One-qubit Quantum Research Articles

Optimizing quantum refrigerators with a qubit on the hot side

We study the performance of one-qubit quantum and semiclassic refrigerators with the qubit on the hot side. We obtain the cooling power and the Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega$$\\end{document} function. We discover that the quantum refrigerators perform differently to classic ones. We also prove that even in the high-temperature limit, where the semiclassic version of the refrigerator is valid, the results of the optimization are different to those obtained by optimizing classic refrigerators.

Encapsulated Atomic Hydrogen in Octamethyl-POSS Cages: A Pulsed EPR Study.

Encapsulated atomic hydrogen in polyhedral oligomeric silsesquioxane (POSS) cages is a promising candidate for spin-based quantum technologies. Key parameters such as spin relaxation times and magnetic interactions with surrounding electron and nuclear spins can be typically probed with advanced electron paramagnetic resonance (EPR) methods. Here we present a detailed pulsed EPR study of the species H@Si8O12R8 with R=CH3, namely encapsulated atomic hydrogen in the octamethyl POSS derivative. The temperature dependence of the spin-lattice relaxation rate 1/ is analyzed in terms of a Raman process with a Debye temperature of K and a thermally activated process with (552 cm-1), whereas, the phase memory time shows the typical shortening behaviour at K observed for all methyl-containing derivatives. The hyperfine coupling of the cage Si nuclei is measured by hyperfine sublevel correlation (HYSCORE) spectroscopy and is found to fulfil the so-called "matching condition" at the low-field EPR transition. The potential of this paramagnetic molecule to perform one-qubit quantum operations is probed by room-temperature Rabi oscillations.

Power and efficient power optimization of one-qubit Novikov quantum heat engines with an external dissipative heat leak

Abstract We optimize one-qubit Novikov quantum heat engines with a dissipative heat leak using the formalisms of open-system Quantum Mechanics and the Finite-Time Thermodynamics. We show that the leak changes the power-efficiency and the efficient-power-efficiency curves, reduces the maximum efficiency of the machine and does not change its power. We also discuss the effects of the leak on the power that is rejected from the machine to the environment. Finally, we study the high-temperature limit to check that the engine reduces in this limit to a classic Novikov heat engine.

Universal Quantum Computation Based on Nanoscale Skyrmion Helicity Qubits in Frustrated Magnets.

We propose a skyrmion-based universal quantum computer. Skyrmions have the helicity degree of freedom in frustrated magnets, where twofold degenerated Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction. We construct a qubit based on them. A skyrmion must become a quantum-mechanical object when its size is of the order of nanometers. It is shown that the universal quantum computation is possible based on nanoscale skyrmions in a magnetic bilayer system. The one-qubit quantum gates are materialized by controlling the electric field and the spin current. The two-qubit gate is materialized with the use of the Ising-type exchange coupling. The merit of the present mechanism is that external magnetic field is not necessary. Our results may open a possible way toward universal quantum computation based on nanoscale topological spin textures.

Energy production in one-qubit quantum Agrawal machines

AbstractWe obtain the power and Ω-function of one-qubit Agrawal quantum heat engines solving the Lindbland equation and using the tools of Finite Time Thermodynamics. We prove that these two thermodynamic functions have their maximum values for efficiencies different to zero and the Carnot efficiency. Finally, analyzing the high temperature limit of AQHEs we discover the range of temperatures for which the quantum behaviour is valid.

Variational Entanglement-Assisted Quantum Process Tomography with Arbitrary Ancillary Qubits.

Quantum process tomography is a pivotal technique in fully characterizing quantum dynamics. However, exponential scaling of the Hilbert space with the increasing system size extremely restrains its experimental implementations. Here, we put forward a more efficient, flexible, and error-mitigated method: variational entanglement-assisted quantum process tomography with arbitrary ancillary qubits. Numerically, we simulate up to eight-qubit quantum processes and show that this tomography with m ancillary qubits (0≤m≤n) alleviates the exponential costs on state preparation (from 4^{n} to 2^{n-m}), measurement settings (at least a 1 order of magnitude reduction), and data postprocessing (efficient and robust parameter optimization). Experimentally, we first demonstrate our method on a silicon photonic chip by rebuilding randomly generated one-qubit and two-qubit unitary quantum processes. Further using the error mitigation method, two-qubit quantum processes can be rebuilt with average gate fidelity enhanced from 92.38% to 95.56%. Our Letter provides an efficient and practical approach to process tomography on the noisy quantum computing platforms.

