidden autoionizing resonances that belong to series of different symmetries, all of which are members of the Hopfield series, and compete with the direct two-photon single ionization.

Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured search. We consider the problem of searching with prior knowledge. More preciously, search for the solution among N items with a prior probability distribution. This letter proposes a new generalization of Grover's search algorithm which performs better than the standard Grover algorithm in average under this setting. We prove that our new algorithm achieves the optimal expected success probability of finding the solution if the number of queries is fixed.

Since violations of inequalities implied by non-contextual and local hidden variable theories are observed, it is essential to determine the set of (non-)contextual states. Along this direction, one should determine the conditions under which quantum contextuality is observed. It is also important to determine how one can find maximally contextual qutrits. In this work, we revisit the Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) scenario where we observe a five-measurement state-dependent contextuality. We investigate possible symmetries of the KCBS pentagram, i.e., the conservation of the contextual characteristic of a qutrit-system. For this purpose, the KCBS operator including five cyclic measurements is rotated around the Z-axis. We then check a set of rotation angles to determine the contextuality and non-contextuality regions for the eigenstates of the spin-1 operator for an arbitrary rotation. We perform the same operation for the homogeneous linear combination of the eigenstates with spin values +1 and -1. More generally, we work on the real subgroup of the three dimensional Hilbert space to determine the set of (non-)contextual states under certain rotations in the physical Euclidean space $\mathbb{E}^3$. Finally, we show data on Euler rotation angles for which maximally contextual retrits (qutrits of the real Hilbert space) are found, and derive mathematical relations through data analysis between Euler angles and qutrit states parameterized with spherical coordinates.

We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable models. We map the time-independent Schr\"odinger equation onto the Heun confluent differential equation, which is solved by using an infinite power series. The coefficients of this series are polynomials in the quantisation parameter, whose roots correspond to the system's eigenenergies. This leads to a quantisation condition that allows us to determine a whole spectrum, instead of individual eigenenergies. This method is then employed to perform an in depth analysis of electronic wave-packet dynamics, with emphasis on intra-well tunneling and the interference-induced quantum bridges reported in a previous publication [H. Chomet et al, New J. Phys. 21, 123004 (2019)]. Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and Wigner quasiprobability distributions. Our results exhibit an excellent agreement with numerical computations, and allow us to disentangle the different eigenfrequencies that govern the phase-space dynamics.

Due to the physics behind quantum computing, quantum circuit designers must adhere to the constraints posed by the limited interaction distance of qubits. Existing circuits need therefore to be modified via the insertion of SWAP gates, which alter the qubit order by interchanging the location of two qubits' quantum states. We consider the Nearest Neighbor Compliance problem on a linear array, where the number of required SWAP gates is to be minimized. We introduce an Integer Linear Programming model of the problem of which the size scales polynomially in the number of qubits and gates. Furthermore, we solve $131$ benchmark instances to optimality using the commercial solver CPLEX. The benchmark instances are substantially larger in comparison to those evaluated with exact methods before. The largest circuits contain up to $18$ qubits or over $100$ quantum gates. This formulation also seems to be suitable for developing heuristic methods since (near) optimal solutions are discovered quickly in the search process.

Privacy amplification (PA) is an indispensable component in classical and quantum cryptography. Error correction (EC) and data compression (DC) algorithms are also indispensable in classical and quantum information theory. We here study quantum algorithms of these three types (PA, EC, and DC) in the one-shot scenario, and show that they all become equivalent if modified properly. As an application of this equivalence, we take previously known security bounds of PA, and translate them into coding theorems for EC and DC which have not been obtained previously. Further, we apply these results to simplify and improve our previous result that the two prevalent approaches to the security proof of quantum key distribution (QKD) are equivalent. We also propose a new method to simplify the security proof of QKD.

Grover's algorithm searches an unstructured database of $N$ entries, finding a marked element in time $\mathcal{O}(\sqrt{N})$. The algorithm was later generalised to amplitude amplification. The original algorithm succeeds with probability close to one and needs to run for a number of iterations chosen ahead of time. We discuss an implementation of amplitude amplification that, instead, runs for a number of iterations unspecified a priori and only halts on success. We prove that this approach maintains the quadratic speed-up of the original quantum algorithm. The key component is a feedback loop controlled by a weak measurement that allows limited monitoring of the evolution of the quantum state.

Suppose we want to implement a unitary $U$, for instance a circuit for some quantum algorithm. Suppose our actual implementation is a unitary $\tilde{U}$, which we can only apply as a black-box. In general it is an exponentially-hard task to decide whether $\tilde{U}$ equals the intended $U$, or is significantly different in a worst-case norm. In this paper we consider two special cases where relatively efficient and lightweight procedures exist for this task.

First, we give an efficient procedure under the assumption that $U$ and $\tilde{U}$ (both of which we can now apply as a black-box) are either equal, or differ significantly in only one $k$-qubit gate, where $k=O(1)$ (the $k$ qubits need not be contiguous). Second, we give an even more lightweight procedure under the assumption that $U$ and $\tilde{U}$ are Clifford circuits which are either equal, or different in arbitrary ways (the specification of $U$ is now classically given while $\tilde{U}$ can still only be applied as a black-box). Both procedures only need to run $\tilde{U}$ a constant number of times to detect a constant error in a worst-case norm. We note that the Clifford result also follows from earlier work of Flammia and Liu, and of da Silva, Landon-Cardinal, and Poulin.

In the Clifford case, our error-detection procedure also allows us to efficiently learn (and hence correct) $\tilde{U}$ if we have a small list of possible errors that could have happened to $U$; for example if we know that only $O(1)$ of the gates of $\tilde{U}$ are wrong, this list will be polynomially small and we can test each possible erroneous version of $U$ for equality with $\tilde{U}$.