Publications of Alan C. Santos

The phenomena where a quantum system can be exponentially accelerated to its stationary state has been refereed to as Quantum Mpemba Effect (QMpE). Due to its analogy with the classical Mpemba effect, hot water freezes faster than cold water, this phenomena has garnered significant attention. Although QMpE has been characterized and experimentally verified in different scenarios, sufficient and necessary conditions to achieve such a phenomenon are still under investigation. In this paper we address a sufficient condition for QMpE through a general approach for open quantum systems dynamics. With help of the Mpemba parameter introduced in this work to quantify how strong the QMpE can be, we discuss how our conditions can predict and explain the emergence of weak and strong QMpE in a robust way. As application, by harnessing intrinsic non-classical nature of squeezed thermal environments, we show how strong QMpE can be effectively induced when our conditions are met. Due to the thermal nature of environment considered in our model, our work demonstrates that a hot qubit freezes faster than a cold qubit only in presence of squeezed reservoirs. Our results provide tools and new insights opening a broad avenue for further investigation at most fundamental levels of this peculiar phenomena in the quantum realm.

A fast and scalable scheme for multi-qubit resetting in superconducting quantum processors is proposed by exploiting the feasibility of frequency-tunable transmon qubits and transmon-like couplers to engineer a full programmable superconducting erasing head. The scalability of the device is verified by simultaneously resetting two qubits, where we show that collectivity effects may emerge as an fundamental ingredient to speed up the erasing process. Conversely, we also describe the appearance of decoherence-free subspace in multi-qubit chips, causing it to damage the device performance. To overcome this problem, a special set of parameters for the tunable frequency coupler is proposed, which allows us to erase even states within such subspace. To end, we offer a proposal to buildup integrated superconducting processors that can be efficiently connected to erasure heads in a scalable way.

Digitizing an adiabatic evolution is a strategy able to combine the good performance of gate-based quantum processors with the advantages of adiabatic algorithms, providing then a hybrid model for efficient quantum information processing. In this work we develop validity conditions for high fidelity digital adiabatic tasks. To this end, we assume a digitizing process based on the Suzuki-Trotter decomposition, which allows us to introduce a $Digitized$ $Adiabatic$ $Theorem$. As consequence of this theorem, we show that the performance of such a hybrid model is limited by the fundamental constraints on the adiabatic theorem validity, even in ideal quantum processors. We argue how our approach predicts the existence of intrinsic non-adiabatic errors reported by R. Barends $et$ $al$., Nature 534, 222 (2016) through an empirical study of digital annealing. In addition, our approach allows us to explain the existence of a scaling of the number of Suzuki-Trotter blocks for the optimal digital circuit with respect to the optimal adiabatic total evolution time, as reported by G. B. Mbeng $et$ $al$, Phys. Rev. B 100, 224201 (2019) through robust numerical analysis of digital annealing. We illustrate our results through two examples of digitized adiabatic algorithms, namely, the two-qubits exact-cover problem and the three-qubits adiabatic factorization of the number 21.

Interference underpins some of the most practical and impactful properties of both the classical and quantum worlds. In this work we experimentally investigate a new formalism to describe interference effects, based on collective states which have enhanced or suppressed coupling to a two-level system. We employ a single trapped ion, whose electronic state is coupled to two of the ion’s motional modes in order to simulate a multi-mode light-matter interaction. We observe the emergence of phononic bright and dark states for both a single phonon and a superposition of coherent states and demonstrate that a view of interference which is based solely on their decomposition in the collective basis is able to intuitively describe their coupling to a single atom. This work also marks the first time that multi-mode bright and dark states have been formed with the bounded motion of a single trapped ion and we highlight the potential of the methods discussed here for use in quantum information processing.