Implementation of one-qubit quantum gates with individual addressing of two rubidium atoms in two optical dipole traps

We report the results of experiments on implementing individually addressable one-qubit quantum gates on a microwave transition with two 87Rb atoms in two optical dipole traps. Addressing is carried out using additional focused laser light, which results in a differential light shift of the microwave transition frequency. In the absence of addressing in each of the atoms, Rabi oscillations are obtained on the microwave clock transition 5S1/2 (F = 2, mF = 0) → 5S1/2(F = 1, mF = 0) between two working levels of qubits with a frequency of up to 5.1 kHz, a contrast up to 98 %, and a coherence time up to 4 ms. When addressing is turned on, the probability of a microwave transition in the addressed atom is suppressed to an average value of less than 5 %. The Rabi oscillations remaining in the other atom have the same contrast and correspond to the implementation of individually addressable basic one-qubit quantum operations (Hadamard gate and NOT gate) from different initial states of a qubit with an average fidelity of 92% ± 3 %. After renormalising this fidelity to the error in the preparation and measurement of quantum states of qubits, an estimate of 97% ± 3% is obtained for the fidelity of individual qubit rotations.

Experimental tests of the density matrix's property-based complementarity relations

Bohr's complementarity principle is of fundamental historic and conceptual importance for Quantum Mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like character of a quantum system, but not both. However, it was eventually realized that these dual behaviors can both manifest partially in the same experimental setup, and, using ad hoc proposed measures for the wave and particle aspects of the quanton, complementarity relations were proposed limiting how strong these manifestations can be. Recently, a formalism was developed and quantifiers for the particleness and waveness of a quantum system were derived from the mathematical structure of QM entailed in the density matrix's basic properties ($\rho\ge 0$, $\mathrm{Tr}\rho=1$). In this article, using IBM Quantum Experience quantum computers, we perform experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.

Quantum teleportation with mutually unbiased bases

During the realization of one-qubit quantum teleportation, an EPR pair shared between two parties is required, followed by a joint Bell state measurement on the teleported qubit and the sender’s qubit. In this paper, we analyze the joint measurements in the case of teleporting multiple qubits. By carefully dividing the sender’s qubit space into several subspaces, we show that the receiver can restore the qubits if the measurement is taken in the mutually unbiased basis. We generalize our protocol to teleporting special entangled states and high-dimensional state. Our protocol may have potential application in multi-qubit quantum teleportation.

Femtosecond laser direct writing of optical quantum logic gates

Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.

Memristive Quantum Computing Simulator

One of the most promising and powerful candidates for future computing is the notion of universal quantum computer. A vital advance towards this direction is the development of quantum simulators and their possible implementation either as standalone quantum systems or as compatible software for classical computers with pros and cons. On the other hand, memristive computing has been proposed recently as a tentative unconventional computing scheme promoting the idea of information storage and processing in the same nanoelectronic device. In this paper we present a memristive quantum computing simulator by coupling quantum simulation principles with memristor aspects and enabling us to tackle the existing difficulties on qubit representation in conventional computing systems. For doing so, we utilize the memristances of identical memristors to represent in 3D the qubit state while its corresponding evolution is defined by the memristors input voltages. In particular, we introduce an appropriate correspondence among the aforementioned memristor voltages and the general qubit state rotation, i.e., the one-qubit quantum gates, and as such we reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Moreover, we also define the action of the CNOT two-qubit gate and simulate entanglement between two qubits paving the way towards the establishment of a universal set for quantum computing. Our results show that, memristor circuits can simulate effectively quantum computations.

Can quantum discord increase in a quantum communication task?

Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver's state has more quantum discord than the sender's state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob's qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting feature in this scenario, when the quantum discord of Alice's qubits increases, then the quantum discord of Bob's prepared qubits decreases. Furthermore, we show that the fidelity of one-qubit quantum teleportation using Bob's prepared qubits as the channel is higher than using Alice's qubits.

