High-dimensional entangled states of light provide novel possibilities for quantum information, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the frequency degree of freedom combines the assets of robustness to propagation and easy handling with standard telecommunication components. Here we use an integrated semiconductor chip to engineer the wavefunction and exchange statistics of frequency-entangled photon pairs directly at the generation stage, without post-manipulation. Tuning the spatial properties of the pump beam allows to generate frequency-anticorrelated, correlated and separable states, and to control the symmetry of the spectral wavefunction to induce either bosonic or fermionic behaviors. These results, supported by analytical and numerical calculations, open promising perspectives for the quantum simulation of fermionic problems with photons on an integrated platform, as well as for communication and computation protocols exploiting antisymmetric high-dimensional quantum states.

It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a bipartite finite-dimensional Hilbert space. These methods amount to joint Schmidt-type decompositions of two pure states where the two sets of coefficients and local bases depend on the properties of either state, however, at the expense of the local bases not all being orthonormal and in one case the complex-valuedness of the coefficients. With these results we derive several generally valid purity-type formulae for one-party reductions of rank-1 operators, and we point out relevant relations between the Schmidt decomposition and the Bloch representation of bipartite pure states.

Synchronisation is a collective phenomenon widely investigated in classical oscillators and, more recently, in quantum systems. However, it remains unclear what features distinguish synchronous behaviour in these two scenarios. Recent works have shown that investigating the dynamics of synchronisation in open quantum systems can give insight into this issue. Here we study transient synchronisation in a bio-inspired vibronic dimer, where the dynamics of electronic excitation is mediated by coherent interactions with intramolecular vibrational modes. We show that the synchronisation dynamics of the displacement of these local modes exhibit a rich behaviour which arises directly from the distinct time-evolutions of different vibronic quantum coherences. Furthermore, our study shows that coherent energy transport in this bio-inspired system is concomitant with the emergence of positive synchronisation between mode displacements. Our work provides further understanding of the relations between quantum coherence and synchronisation in open quantum systems and suggests an interesting role for coherence in biomolecules, that is promoting the synchronisation of vibrational motions driven out of thermal equilibrium.

We exploit the nonlinearity arising from the spin-photon interaction in an InAs quantum dot to demonstrate phase shifts of scattered light pulses at the single-photon level. Photon phase shifts of close to 90 degrees are achieved using a charged quantum dot in a micropillar cavity. We also demonstrate a photon phase switch by using a spin-pumping mechanism through Raman transitions in an in-plane magnetic field. The experimental findings are supported by a theoretical model which explores the dynamics of the system. Our results demonstrate the potential of quantum dot-induced nonlinearities for quantum information processing.

We demonstrate homodyne detection of quantum states originating from a genuinely spatially and temporally singlemode parametric downconversion source in non-linear waveguides. By using single photon subtraction, we implement the distillation of squeezed states witnessing an improvement of 0.1 dB from an initial squeezing value of 1.62 +/- 0.01 dB, while achieving a purity of 0.58, and confirm the non-Gaussianity of the distilled state via the higher order cumulants. With this we demonstrate the source's suitability for scalable hybrid quantum network applications.

Critical to the construction of large scale quantum networks, i.e. a quantum internet, is the development of fast algorithms for managing entanglement present in the network. One fundamental building block for a quantum internet is the distribution of Bell pairs between distant nodes in the network. Here we focus on the problem of transforming multipartite entangled states into the tensor product of bipartite Bell pairs between specific nodes using only a certain class of local operations and classical communication. In particular we study the problem of deciding whether a given graph state, and in general a stabilizer state, can be transformed into a set of Bell pairs on specific vertices using only single-qubit Clifford operations, single-qubit Pauli measurements and classical communication. We prove that this problem is NP-Complete.