In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In the context of adiabatic dynamics in closed systems, it is introduced a validation mechanism for the adiabaticity conditions by studing the system dynamics from a non-inertial reference frame. By considering a decohering scenario, validity conditions of the adiabatic approximation are also studied. As a fresh general result with potential applications, it is shown that under decoherence the adiabaticity may still occur in the infinite time limit, as it happens for closed systems, for a class of initial quantum states. To end, the original contributions of this thesis to the theory of shortcuts to adiabaticity refers to a generalized approach of transitionless quantum driving, where one explores the gauge freedom of the quantal phase factors accompanying adiabatic trajectories. A number of theoretical applications are studied, where some theoretical prediction presented in this thesis are experimentally verified through two different experimental setups, namely a qubit encoded in the energy hyperfine structure of a Ytterbium trapped ion, and in nuclear magnetic resonance with a nuclear spin qubit.

Designing quantum analogous of classical computers components is the heart of quantum information processors. In this sense, for quantum devices, quantum transistors are believed to be as necessary as the classical ones for classical devices. In this paper we design the smallest spin-based quantum transistor. In fact, while previous schemes explore entangled quantum state for simulating the performance of quantum transistors gate (open and close it), in this paper we show that such task can be achieved by a controllable external magnetic field in a three-spin quantum system. Thus, we could reduce the number of physical spins required to design the quantum transistor, since the gate in our transistor is composed by a single-spin, instead two-spin systems. To analyze the performance of our quantum transistor, we consider its robustness against two decohering environments.

Adiabatic evolution is a powerful technique in quantum information and computation. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. In this dissertation we introduce two different models to perform universal superadiabatic quantum computing, which are based on the use of shortcuts to adiabaticity by counter-diabatic Hamiltonians. The first model is based on the use of superadiabatic quantum teleportation, introduced in this dissertation, as a primitive to quantum computing. Thus, we provide the counter-diabatic driving for arbitrary $n$-qubit gates. In addition, our approach maps the counter-diabatic Hamiltonian for an arbitrary $n$-qubit {\it gate} teleportation into the implementation of a rotated counter-diabatic Hamiltonian for an $n$-qubit {\it state} teleportation. In the second model we use the concept of controlled superadiabatic evolutions to show how we can implement arbitrary $n$-controlled quantum gates. Remarkably, this task can be performed by simple time-independent counter-diabatic Hamiltonians. These two models can be used to design different sets of universal quantum gates. We show that the use of the quantum speed limit suggests that the superadiabatic time evolution is compatible with arbitrarily small time intervals, where this arbitrariness is constrained to the energetic cost necessary to perform the superadiabatic evolution.

We introduce a counter-diabatic approach for deriving Hamiltonians modeling superchargable quantum batteries (QBs). A necessary requirement for the supercharging process is the existence of multipartite interactions among the cells of the battery. Remarkably, this condition may be insufficient no matter the number of multipartite terms in the Hamiltonian. We analytically illustrate this kind of insufficiency through a model of QB based on the adiabatic version for the Grover search problem. On the other hand, we provide QB supercharging with just a mild number of global connections in the system. To this aim, we consider a spin-$1/2$ chain with $n$ sites in the presence of Ising multipartite interactions. We then show that, by considering the validity of the adiabatic approximation and by adding $n$ terms of $(n-1)$-site interactions, we can achieve a Hamiltonian exhibiting maximum QB power, with respect to a normalized evolution time, growing quadratically with $n$. Therefore, supercharging can be achieved by $O(n)$ terms of multipartite connections. The time constraint required by the adiabatic approximation can be surpassed by considering a counter-diabatic expansion in terms of the gauge potential for the original Hamiltonian, with a limited $O(n)$ many-body interaction terms assured via a Floquet approach for the counter-diabatic implementation.

We propose a novel quantum battery realized with a few interacting particles in a three-well system with different on-site energies, which could be realized with ultracold atom platforms. We prepare the initial state in the lowest energy well and charge the battery using a Spatial Adiabatic Passage (SAP)-based protocol, enabling the population of a higher energy well. We examine the charging under varying interaction strengths and reveal that the consideration of collective charging results in an intriguing oscillatory behavior of the final charge for finite interactions, through diabatic evolution. Our findings open a new avenue for building stable and controllable quantum batteries.

