Author(s): Mao-Sheng Li and Yan-Ling Wang

A pure quantum state of N subsystems with local dimension d is called a k-uniform state if every reduction to k qudits is maximally mixed. Based on a special class of combinatorial design, namely irredundant orthogonal arrays, we show the existence of 2-uniform N-qudit states when N≥4 and d is a pri...

[Phys. Rev. A 99, 042332] Published Thu Apr 25, 2019

Quantum algorithms for Noisy Intermediate-Scale Quantum (NISQ) machines have recently emerged as new promising routes towards demonstrating near-term quantum advantage (or supremacy) over classical systems. In these systems samples are typically drawn from probability distributions which --- under plausible complexity-theoretic conjectures --- cannot be efficiently generated classically. Rather than first define a physical system and then determine computational features of the output state, we ask the converse question: given direct access to the quantum state, what features of the generating system can we efficiently learn? In this work we introduce the Variational Quantum Unsampling (VQU) protocol, a nonlinear quantum neural network approach for verification and inference of near-term quantum circuits outputs. In our approach one can variationally train a quantum operation to unravel the action of an unknown unitary on a known input state; essentially learning the inverse of the black-box quantum dynamics. While the principle of our approach is platform independent, its implementation will depend on the unique architecture of a specific quantum processor. Here, we experimentally demonstrate the VQU protocol on a quantum photonic processor. Alongside quantum verification, our protocol has broad applications; including optimal quantum measurement and tomography, quantum sensing and imaging, and ansatz validation.

Quantum chemistry often considers atoms and molecules with non-zero spin. In such cases, the need for proper spin functions results in the theory of configuration state functions. Here, we consider the construction of such wavefunctions using the symmetric group and more specifically Young projectors. We discuss the formalism and detail an example to illustrate the theory. Additionally, we consider the pros and cons of specific implementations of spin symmetry in quantum simulation.

Photon echo is one of the basic tools for studying the coherent nonlinear interaction of light pulses with inhomogeneously broadened resonant atomic media. We generalize the McCall-Hahn area theorem to the formation of photon echo in the optically dense media and we find the analytic solutions for the pulse areas of the photon echo signals arising after the two-pulse excitation. The solutions allowed us for the first time to reveal the picture and mechanism of the photon echo train generation in such medium. We show that the series of self-reviving echo signals each having pulse area less than {\pi} can have total area of 2{\pi} or 0{\pi} in accordance with the area theorem while they propagate deep into the medium remaining separate in time. The resulting echo pulse train is a new alternative to the well-known soliton or breather.

We perform quantum logic spectroscopy with a $^{27}$Al$^{+}$/$^{40}$Ca$^{+}$ mixed ion crystal in a linear Paul trap for a measurement of the $(3s^{2})\,^{1}\mathrm{S}_{0} \leftrightarrow \, (3s3p)\,^{3}\mathrm{P}_{1}, F=7/2$ intercombination transition in $^{27}$Al$^{+}$. Towards this end, Ramsey spectroscopy is used for probing the transition in $^{27}$Al$^{+}$ and the $(4s^{2})\,\mathrm{S}_{1/2} \leftrightarrow \, (4s3d)\,\mathrm{D}_{5/2}$ clock transition in $^{40}$Ca$^{+}$ in interleaved measurements. By using the precisely measured frequency of the clock transition in $^{40}$Ca$^{+}$ as a frequency reference, we determine the frequency of the intercombination line to be $\nu_{^{1}\mathrm{S}_{0} \leftrightarrow \,^{3}\mathrm{P}_{1},F=7/2}$=1122 842 857 334 736(93) Hz and the Land\'e g-factor of the excited state to be $g_{^{3}\mathrm{P}_{1}, F=7/2}$=0.428132(2).

It has become increasingly common for high-school students to see media reports on the importance of quantum mechanics in the development of next-generation industries such as drug development and secure communication, but few of them have been exposed to fundamental quantum mechanical concepts in a meaningful classroom activity. In order to bridge this gap, we design and test a low-cost 20-minute demonstration of the Bell test, which is used in several entanglement-based quantum key distribution protocols. The demonstration introduces ideas such as the quantum state, quantum measurement, spin quantization, cryptography, and entanglement; all without using concepts beyond the 9th grade of the Chilean high-school curriculum. The demonstration can serve to promote early exposure of the future adopters and developers of quantum technology with its conceptual building blocks, and also to educate the general public about the importance of quantum mechanics in modern industry

For a native gate set which includes all single-qubit gates, we apply results from symplectic geometry to analyze the spaces of two-qubit programs accessible within a fixed number of gates. These techniques yield an explicit description of this subspace as a convex polytope, presented by a family of linear inequalities themselves accessible via a finite calculation. We completely describe this family of inequalities in a variety of familiar example cases, and as a consequence we highlight a certain member of the "XY-family" for which this subspace is particularly large, i.e., for which many two-qubit programs admit expression as low-depth circuits.