The complexity of experimental quantum information processing devices is increasing rapidly, requiring new approaches to control them. In this paper, we address the problems of practically modeling and controlling an integrated optical waveguide array chip, a technology expected to have many applications in telecommunications and optical quantum information processing. This photonic circuit can be electrically reconfigured, but only the output optical signal can be monitored. As a result, the conventional control methods cannot be naively applied. Characterizing such a chip is challenging for three reasons. First, there are uncertainties associated with the Hamiltonian describing the chip. Second, we expect distortions of the control voltages caused by the chip's electrical response, which cannot be directly observed. Finally, there are imperfections in the measurements caused by losses from coupling the chip externally to optical fibers. We developed a deep neural network approach to solve these problems. The architecture is designed specifically to overcome the aforementioned challenges using a Gated Recurrent Unit (GRU)-based network as the central component. The Hamiltonian is estimated as a blackbox, while the rules of quantum mechanics such as state evolution is embedded in the structure as a whitebox. The resulting overall graybox model of the chip shows good performance both quantitatively in terms of the mean square error and qualitatively in terms of the predicted waveforms. We use this neural network to solve a classical and a quantum control problem. In the classical application we find a control sequence to approximately realize a time-dependent output power distribution. For the quantum application we obtain the control voltages to realize a target set of quantum gates. The proposed method is generic and can be applied to other systems that can only be probed indirectly.

Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit Clifford operations is known to be decidable in polynomial time and have been studied both in the context of producing certain required states in a quantum network but also in relation to stabilizer codes. The reason for the latter this is that single-qubit Clifford equivalent graph states exactly corresponds to equivalent stabilizer codes. We here consider the computational complexity of, given a graph state |G>, counting the number of graph states, single-qubit Clifford equivalent to |G>. We show that this problem is #P-Complete. To prove our main result we make use of the notion of isotropic systems in graph theory. We review the definition of isotropic systems and point out their strong relation to graph states. We believe that these isotropic systems can be useful beyond the results presented in this paper.

Trapped ions are among the most promising candidates for performing quantum information processing tasks. Recently, it was demonstrated how the properties of geometric phases can be used to implement an entangling two qubit phase gate with significantly reduced operation time while having a built-in resistance against certain types of errors. In this article, we investigate the influence of dissipation on the geometric phase in the Markov regime. We show that additional environmentally induced phases as well as a loss of coherence result from the non-unitary evolution and connect these effects to the associated dynamical and geometrical phases. This suggests a strategy to compensate the detrimental environmental influences and restore some of the properties of the ideal implementation. In particular, we present a way to construct forces for the geometric phase gate which compensate the dissipative effects and leave the produced phase as well as the final motional state identical to the isolated case. Finally, we examine the effects of dissipation on the fidelity and the robustness of a two qubit phase gate against certain error types.

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cram\'{e}r-Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.

In this article, the dynamics of an unbalanced two-ion crystal comprising the 'target' and the 'sensor' ions confined in a Penning trap has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron and reduced-cyclotron modes split up into the so-called 'stretch' and 'common' modes, that are generalizations of the well-known 'breathing' and 'center-of-mass' motions of a balanced crystal made of two ions. By measuring the frequency modes of the crystal and the sensor ion eigenfrequencies using optical detection, it will be possible to determine the target ion's free-cyclotron frequency. The measurement scheme is described and the non-harmonicity of the Coulomb interaction is discussed since this might cause large systematic effects.

It is promising to achieve quantum supremacy with boson sampling given the rapid development of physical implementations. However, the sample loss issue, which exists in both the physical experiments and classical simulation, has a strong impact on where the frontier of quantum supremacy is. Addressing this, we present Sample Caching Markov Chain Monte Carlo (SC-MCMC), a sampling method that can generate samples without loss. SC-MCMC can reduce the estimated time for a 50-photon sample in ~10 days to <100 minutes with state-of-the-art classical computing platform. Further, our results indicate that to experimentally approach quantum supremacy, reducing sample loss within an experimental setup is an important and effective method.

For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixing. We show that the fluctuations around this limiting value, evaluated according to the invariant measure of these unitary flows, are captured by the Gaussian unitary ensemble (GUE) of random matrix theory. An extension of this statement, applicable when the unitary transformations conserve the energy but are maximally noisy or ergodic on any energy shell, allows to decipher the fluctuations around canonical typicality. According to typicality, if the large system is prepared in a generic pure state in a given energy shell, the reduced density matrix of the sub-system is almost surely the canonical Gibbs state of that sub-system. We show that the fluctuations around the Gibbs state are encoded in a deformation of the GUE whose covariance is specified by the Gibbs state. Contact with the eigenstate thermal hypothesis (ETH) is discussed.