To address the outstanding task of detecting entanglement in large quantum systems, entanglement witnesses have emerged, addressing the separable nature of a state. Yet optimizing witnesses, or accessing them experimentally, often remains a challenge. We here introduce a family of entanglement witnesses for open quantum systems, based on the electric field — its quadratures and the total fluorescence. More general than spin-squeezing inequalities, it can detect new classes of entangled states, as changing the direction for far-field observation opens up a continuous family of witnesses, without the need for a state tomography. Their efficiency is demonstrated by detecting, from almost any direction, the entanglement of collective single-photon states, such as long-lived states generated by cooperative spontaneous emission. Able to detect entanglement in large quantum systems, these electric-field-based witnesses can be used on any set of emitters described by the Pauli group, such as atomic systems (cold atoms and trapped ions), giant atoms, color centers, and superconducting qubits.

Quantum obesity (QO) is new function used to quantify quantum correlations beyond entanglement, which also works as a witness for entanglement. Thanks to its analyticity for arbitrary state of bipartite systems, it represents an advantage with respect to other quantum correlations, like quantum discord for example. In this work we show that QO is a fundamental quantity to observe signature of quantum phase transitions. We also describe a mechanism based on local filtering operations able to intensify the critical behavior of the QO near to the transition point. To this end, we introduce a theorem stating how QO changes under local quantum operations and classical communications. This work opens perspective for the characterization of new phenomena in quantum critical systems through the analytically computable pairwise QO.

We investigate the effect of localization on the local charging of quantum batteries (QBs) modeled by disordered spin systems. Two distinct schemes based on the transverse-field random Ising model are considered, with Ising couplings defined on a Chimera graph and on a linear chain with up to next-to-nearest neighbor interactions. By adopting a low-energy demanding charging process driven by local fields only, we obtain that the maximum extractable energy by unitary processes (ergotropy) is highly enhanced in the ergodic phase in comparison with the many-body localization (MBL) scenario. As we turn off the next-to-nearest neighbor interactions in the Ising chain, we have the onset of the Anderson localization phase. We then show that the Anderson phase exhibits a hybrid behavior, interpolating between large and small ergotropy as the disorder strength is increased. We also consider the splitting of total ergotropy into its coherent and incoherent contributions. This incoherent part implies in a residual ergotropy that is fully robust against dephasing, which is a typical process leading to the self-discharging of the battery in a real setup. Our results are experimentally feasible in scalable systems, such as in superconducting integrated circuits.

We propose a general scheme to generate entanglement encoded in the photon-number basis, via a sequential resonant two-photon excitation of a three-level system. We apply it to the specific case of a quantum dot three-level system, which can emit a photon pair through a biexciton-exciton cascade. The state generated in our scheme constitutes a tool for secure communication, as the multipartite correlations present in the produced state may provide an enhanced rate of secret communication with respect to a perfect GHZ state.

Controlling the flow of quantum information is a fundamental task for quantum computers, which is unfeasible to realize on classical devices. Coherent devices which can process quantum states are thus required to route the quantum states that encode information. In this paper we demonstrate experimentally the smallest quantum transistor with a superconducting quantum processor which is composed of a collector qubit, an emitter qubit, and a coupler (transistor gate). The interaction strength between the collector and emitter qubits is controlled by the frequency and state of the coupler, effectively implementing a quantum switch. Through the coupler-state-dependent Heisenberg (inherent) interaction between the qubits, a single-step (native) conditional $i$SWAP operation can be applied. To this end, we find that it is important to take into consideration higher energy level for achieving a native and high-fidelity transistor operation. By reconstructing the Quantum Process Tomography, we obtain an operation fidelity of $92.36\%$ when the transistor gate is open ($i$SWAP implementation) and $95.23 \%$ in the case of closed gate (identity gate implementation). The architecture has strong potential in quantum information processing applications with superconducting qubits.