Wigner process tomography: Visualization of spin propagators and their spinor properties

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin 1/2 particle.

Wafer-Scale Fabrication and Room-Temperature Experiments on Graphene-Based Gates for Quantum Computation

We have fabricated at wafer scale graphene-based configurations suitable for implementing at room temperature one-qubit quantum gates and a modified Deutsch-Jozsa algorithm. Our measurements confirmed the (quasi-)ballistic nature of charge carrier propagation through both types of devices, which have dimensions smaller than the room-temperature mean-free-path in graphene. As such, both graphene-based configurations were found to be suitable for quantum computation. These results are encouraging for demonstrating a miniaturized, room-temperature quantum computer based on graphene.

Linking the rotation of a rigid body to the Schr\xf6dinger equation: The quantum tennis racket effect and beyond

The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role in the control of two-level quantum systems by means of external electromagnetic pulses. For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which is a geometric property of any classical rigid body. This effect is demonstrated experimentally for the control of a spin 1/2 particle by using techniques of Nuclear Magnetic Resonance. We also show that the dynamics of a rigid body can be used to implement one-qubit quantum gates. In particular, non-adiabatic geometric quantum phase gates can be realized based on the Montgomery phase of a rigid body. The robustness issue of the gates is discussed.

High-Capacity Quantum Associative Memories

We review our models of quantum associative memories that represent the "quantization" of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely {\it eliminate crosstalk and spurious memories}. The number of control qubits plays the role of an inverse fictitious temperature, the accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models solve thus the capacity shortage problem of classical associative memories, providing a {\it polynomial improvement} in capacity. The price to pay is the probabilistic nature of information retrieval.

Solutions to the quantum Rabi model with two equivalent qubits

Using extended coherent states, an analytically exact study has been carried out for the quantum Rabi model with two equivalent qubits. Compact transcendental functions of one variable have been derived leading to exact solutions. The energy spectrum is clearly identified and analyzed. Also obtained analytically are the necessary and sufficient conditions for the occurrence of isolated exceptional solutions, which are not doubly degenerate as in the one-qubit quantum Rabi model.

Quantum holonomies for displaced Landau–Aharonov–Casher states

We construct displaced Fock states for a Landau---Aharonov---Casher system for neutral particles. Abelian and non-Abelian geometric phases can be obtained in an adiabatic cyclic evolution using this displaced states. Moreover, we show that a possible logical base related to the angular momenta of the neutral particle with permanent magnetic dipole moment can be defined, and then quantum holonomies for specific paths can be built and used to implement one-qubit quantum gates.

Nakajima-Zwanzig and Time-Convolutionless Master Equations for a One-Qubit System in a Non-Markovian Layered Environment

Quantum operations, are completely positive (CP) and trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of one-qubit open quantum system in layered environment which is a generalized spin star model. The Nakajima-Zwanzig and time-convolutionless projection operators technique are applied for deriving the master equations. Finally, a simple example will be studied to consider the relation between completely positive maps and initial quantum correlation and show that vanishing quantum discord is not necessary for CP maps.

One-qubit quantum gates in a circular graphene quantum dot: genetic algorithm approach

The aim of this work was to design and control, using genetic algorithm (GA) for parameter optimization, one-charge-qubit quantum logic gates σx, σy, and σz, using two bound states as a qubit space, of circular graphene quantum dots in a homogeneous magnetic field. The method employed for the proposed gate implementation is through the quantum dynamic control of the qubit subspace with an oscillating electric field and an onsite (inside the quantum dot) gate voltage pulse with amplitude and time width modulation which introduce relative phases and transitions between states. Our results show that we can obtain values of fitness or gate fidelity close to 1, avoiding the leakage probability to higher states. The system evolution, for the gate operation, is presented with the dynamics of the probability density, as well as a visualization of the current of the pseudospin, characteristic of a graphene structure. Therefore, we conclude that is possible to use the states of the graphene quantum dot (selecting the dot size and magnetic field) to design and control the qubit subspace, with these two time-dependent interactions, to obtain the optimal parameters for a good gate fidelity using GA.