The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.

Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions between system and thermal bath will take finite time, and precise control of their interaction is usually out of reach. Motivated by this observation, we consider finite-time and uncontrolled operations between system and bath, which result in thermalizations that are only partial in each step. Our main result is that optimal processes can still be achieved for any non-trivial partial thermalizations, at the price of increasing the number of operations. We focus on work extraction protocols and show our results in two different frameworks: A collision model and a model where the Hamiltonian of the working system is controlled over time and the system can be brought into contact with a heat bath. Our results show that optimal processes are robust to noise and imperfections in small quantum systems, and can be achieved by a large set of interactions between system and bath.

The accessible information and the informational power quantify the maximum amount of information that can be extracted from a quantum ensemble and by a quantum measurement, respectively. Here, we investigate the tradeoff between the accessible information (informational power, respectively) and the purity of the states of the ensemble (the elements of the measurement, respectively). Under any given lower bound on the purity, i) we compute the minimum informational power and show that it is attained by the depolarized uniformly-distributed measurement; ii) we give a lower bound on the accessible information. Under any given upper bound on the purity, i) we compute the maximum accessible information and show that it is attained by an ensemble of pairwise commuting states with at most two distinct non-null eigenvalues; ii) we give a lower bound on the maximum informational power. The present results provide, as a corollary, novel sufficient conditions for the tightness of the Jozsa-Robb-Wootters lower bound to the accessible information.

Rapid and efficient preparation, manipulation and transfer of quantum states through an array of quantum dots (QDs) is a demanding requisite task for quantum information processing and quantum computation in solid-state physics. Conventional adiabatic protocols, as coherent transfer by adiabatic passage (CTAP) and its variations, provide slow transfer prone to decoherence, which could lower the fidelity to some extent. To achieve the robustness against decoherence, we propose a protocol of speeding up the adiabatic charge transfer in multi-QD systems, sharing the concept of "Shortcuts to Adiabaticity" (STA). We first apply the STA techniques, including the counterdiabatic driving and inverse engineering, to speed up the direct (long range) transfer between edge dots in triple QDs. Then, we extend our analysis to a multi-dot system. We show how by implementing the modified pulses, fast adiabatic-like charge transport between the outer dots can be eventually achieved without populating intermediate dots. We discuss as well the dependence of the transfer fidelity on the operation time in the presence of dephasing. The proposed protocols for accelerating adiabatic charge transfer directly between the outer dots in a QD array offers a robust mechanism for quantum information processing, by minimizing decoherence and relaxation processes.

Quantum optimal control can play a crucial role to realize a set of universal quantum logic gates with error rates below the threshold required for fault-tolerance. Open-loop quantum optimal control relies on accurate modeling of the quantum system under control, and does not scale efficiently with system size. These problems can be avoided in closed-loop quantum optimal control, which utilizes feedback from the system to improve control fidelity. In this paper, two gradient-based closed-loop quantum optimal control algorithms, the hybrid quantum-classical approach (HQCA) described in [Phys. Rev. Lett. 118, 150503 (2017)] and the finite-difference (FD) method, are experimentally investigated and compared to the open-loop quantum optimal control utilizing the gradient ascent method. We employ a solid-state ensemble of coupled electron-nuclear spins serving as a two-qubit system. Specific single-qubit and two-qubit state preparation gates are optimized using the closed-loop and open-loop methods. The experimental results demonstrate the implemented closed-loop quantum control outperforms the open-loop control in our system. Furthermore, simulations reveal that HQCA is more robust than the FD method to gradient noise which originates from measurement noise in this experimental setting. On the other hand, the FD method is more robust to control field distortions coming from non-ideal hardware

Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalise this idea and to look for potential applications. In this work, we derive an adversarial algorithm for the problem of approximating an unknown quantum pure state. Although this could be done on universal quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers. Two parametrized circuits are optimized in tandem: One tries to approximate the target state, the other tries to distinguish between target and approximated state. Supported by numerical simulations, we show that resilient backpropagation algorithms perform remarkably well in optimizing the two circuits. We use the bipartite entanglement entropy to design an efficient heuristic for the stopping criterion. Our approach may find application in quantum state tomography.