Superconducting circuits are highly controllable platforms to manipulate quantum states, which make them particularly promising for quantum information processing. We here show how the existence of a distance-independent interaction between microwave resonators coupled capacitively through a qubit offers a new control parameter toward this goal. This interaction is able to induce an idling point between resonant resonators, and its state-dependent nature allows one to control the flow of information between the resonators. The advantage of this scheme over previous one is demonstrated through the generation of high-fidelity NOON states between the resonators, with a lower number of operations than previous schemes. Beyond superconducting circuits, our proposal could also apply to atomic lattices with clock transitions in optical cavities, for example.

In this paper we show how to generate efficiently entanglement between two artificial giant atoms with photon-mediated interactions in a waveguide. Taking advantage of the adjustable decay processes of giant atoms into the waveguide, and of the interference processes, spontaneous sudden birth of entanglement can be strongly enhanced with giant atoms. Highly entangled states can also be generated in the steady-state regime when the system is driven by a resonant classical field. We show that the statistics of the light emitted by the system can be used as a witness of the presence of entanglement in the system, since giant photon bunching is observed close to the regime of maximal entanglement. Given the degree of quantum correlations incoherently generated in this system, our results open a broad avenue for the generation of quantum correlations and manipulation of photon statistics in systems of giant atoms.

In this work we study the role of parasitic interactions and microwave crosstalk in a system of two superconducting artificial atoms interacting via a single-mode coplanar waveguide. Through a general description of the effective dynamics of the atoms, beyond the two-level approximation, we show that the atom selectivity (ability to individually address an atom) is only dependent on the resultant phasor associated to the drives used to control the system. We then exploit the benefits of such a drive-dependent selectivity to describe how the coherent population inversion occurs in the atoms simultaneously, with no interference of residual atom-atom interaction. In this scenario the parasitic interaction works as a resource to fast and high fidelity control, as it gives rise to a new regime of frequencies for the atoms able to suppress effective atom-atom coupling (idling point). To end, we show how an entangling $i$SWAP gate is implemented with fidelity higher than $99\%$, even in presence of parasitic interactions. More than that, we argue that the existence of this interaction can be helpful to speed up the gate performance. Our results open prospects to a new outlook on the real role of such “undesired” effects in a system of superconducting artificial atoms.

Quantum batteries are miniature energy storage devices and play a very important role in quantum thermodynamics. In recent years, quantum batteries have been extensively studied, but limited in theoretical level. Here we report the experimental realization of a quantum battery based on superconducting qubits. Our model explores dark and bright states to achieve stable and powerful charging processes, respectively. Our scheme makes use of the quantum adiabatic brachistochrone, which allows us to speed up the {battery ergotropy injection. Due to the inherent interaction of the system with its surrounding, the battery exhibits a self-discharge, which is shown to be described by a supercapacitor-like self-discharging mechanism. Our results paves the way for proposals of new superconducting circuits able to store extractable work for further usage.

Quantum mechanics dictates the band-structure of materials that is essential for functional electronic components. With increased miniaturization of devices, it becomes possible to exploit the full potential of quantum mechanics through the principles of superposition and entanglement. We propose a new class of quantum rectifiers that can leverage entanglement to dramatically increase performance by coupling two small spin chains through an effective double-slit interface. Simulations show that rectification is enhanced by several orders of magnitude even in small systems, and that the effect survives in a noisy environment. Realizable using several of the quantum technology platforms currently available, our findings reveal the importance of quantum entanglement in seemingly contradictory applications such as heat and noise control.

Considering the paradigmatic case of a cloud of two-level atoms interacting through common vacuum modes, we show how cooperative spontaneous emission, which is at the origin of superradiance, leads the system to long-lived entangled states at late times. These subradiant modes are characterized by an entanglement between all particles, independently of their geometrical configuration. While there is no threshold on the interaction strength necessary to entangle all particles, stronger interactions lead to longer-lived entanglement.

