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Hybrid scheme for magnetic-based quantum devices

Davide Nuzzi

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

The realization of a quantum computer, after being considered only a wishful thinking for many years, \nlooks now more solid, with the major issues about its realization looking like “engineering problems”, whose \nsolution is not far to be found. \nThe most considerable open problems concerning the realization of a quantum computer concern: the \nsensitivity to external disturbances, the addressability of any single qubit, and the scalability of the proposed \narchitectures. These problems may have opposite solutions, since a good scalability would require high \ndensity of qubits embedded in solid state matrices, making it more difficult to address and protect each of \nthem. Conversely, well separated qubits realized by atoms or ions are easily addressed and protected, but \nmake it more difficult to achieve scalability. \nAnother aspect related to the realization of generic quantum devices (i.e. devices which exploit the \nquantum features of their constituents to realize some operations) is connected to the way one interfaces \nwith them: we live in a “classical world”, and any quantum device will have to interface with it at some \nstage, e.g. to be controlled or measured. The problem, in this case, is keeping our classical disturbances as \nfar as possible from the action taking place at the heart of the quantum device. \nHowever, the problem of being able to find the proper “interface” can be turned into an advantage, \nsince macroscopic systems may posses robustness features which can be exploited for the realization of novel \nquantum devices where the sensitivity problem is much alleviated. A good interface can be thus provided by \nsemi-classical systems, i.e. objects whose nature is intimately quantum, but whose features and behaviour is \nwell framed within a classical description. Any scheme, application or device, where a semi-classical system \ninteracts with some pure quantum object (e.g. a qubit) for realizing a quantum operation, will be referred \nto as hybrid. \nIn this thesis, we have developed the idea of exploiting the robustness features of some non-linear classical \nsystems in order to realize quantum devices where the sensitivity problem is alleviated. Hence, we have \nproposed a hybrid scheme for accomplishing the most basic actions related with the realization of a magnetic- \nbased quantum device, i.e. the control of a qubit state and entanglement generation. In particular, we have \ndeveloped it focusing on magnetic one-dimensional systems, i.e. spin chains, as channels connecting one or \nmore qubits to some external control apparatus. \nThis choice follows from the observation that classical spin chains are non-linear systems which enumerate \nsolitons among their dynamical configurations which are solutions of their equations of motion. In fact, \nsolitons are those particular solutions of non-linear systems which show space-time localization and shape- \ninvariant evolution and are celebrated for their impressive properties of robustness against scattering and \nexternal disturbances. These properties make them suitable candidates for practical purposes. \nWe have considered systems made by one-dimensional discrete lattices hosting, at each lattice site, one \nclassical spin (classical spin chain) or a large-S spin, i.e. a quantum spin characterized by a S-value large \nenough for the spin to be well described by a semi-classical behaviour (large-S spin chain). \nA classical, or a large-S, spin chain (with its solitons) can play the role of the robust partner while \nthe role of the fragile quantum system is played by the qubit, which is the agent of the relevant quantum \noperations in our hybrid quantum device.We have first introduced a method for generating solitons on discrete, classical Heisenberg chains by \napplying a time-dependent magnetic field to one of the chain extremities. The method has been numerically \nchecked, revealing the actual possibility of producing soliton-like dynamical configurations running on the \nspin chain, which resemble the known analytical solitons of the continuous chain if their typical width is \nlarge with respect to the chain spacing. The robustness of the generated solitons has been also tested with \nrespect to thermal noise present in the system. \nWe have then proposed a set-up where the generated soliton acts as a magnetic signal that travels along \nthe chain and eventually reaches a qubit and changes its quantum state. Since any unitary action on a single \nqubit can be represented in terms of a Zeeman interaction lasting for a precise time interval, qubit state \ncontrol is usually assumed to be obtained by applying suitable sequences of external magnetic fields. Indeed, \nfor this particular application, the spin chain needs not to be quantum and the suitable magnetic field is \nprovided by the moving deformation of the uniform chain represented by the magnetic soliton travelling \nalong the chain. Numerical results confirm that solitons are suitable for this task, giving the possibility to \nremotely control the qubit state by an appropriate choice of soliton shape and qubit-chain coupling. \nWe have finally addressed the problem of generating entanglement between distant qubits by introducing \na model where two qubits, distant and non-interacting, are locally coupled with a large-S Heisenberg chain, \nwhose dynamics is assumed to be characterized by the presence of solitons. The aim of this study was to \nverify if, by properly choosing the state of the spin chain, the evolution of such a robust semi-classical system \ncan bring the two qubits from a separable initial state to a non-separable state after a certain amount of \ntime, i.e., if a semi-classical channel could generate entanglement between the two qubits. \nAt variance with the previous application, the spin chain must here be considered, and consequently \ntreated, as a quantum system in order to allow for entanglement generation/transfer, but a suitable approximation \nis needed to solve the chain dynamics, as accounting for the exact evolution of large-S spin chain \nis out of reach, even numerically. This leads us to introduce a particular set of chain states built as product \nof single-spin coherent states which are in one-to-one correspondence with the configurations of the classical \nspin chain and are thus referred to as the semi-classical states of the chain. Being able to solve the evolution \nof the coherent state products, allow us to complete the hybrid scheme for entanglement generation: in \nfact, it is shown that, choosing the chain initial state as a semi-classical state corresponding to a soliton \nconfiguration, the correlations, generated between one qubit and the corresponding spin-S, are efficiently \ntransferred along the chain up to the other qubit, finally leaving the two qubits in an entangled state. \nThe results about the proposed hybrid schemes, showing their effectiveness for remotely controlling qubit \nstates and generating entanglement between distant qubits, encourage further studies opening also new \nperspectives for the realization of novel quantum devices based on the exploitation of the robustness features \nof semi-classical systems.