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where just two solenoids are sufficient to create topological bound states.

Quantum simulations of Fermi-Hubbard models have been attracting considerable efforts in the optical lattice research, with the ultracold anti-ferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping that shows up is atomic localization in the incommensurate lattice, potentially causing exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.

Quantum computing technologies promise to revolutionize calculations in many areas of physics, chemistry, and data science. Their power is expected to be especially pronounced for problems where direct analogs of a quantum system under study can be encoded coherently within a quantum computer. A first step toward harnessing this power is to express the building blocks of known physical systems within the language of quantum gates and circuits. In this paper, we present a quantum calculation of an archetypal quantum system: neutrino oscillations. We define gate arrangements that implement the neutral lepton mixing operation and neutrino time evolution in two-, three-, and four-flavor systems. We then calculate oscillation probabilities by coherently preparing quantum states within the processor, time evolving them unitarily, and performing measurements in the flavor basis, with close analogy to the physical processes realized in neutrino oscillation experiments, finding excellent agreement with classical calculations. We provide recipes for modeling oscillation in the standard three-flavor paradigm as well as beyond-standard-model scenarios, including systems with sterile neutrinos, non-standard interactions, Lorentz symmetry violation, and anomalous decoherence.

We present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum annealer, the D-Wave 2000Q, is used to sample from this model. This algorithm joins a growing family of algorithms that use a quantum annealing subroutine in deep learning, and provides a framework to test the advantages of quantum-assisted learning in GANs. Fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum annealing sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies, and is also applied to the LSUN dataset bedrooms class for the Chimera topology. Evaluated using the Fr\'{e}chet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset.

We propose a generalized Dicke model which supports a quantum tricritical point. We map out the phase diagram and investigate the critical behaviors of the model through exact low-energy effective Hamiltonian in the thermodynamic limit. As predicted by the Landau theory of phase transition, the order parameter shows non-universality at the tricritical point. Nevertheless, as a result of the separation of the classical and the quantum degrees of freedom, we find a universal relation between the excitation gap and the entanglement entropy for the entire critical line including the tricritical point. Here the universality is carried by the emergent quantum modes, whereas the order parameter is determined classically.

Topological insulators are materials that have a gapped bulk energy spectrum, but contain protected in-gap states appearing at their surface. These states exhibit remarkable properties such as unidirectional propagation and robustness to noise that offer an opportunity to improve the performance and scalability of quantum technologies. For quantum applications, it is essential that the topological states are indistinguishable. Here we report high-visibility quantum interference of single photon topological states in an integrated photonic circuit. Two topological boundary-states, initially at opposite edges of a coupled waveguide array, are brought into proximity, where they interfere and undergo a beamsplitter operation. We observe $93.1\pm2.8\%$ visibility Hong-Ou-Mandel (HOM) interference, a hallmark non-classical effect that is at the heart of linear optics-based quantum computation. Our work shows that it is feasible to generate and control highly indistinguishable single photon topological states, opening pathways to enhanced photonic quantum technology with topological properties, and to study quantum effects in topological materials.

The real stabilizer fragment of quantum mechanics was shown to have a complete axiomatization in terms of the angle-free fragment of the ZX-calculus. This fragment of the ZXcalculus--although abstractly elegant--is stated in terms of identities, such as spider fusion which generally do not have interpretations as circuit transformations. We complete the category CNOT generated by the controlled not gate and the computational ancillary bits, presented by circuit relations, to the real stabilizer fragment of quantum mechanics. This is performed first, by adding the Hadamard gate and the scalar sqrt 2 as generators. We then construct translations to and from the angle-free fragment of the ZX-calculus, showing that they are inverses. We remove the generator sqrt 2 and then prove that the axioms are still complete for the remaining generators. This yields a category which is not compact closed, where the yanking identities hold up to a non-invertible, non-zero scalar. We then discuss how this could potentially lead to a complete axiomatization, in terms of circuit relations, for the approximately universal fragment of quantum mechanics generated by the Toffoli gate, Hadamard gate and computational ancillary bits.