One of the most important devices emerging from quantum technology are quantum batteries. However, self-discharging, the process of charge wasting of quantum batteries due to decoherence phenomenon, limits their performance, measured by the concept of ergotropy and half-life time of the quantum battery. The effects of local field fluctuation, introduced by disorder term in Hamiltonian of the system, on the performance of the quantum batteries is investigated in this paper. The results reveal that the disorder term could compensate disruptive effects of the decoherence, i.e. self-discharging, and hence improve the performance of the quantum battery via “incoherent gain of ergotropy” procedure. Adjusting the strength of disorder parameter to a proper value and choosing a suitable initial state of quantum battery, the amount of free ergotropy, defined with respect to free Hamiltonian, could exceed the amount of initial stored ergotropy. In addition harnessing the degree of disorder parameter could help to enhance the half-life time of the quantum battery. This study opens perspective to further investigation of the performance of quantum batteries that explore disorder and many-body effects.

We propose to use the quantum states of an electron trapped on the inner surface of a graphene nanotorus to realize as a new kind of physical quantum bit, which can be used to encode quantum information. Fundamental tasks for quantum information processing, such as the qubit initialization and the implementation of arbitrary single qubit gates, can then be performed using external magnetic and electric fields. We also analyze the robustness of the device again systematic errors, which can be suppressed by a suitable choice of the external control fields. These findings open new prospects for the development an alternative platform for quantum computing, the scalability of which remains to be determined.

The study of advanced quantum devices for energy storage has attracted the attention of the scientific community in the past few years. Although several theoretical progresses have been achieved recently, experimental proposals of platforms operating as quantum batteries under ambient conditions are still lacking. In this context, this work presents a feasible realization of a quantum battery in a carboxylate-based metal complex, which can store a finite amount of extractable work under the form of quantum discord at room temperature, and recharge by thermalization with a reservoir. Moreover, the stored work can be evaluated through non-destructive measurements of the compound’s magnetic susceptibility. These results pave the way for the development of enhanced energy storage platforms through material engineering.

Quantum information processing has been one of the pillars of the new information age. In this sense, the control and processing of quantum information plays a fundamental role, and computers capable of manipulating such information have become a reality. In this article we didactically present basic elements of the latest version of IBM’s quantum computer and its main tools. We also present in detail the Deutsch-Jozsa algorithm used to differentiate constant functions from balanced functions, also, including a discussion of its efficiency against classical algorithms for the same task. The experimental implementation of the algorithm in a 4-qbit system is presented. Our article paves the way for a series of didactic investigations into the IBM system as well as the best known quantum algorithms.

A general approach for transitionless quantum driving in open quantum systems is introduced. Under the assumption of adiabatic evolution for time-local master equations, we derive the generalized transitionless Lindbladian required to implement a shortcut to adiabaticity in an open system scenario. The general counter-diabatic Lindbladian obtained accounts for a phase freedom, which translates into a set of free parameters throughout the dynamics. We then discuss how our generalized approach allows us to recover the transitionless Lindbladian introduced by G. Vacanti et al. [New J. Phys. 16, 053017 (2014)]. We then show how to engineer time-independent master equations that provide the same dynamics as the time-dependent master equation provided by the standard transitionless quantum driving in open systems. We illustrate our results by applying them both to the adiabatic Deutsch algorithm under dephasing and to the Landau-Zener Hamiltonian under bit-phase-flip.

Work extraction protocol is always a significant issue in the context of quantum batteries, in which the notion of ergotropy is used to quantify a particular amount of energy that can be extracted through unitary processes. Given the total amount of energy stored in a quantum system, quantifying wasted energy after the ergotropy extraction is a question to be considered when undesired coupling with thermal reservoirs is taken into account. In this paper, we show that some amount of energy can be lost when we extract ergotropy from a quantum system and quantified by the exergy of passive states. Through a particular example, one shows that ergotropy extraction can be done by preserving the quantum correlations of a quantum system. Our study opens the perspective for new advances in open system quantum batteries able to explore exergy stored as quantum correlations.

The storage and transfer of energy through quantum batteries are key elements in quantum networks. Here, we propose a charger design based on transitionless quantum driving (TQD), which allows for inherent control over the battery charging time, with the speed of charging coming at the cost of the internal energy available to implement the dynamics. Moreover, the TQD-based charger is also shown to be locally stable, which means that the charger can be disconnected from the quantum battery (QB) at any time after the energy transfer to the QB, with no fully energy backflow to the charger. This provides a highly charged QB in an always-on asymptotic regime. We illustrate the robustness of the QB charge against time fluctuations and the full control over the evolution time for a feasible TQD-based charger.