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival, reduced density matrix, Von Neumann entropy, coherence factor, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. The effective magnetic field $B$, homogenous coupling constant $A$, and longitudinal interaction $\Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. In particular, the presence of a finite longitudinal interaction $\Delta$ allows for quantum revivals even at a very small number of bath spins $N$, facilitating experimental control of entangled states. Under the resonance condition $B=\Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{\pi N}{A} m$ for a large $N$. For $\Delta =0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the quantum collapse and revival recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problem and the light-matter interacting system in quantum nonlinear optics, and revealing the statistical nature of Holstein-Primakoff transformation.

By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl's law.

Quantum circuits for basic image processing functions such as bilinear interpolation are required to implement image processing algorithms on quantum computers. In this work, we propose quantum circuits for the bilinear interpolation of NEQR encoded images based on Clifford+T gates. Quantum circuits for the scale up operation and scale down operation are illustrated. The proposed quantum circuits are based on quantum Clifford+T gates and are optimized for T-count. Quantum circuits based on Clifford+T gates can be made fault tolerant but the T gate is very costly to implement. As a result, reducing T-count is an important optimization goal. The proposed quantum bilinear interpolation circuits are based on (i) a quantum adder, (ii) a proposed quantum subtractor, and (iii) a quantum multiplication circuit. Further, both designs are compared and shown to be superior to existing work in terms of T-count. The proposed quantum bilinear interpolation circuits for the scale down operation and for the scale up operation each have a 92.52\% improvement in terms of T-count compared to the existing work.

There are two standard ways of classifying transport behavior of systems. The first is via time scaling of spread of correlations in the isolated system in thermodynamic limit. The second is via system size scaling of conductance in the steady state of the open system. We show here that these correspond to taking the thermodynamic limit and the long time limit of the integrated equilibrium current-current correlations of the open system in different order. In general, the limits may not commute leading to a conflict between the two standard ways of transport classification. Nevertheless, the full information is contained in the equilibrium current-current correlations of the open system. We show this analytically by rigorously deriving the open-system current fluctuation dissipation relations (OCFDR) starting from an extremely general open quantum set-up and then carefully taking the proper limits. We test our theory numerically on the non-trivial example of the critical Aubry-Andr{\'e}-Harper (AAH) model, where, it has been recently shown that, the two standard classifications indeed give different results. We find that both the total current autocorrelation and the long-range local current correlations of the open system in equilibrium show signatures of diffusive transport up to a time scale. This time scale grows as square of system size. Beyond this time scale a steady state value is reached. The steady state value is conductance, which shows sub-diffusive scaling with system size.

The Hodgkin-Huxley model describes the behavior of the membrane voltage in neurons, treating each element of the cell membrane as an electric circuit element, namely capacitors, memristors and voltage sources. We focus on the activation channel of potassium ions, since it is simpler, while keeping the majority of the features identified with the original Hodgkin-Huxley model. This reduces to a memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. Here, we take advantage of the recent quantization of the memristor to look into the Hodgkin-Huxley model in the quantum regime. We compare the behavior of the membrane voltage and the potassium channel conductance in both the classical and quantum realms, subjected to AC sources. Numerical simulations show an expected increment and adaptation depending on the history of signals in all regimes. We find that the response of this circuit can be reproduced classically; however, when computing higher moments of the voltage, we encounter purely quantum terms related to the zero-point energy of the circuit. This result paves the way for the construction of quantum neuron networks inspired in the brain function but capable of dealing with quantum information. This could be considered a step forward towards the design of neuromorphic quantum architectures with direct applications in quantum machine learning.

We describe sensitive magnetometry using lumped-element resonators fabricated from a superconducting thin film of NbTiN. Taking advantage of the large kinetic inductance of the superconductor, we demonstrate a continuous resonance frequency shift of $27$ MHz for a change in magnetic field of $1.8~\mu$T within a perpendicular background field of 60 mT. By using phase-sensitive readout of microwaves transmitted through the sensors, we measure phase shifts in real time with a sensitivity of $1$ degree/nT. We present measurements of the noise spectral density of the sensors, and find their field sensitivity is at least within one to two orders of magnitude of superconducting quantum interference devices operating with zero background field. Our superconducting kinetic inductance field-frequency sensors enable real-time magnetometry in the presence of moderate perpendicular background fields up to at least 0.2 T. Applications for our sensors include the stabilization of magnetic fields in long coherence electron spin resonance measurements and quantum computation.