Monte Carlo simulations are performed in classical phase space for a one-dimensional quantum harmonic crystal. Symmetrization effects for spinless bosons and fermions are quantified. The algorithm is tested for a range of parameters against exact results that use 20,000 energy levels. It is shown that the singlet mean field approximation is very accurate at high temperatures, and that the pair mean field approximation gives a systematic improvement in the intermediate and low temperature regime. The latter is derived from a cluster mean field approximation that accounts for the non-commutativity of position and momentum, and that can be applied in three dimensions.

In the past decades, quantum plasmonics has become an active area due to its potential applications in on-chip plasmonic devices for quantum information processing. However, the fundamental physical process, i.e., how a quantum state of light evolves in the photon-plasmon conversion process, has not been clearly understood. Here, we report a complete characterization of the plasmon-assisted extraordinary optical transmission process through quantum process tomography. By inputting various coherent states to interact with the plasmonic structure and detecting the output states with a homodyne detector, we reconstruct the process tensor of the photon-plasmon conversion process. Both the amplitude and phase information of the process are extracted, which explains the evolution of the quantum-optical state after the coupling with plasmons. Our experimental demonstration constitutes a fundamental block for future on-chip applications of quantum plasmonic circuits.

We aim to devise feasible, efficient verification schemes for bosonic channels. To this end, we construct an average-fidelity witness that yields a tight lower bound for average fidelity plus a general framework for verifying optimal quantum channels. For both multi-mode unitary Gaussian channels and single-mode amplification channels, we present experimentally feasible average-fidelity witnesses and reliable verification schemes, for which sample complexity scales polynomially with respect to all channel specification parameters. Our verification scheme provides an approach to benchmark the performance of bosonic channels on a set of Gaussian-distributed coherent states by employing only two-mode squeezed vacuum states and local homodyne detections. Our results demonstrate how to perform feasible tests of quantum components designed for continuous-variable quantum information processing.

We present a construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that the family of generalized negativity functions we present are suitable for studying entanglement in many-body systems due their interesting algebraic properties. Indeed, under mild hypotheses, the new measures are computable entanglement monotones, non-increasing under LOCC. Also, they are composable: their evaluation over tensor products can be computed in terms of the evaluations over each factor, by means of a certain group law. In principle, being multi-parametric witnesses of entanglement, they could be useful to study separability and (in perspective) criticality of mixed states, playing a role similar to that of R\'enyi's entanglement entropy in the discrimination of criticality and conformal sectors for pure states.

As the Quantum Key Distribution (QKD) technology supporting the pointto-point application matures, the need to build the Quantum Secure Communication Network (QSCN) to guarantee the security of a large scale of nodes becomes urgent. Considering the project time and expense control, it is the first choice to build the QSCN based on an existing classical network. Suitable modeling and simulation are very important to construct a QSCN successfully and efficiently. In this paper, a practical QSCN model, which can reflect the network state well, is proposed. The model considers the volatile traffic demand of the classical network and the real key generation capability of the QKD devices, which can enhance the accuracy of simulation to a great extent. In addition, two unique QSCN performance indicators, ITS (information-theoretic secure) communication capability and ITS communication efficiency, are proposed in the model, which are necessary supplements for the evaluation of a QSCN except for those traditional performance indicators of classical networks. Finally, the accuracy of the proposed QSCN model and the necessity of the proposed performance indicators are verified by plentiful simulations results.

Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm caused by interacting leaked states with qubit states. Ion trap qubits driven by Raman gates have a natural choice between qubits encoded in magnetically insensitive hyperfine states that can leak and qubits encoded in magnetically sensitive Zeeman states of the electron spin that cannot leak. In our previous work, we compared these two qubits in the context of the toric code with a depolarizing leakage error model and found that for magnetic field noise with a standard deviation less than 32 $\mu$G that the $^{174}$Yb$^+$ Zeeman qubit outperforms the $^{171}$Yb$^+$ hyperfine qubit. Here we examine a physically motivated leakage error model based on ions interacting via the Molmer-Sorenson gate. We find that this greatly improves the performance of hyperfine qubits but the Zeeman qubits are more effective for magnetic field noise with a standard deviation less than 10 $\mu$G. At these low magnetic fields, we find that the best choice is a mixed qubit scheme where the hyperfine qubits are the ancilla and the leakage is handled without the need of an additional leakage reduction circuit.