Devices that use quantum advantages for storing energy in the degree of freedom of quantum systems have drawn attention due to their properties of working as quantum batteries. However, one can identify a number of problems that need to be adequately solved before a real manufacturing process of these devices. In particular, it is important paying attention to the ability of quantum batteries in storing energy when no consumption center is connected to them. In this paper, by considering quantum batteries disconnected from external charging fields and consumption center, we study the decoherence effects that lead to charge leakage to the surrounding environment. We identify this phenomena as a self-discharging of QBs, in analogy to the inherent decay of the stored charge of conventional classical batteries in a open-circuit configuration. The quantum advantage concerning the classical counterpart is highlighted for single- and multi-cell quantum batteries.

We propose a variational principle to compute a quantum adiabatic brachistochrone (QAB) for open systems. Using the notion of “adiabatic speed” based on the energy gaps, we derive a Lagrangian associated to the functional measuring the time spent to achieve adiabatic behavior, which in turn allows us to perform the optimization. The QAB is illustrated for non-unitary dynamics of STIRAP process, the Deutsch-Jozsa quantum computing algorithm and of a transmon qutrit. A numerical protocol is devised, which allows to compute the QAB for arbitrary quantum systems for which exact simulations can be afforded. We also establish sufficient conditions for the equivalence between the Lagrangians, and thus the QAB, of open and closed systems.

The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard adiabatic theorem is specifically derived for closed quantum systems. In a realistic open system scenario, the inevitable system-reservoir interaction must be taken into account, which strongly impacts the generalization of the adiabatic behavior. In this paper, we introduce sufficient conditions for the adiabatic approximation in open quantum systems. These conditions are simple yet general, providing a suitable instrument to investigate adiabaticity for arbitrary initial mixed states evolving under time local master equations. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium, where irreversible entropy production is vanishing. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.

Quantum thermodynamics aims at investigating both the emergence and the limits of the laws of thermodynamics from a quantum mechanical microscopic approach. In this scenario, thermodynamic processes with no heat exchange, namely, adiabatic transformations, can be implemented through quantum evolutions in closed systems, even though the notion of a closed system is always an idealization and approximation. Here, we begin by theoretically discussing thermodynamic adiabatic processes in open quantum systems, which evolve non-unitarily under decoherence due to its interaction with its surrounding environment. From a general approach for adiabatic non-unitary evolution, we establish heat and work in terms of the underlying Liouville superoperator governing the quantum dynamics. As a consequence, we derive the conditions that an adiabatic open-system quantum dynamics implies in the absence of heat exchange, providing a connection between quantum and thermal adiabaticity. Moreover, we determine families of decohering systems exhibiting the same maximal heat exchange, which imply in classes of thermodynamic adiabaticity in open systems. We then approach the problem experimentally using a hyperfine energy-level quantum bit of an Ytterbium $^{171}$Yb$^+$ trapped ion, which provides a work substance for thermodynamic processes, allowing for the analysis of heat and internal energy throughout a controllable engineered dynamics.

A fully operational loss-free quantum battery requires an inherent control over the energy transfer process, with the ability of keeping the energy retained with no leakage. Moreover, it also requires a stable discharge mechanism, which entails that no energy revivals occur as the device starts its energy distribution. Here, we provide a scalable solution for both requirements. To this aim, we propose a general design for a quantum battery based on an {\it{energy current}} (EC) observable quantifying the energy transfer rate to a consumption hub. More specifically, we introduce an instantaneous EC operator describing the energy transfer process driven by an arbitrary interaction Hamiltonian. The EC observable is shown to be the root for two main applications: (i) a trapping energy mechanism based on a common eigenstate between the EC operator and the interaction Hamiltonian, in which the battery can indefinitely retain its energy even if it is coupled to the consumption hub; (ii) an asymptotically stable discharge mechanism, which is achieved through an adiabatic evolution eventually yielding vanishing EC. These two independent but complementary applications are illustrated in quantum spin chains, where the trapping energy control is realized through Bell pairwise entanglement and the stability arises as a general consequence of the adiabatic spin dynamics.