A simpler quantum counting algorithm based on consecutive measurements is presented. This algorithm terminates within log(sqrt(N/M)) measurement steps, where M is the number of marked states and N is the total number of states in the search space, and is followed by a classical post processing. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator. This simpler algorithm requires less quantum resources in terms of the width and depth of the quantum circuit, and runs significantly faster than the phase estimation-based quantum counting algorithm when the ratio M/N is small. We compare these two quantum counting algorithms by simulating various cases with a different M/N ratio, such as M/N > 0.125 or M/N < 0.001.

Synchronization phenomena have been recently reported in the quantum realm at atomic level due to collective dissipation. In this work we propose a dimer lattice of trapped atoms realizing a dissipative spin model where quantum synchronization occurs instead in presence of local dissipation. Atoms synchronization is enabled by the inhomogeneity of staggered local losses in the lattice and is favored by an increase of spins detuning. A comprehensive approach to quantum synchronization based on different measures considered in the literature allows to identify the main features of different synchronization regimes.

Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum, correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system, and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems but can also be implemented in quantum-optical systems.

The traditional pedagogical paradigm in physics is based on a deductive approach. However, with the recent advances in information technology, we are facing a dramatic increase in the amount of readily available information; hence, the ability to memorize the material and provide rigorous derivations lacks significance. Our success in navigating the current "sea" of information depends increasingly on our skills in pattern recognition and prompt qualitative analysis. Inductive learning (using examples and intuition-based) is most suitable for the development of such skills. This needed change in our pedagogical paradigm remains yet to be addressed in physics curricula. We propose that incorporating inductive elements in teaching -by infusing qualitative methods - will better prepare us to deal with the new information landscape. These methods bring the learning experience closer to the realities of active research. As an example, we are presenting a compendium for teaching qualitative methods in quantum mechanics, a traditionally non-intuitive subject.

Variational quantum eigensolvers are a promising class of quantum algorithms for preparing approximate ground states, due to their relatively low circuit depth. Minimizing the error in such an approximation requires designing the ansatzes to target the studied system. In this work, we present a novel approach for the design of VQE ansatzes. Motivated by the stabilizer formalism of quantum error correction, we construct a class of ansatzes that explore the entire Hilbert space using the minimum number of free parameters. We then demonstrate how one may compress an arbitrary ansatz by enforcing symmetry constraints of the target system, or by using them as parent ansatzes for a hierarchy of increasingly long but increasingly accurate sub-ansatzes. We apply a perturbative analysis and develop a diagrammatic formalism to optimize the generation of these hierarchies within a weak-coupling regime. We test our methods on a short spin chain, finding good convergence to the ground state in the paramagnetic and the ferromagnetic phase of the transverse-field Ising model.

In the task of quantum state learning, one receives some data about measurements performed on a state, and using that, must make predictions on the outcomes of unseen measurements. Computing a prediction is generally hard but it has been shown that learning can be performed efficiently for states that are generated by Clifford circuits, which are known to be efficiently classically simulable. This naturally leads to the question, how does efficient state learnability compare with efficient classical simulation? In this work we introduce an extra condition on top of classical simulablity that guarantees efficiently learnability. To illustrate this we prove two new examples of efficient learnability: states with low (Schmidt rank) entanglement and states described by an 'efficient' ontological model.

Neural quantum states (NQS) attract a lot of attention due to their potential to serve as variational wave functions for quantum many-body systems. Here we study the main factors governing the applicability of NQS to frustrated magnets. We consider exact ground states of several moderately sized spin Hamiltonians solvable by means of exact diagonalization. We have found that it is the sign structure that is responsible for the difficulty of the variational approach, especially in frustrated regime. We show that, if a neural network is exposed to a small fraction of signs of the ground state wave function during training, its generalization accuracy, i.e. the capability to learn from a limited number of samples and correctly predict signs on the rest of the Hilbert space basis, drops as the frustration increases (the network fails to generalize in the most difficult cases). When a larger portion of the space is used for training, the generalization accuracy undergoes a sharp transition, and the network approximates the ground state with high precision. We conclude that the main issue to be addressed at this stage, in order to bring the method of NQS to the point where it can be used to simulate realistic models, is that of generalization rather than expressibility.