Following detailed analysis of data the domain of applicability of Non-Relativistic QED (NRQED) with static nuclei is described for ground state energy of helium-like (and lithium-like) ions for $Z \leq 20$. It is demonstrated that finite nuclear mass effects do not change 4-5 significant digits (s.d.) and the leading relativistic and QED effects leave unchanged 3-4 s.d. for $Z \leq 20$ in ground state energy for both helium and lithium-like ions. It is shown that the non-relativistic ground state energy can be easily interpolated in full physics range of nuclear charge $Z$ with accuracy of not less than 6 decimal digits (d.d.) (or 7-8 s.d.) for $Z \leq 50$ for helium-like ions and for $Z \leq 20$ for lithium-like ions using a meromorphic function in variable ${\lambda}=\sqrt{Z-{Z_B}}$ (here $Z_B$ is the 2nd critical charge \cite{TLO:2016}), which is well inside the domain of applicability of non-relativistic QED. In turn, it is found a fourth degree polynomial in ${\lambda}$ which reproduces the ground state energy of the helium-like and lithium-like ions for $Z \leq 20$ in the domain of applicability of NRQED with static nuclei, thus, 3 s.d. It is noted that $\sim 99.9\%$ of the ground state energy (and some expectation values) is given by the variational energy for properly optimized trial function of the form of (anti)-symmetrized product of three (six) Coulomb orbitals for two-(three) electron system with 3 (7) free parameters for $Z \leq 20$, respectively. It implies that these trial functions are, in fact, the {\it exact} wavefunctions for non-relativistic QED.

Author(s): Jin Hyoun Kang, Jeong Ho Han, and Y. Shin

We report the experimental realization of a cross-linked chiral ladder with ultracold fermionic atoms in a 1D optical lattice. In the ladder, the legs are formed by the orbital states of the optical lattice and the complex interleg links are generated by the orbital-changing Raman transitions that a...

[Phys. Rev. Lett. 121, 150403] Published Fri Oct 12, 2018

Author(s): Hatem Barghathi, C. M. Herdman, and Adrian Del Maestro

Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. **91**, 097902 (2003)] intro...

[Phys. Rev. Lett. 121, 150501] Published Fri Oct 12, 2018

Author(s): Yaoyao Zhou, Juan Yu, Zhihui Yan, Xiaojun Jia, Jing Zhang, Changde Xie, and Kunchi Peng

Secret sharing is a conventional technique for realizing secure communications in information networks, where a dealer distributes to n players a secret, which can only be decoded through the cooperation of k (n/2<k≤n) players. In recent years, quantum resources have been employed to enhance secu...

[Phys. Rev. Lett. 121, 150502] Published Fri Oct 12, 2018

Author(s): Johnnie Gray, Leonardo Banchi, Abolfazl Bayat, and Sougato Bose

Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an expo...

[Phys. Rev. Lett. 121, 150503] Published Fri Oct 12, 2018

Author(s): Daniel Martínez, Armin Tavakoli, Mauricio Casanova, Gustavo Cañas, Breno Marques, and Gustavo Lima

Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the pr...

[Phys. Rev. Lett. 121, 150504] Published Fri Oct 12, 2018

Author(s): Mihail Poplavskyi and Grégory Schehr

We compute the persistence for the 2D-diffusion equation with random initial condition, i.e., the probability p0(t) that the diffusion field, at a given point x in the plane, has not changed sign up to time t. For large t, we show that p0(t)∼t−θ(2) with θ(2)=3/16. Using the connection between the 2D...

[Phys. Rev. Lett. 121, 150601] Published Fri Oct 12, 2018

Author(s): A. Grankin, P. O. Guimond, D. V. Vasilyev, B. Vermersch, and P. Zoller

We present the design of a chiral photonic quantum link, where distant atoms interact by exchanging photons propagating in a single direction in free space. This is achieved by coupling each atom in a laser-assisted process to an atomic array acting as a quantum phased-array antenna. This provides a...

[Phys. Rev. A 98, 043825] Published Fri Oct 12, 2018