High performance quantum information processing requires efficient control of undesired decohering effects, which are present in realistic quantum dynamics. To deal with this issue, a powerful strategy is to employ transitionless quantum driving (TQD), where additional fields are added to speed up the evolution of the quantum system, achieving a desired state in a short time in comparison with the natural decoherence time scales. In this paper, we provide an experimental investigation of the performance of a generalized approach for TQD to implement shortcuts to adiabaticity in nuclear magnetic resonance (NMR). As a first discussion, we consider a single nuclear spin-$\frac{1}{2}$ system in a time-dependent rotating magnetic field. While the adiabatic dynamics is violated at a resonance situation, the TQD Hamiltonian is shown to be robust against resonance, allowing us to mimic the adiabatic behavior in a fast evolution even under the resonant configurations of the original (adiabatic) Hamiltonian. Moreover, we show that the generalized TQD theory requires less energy resources, with the strength of the magnetic field less than that required by standard TQD. As a second discussion, we analyze the experimental implementation of shortcuts to single-qubit adiabatic gates. By adopting generalized TQD, we can provide feasible time-independent driving Hamiltonians, which are optimized in terms of the number of pulses used to implement the quantum dynamics. The robustness of adiabatic and generalized TQD evolutions against typical decoherence processes in NMR is also analyzed.

In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. We experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show the theoretical and real experimental implementation. This article could be useful in introductory courses on quantum mechanics and nuclear magnetic resonance foundations, for example.

We introduce both a theoretical and an experimental scheme for simulating a quantum thermal engine through an all-optical approach, with the behavior of the working substance and the thermal reservoirs implemented via internal degrees of freedom of a single photon. By using the polarization and propagation path, we encode two quantum bits and then implement the thermodynamical steps of an Otto cycle. To illustrate the feasibility of our proposal, we experimentally realize such simulation through an intense laser beam, evaluating heat and work at each individual step of the thermodynamical cycle. In addition, from the analysis of the entropy production during the entire cycle, we can study the amount of quantum friction produced in the Otto cycle as a function of the difference of temperature between hot and cold reservoirs. Our paper constitutes, therefore, an all-optical-based thermal machine simulation and opens perspectives for other optical simulations in quantum thermodynamics.

In this article, we present a quantum transistor model based on a network of coupled quantum oscillators destined to quantum information processing tasks in linear optics. To this end, we show in an analytical way how a set of $N$ quantum oscillators (data-bus) can be used as an optical quantum switch, in which the energy gap of the data bus oscillators plays the role of an adjustable “potential barrier”. This enables us to “block or allow” the quantum information to flow from the source to the drain. In addition, we discuss how this device can be useful for implementing single qubit phase-shift quantum gates with high fidelity, so that it can be used as a useful tool. To conclude, during the study of the performance of our device when considering the interaction of this with a thermal reservoir, we highlight the important role played by the set of oscillators which constitute the data-bus in reducing the unwanted effects of the thermal reservoir. This is achieved by reducing the information exchange time (shortening time scale) between the desired oscillators. In particular, we have identified a non-trivial criterion in which the ideal size of the data-bus can be obtained so that it presents the best possible performance. We believe that our study can be perfectly adapted to a large number of thermal reservoir models.

Validity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario, inconsistencies in the application of quantitative adiabatic conditions have led to a sequence of new approaches for adiabaticity. Here, by adopting a different strategy, we introduce a validation mechanism for the adiabatic approximation by driving the quantum system to a non-inertial reference frame. More specifically, we begin by considering several relevant adiabatic approximation conditions previously derived and show that all of them fail by introducing a suitable oscillating Hamiltonian for a single quantum bit (qubit). Then, by evaluating the adiabatic condition in a rotated non-inertial frame, we show that all of these conditions, including the standard adiabatic condition, can correctly describe the adiabatic dynamics in the original frame, either far from resonance or at a resonant point. Moreover, we prove that this validation mechanism can be extended for general multi-particle quantum systems, establishing the conditions for the equivalence of the adiabatic behavior as described in inertial or non-inertial frames. In order to experimentally investigate our method, we consider a hyperfine qubit through a single trapped Ytterbium ion $^{171}$Yb$^{+}$, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system. By monitoring the quantum evolution, we explicitly show the consistency of the adiabatic conditions in the non-inertial frame.

Suppressing undesired nonunitary effects is a major challenge in quantum computation and quantum control. In this work, by considering the adiabatic dynamics in presence of a surrounding environment, we theoretically and experimentally analyze the robustness of adiabaticity in open quantum systems. More specifically, by considering a decohering scenario, we exploit the validity conditions of the adiabatic approximation as well as its sensitiveness to the resonance situation, which typically harm adiabaticity in closed systems. As an illustration, we implement an oscillating Landau-Zener Hamiltonian, which shows that decoherence may drive the resonant system with high fidelities to the adiabatic behavior of open systems. Moreover we also implement the adiabatic quantum algorithm for the Deutsch problem, where a distinction is established between the open system adiabatic density operator and the target pure state expected in the computation process. Preferred time windows for obtaining the desired outcomes are then analyzed. We experimentally realize these systems through a single trapped Ytterbium ion $^{171}$Yb$^+$, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system, with both driven field and decohering strength efficiently controllable.

In this paper we discuss how we can design Hamiltonians to implement quantum algorithms, in particular we focus in Deutsch and Grover algorithms. As main result of this paper, we show how Hamiltonian inverse quantum engineering method allow us to obtain feasible and time-independent Hamiltonians for implementing such algorithms. From our approach for the Deutsch algorithm, different from others techniques, we can provide an alternative approach for implementing such algorithm where no auxiliary qubit and additional resources are required. In addition, by using a single quantum evolution, the Grover algorithm can be achieved with high probability $1-\epsilon^2$, where $\epsilon$ is a very small arbitrary parameter.

Inverse engineering of Hamiltonian (IEH) from an evolution operator is a useful technique for protocol of quantum control with potential applications in quantum information processing. In this paper we introduce a particular protocol to perform IEH and we show how this scheme can be used for implementing a set of quantum gates by using minimal quantum resources (such as entanglement, interactions between more than two quits or auxiliary quits). Remarkably, while previous protocols request three-quits interactions and/or auxiliary quits for implementing such gates, our protocol requires just two-qubit interactions and no auxiliary qubits. By using this approach, we can obtain a large class of Hamiltonians that allow us to implement single and two-quit gates necessary to quantum computation. To conclude this article, we analyze the performance of our scheme against systematic errors related to amplitude noise, where we show that the free parameters introduced in our scheme can be useful for enhancing the robustness of the protocol against such errors.

Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.

The announcement of a quantum computer that can be accessed remotely by anyone from its laptop is a big event for the quantum computation scientist. In this work we present the International Business Machines (IBM) quantum computer and its platform IBM Quantum Experience (IBM-QE) as a didactic proposal in quantum computation and information. In addition we also consider this paper as scientific divulgation of the IMB advertisement. In this paper we show the main tool (quantum gates) present in the IBM-QE and, through a simple strategy, we discuss about a possible decoherence source in the IBM 5 q-bit chips. As an example of application of our study, we show how to implement the quantum teleportation using the IBM-QE.

We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In this scenario, we provide the counterdiabatic driving for arbitrary n-qubit gates, which allows to achieve universality through a variety of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian for an arbitrary n-qubit gate teleportation into the implementation of a rotated superadiabatic dynamics of an n-qubit state teleportation. This result is rather general, with the speed of the evolution only dictated by the quantum speed limit. In particular, we analyze the energetic cost for different Hamiltonian interpolations in the context of the energy-time complementarity.