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It was Richard Feynman who first proposed, in 1982, the far-reaching concept of \na ”quantum computer”—a device more powerful than classical computers. The idea \nof a quantum computer is to employ the fascinating and often counterintuitive \nlaws of quantum mechanics to process information. It is far from obvious that \nthe proposed concept of a quantum computer is more powerful than its classical \ncounterpart, it was only in 1994 when Peter Shor theoretically demonstrated the \nexistence of a quantum algorithm for factorizing integers into prime factors \nthat runs in polynomial time unlike its classical counterpart which works in \nsub-exponential time. The factorization of integers into prime factors is the \nbasis of asymmetric cryptography. These early theoretical results lunched an \nimmense interest of the scientific community. Already during ’90s, the first \nproposals for the physical implementation of quantum computation emerged. Ever \nsince, many experimental groups around the world pursued different physical \nimplementations of quantum bits (qubits). The first decade of the new century \nsaw a steady improvement in the control and decoherence time (the time over \nwhich the information carried by the qubit is lost) for various qubits by many \norders of magnitude. The natural next step in this context is to answer the \nquestion of how to scale the system up to include many qubits and thus build a \nquantum computer? One of the main parts of this thesis addresses exactly this \nquestion, namely the question of architecture and scalability of future quantum \ncomputer. \n \nAmong various different physical realizations of qubits, the idea of using \nelectron spins trapped in electrostatic semiconductor quantum dots as the \nbuilding blocks of a quantum computer (the so-called spin qubits), put forward \nby Daniel Loss and David DiVincenzo in 1997, triggered tremendous interest in \nscientific community. Nevertheless, the implementation of the original \nLoss-DiVincenzo proposal posed a considerable technical challenge. It used \nquantum tunneling between qubits to enable their communication with each other, \nand thus required that the qubits to be placed very close to each other. This \nrequirement not only leaves little \nspace for the placement of the vast amount of gates and wirings needed to define \nthe electrostatic quantum dots, but also makes it challenging to control the \nlocal magnetic field needed for single-qubit operations. For these reasons, no \nsystem with more than a couple of spin qubits has been \nsuccessfully implemented thus far. In the first part of this thesis, we leap \nover this long-standing problem with an entirely different strategy of using \nmetallic floating gates or ferromagnets to couple together qubits that are \nseparated over a long distance. 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•Sep 15, 2021•4 citations
The realization of a quantum computer, after being considered only a wishful thinking for many years, \nlooks now more solid, with the major issues about its realization looking like “engineering problems”, whose \nsolution is not far to be found. \nThe most considerable open problems concerning the realization of a quantum computer concern: the \nsensitivity to external disturbances, the addressability of any single qubit, and the scalability of the proposed \narchitectures. These problems may have opposite solutions, since a good scalability would require high \ndensity of qubits embedded in solid state matrices, making it more difficult to address and protect each of \nthem. Conversely, well separated qubits realized by atoms or ions are easily addressed and protected, but \nmake it more difficult to achieve scalability. \nAnother aspect related to the realization of generic quantum devices (i.e. devices which exploit the \nquantum features of their constituents to realize some operations) is connected to the way one interfaces \nwith them: we live in a “classical world”, and any quantum device will have to interface with it at some \nstage, e.g. to be controlled or measured. The problem, in this case, is keeping our classical disturbances as \nfar as possible from the action taking place at the heart of the quantum device. \nHowever, the problem of being able to find the proper “interface” can be turned into an advantage, \nsince macroscopic systems may posses robustness features which can be exploited for the realization of novel \nquantum devices where the sensitivity problem is much alleviated. A good interface can be thus provided by \nsemi-classical systems, i.e. objects whose nature is intimately quantum, but whose features and behaviour is \nwell framed within a classical description. Any scheme, application or device, where a semi-classical system \ninteracts with some pure quantum object (e.g. a qubit) for realizing a quantum operation, will be referred \nto as hybrid. \nIn this thesis, we have developed the idea of exploiting the robustness features of some non-linear classical \nsystems in order to realize quantum devices where the sensitivity problem is alleviated. Hence, we have \nproposed a hybrid scheme for accomplishing the most basic actions related with the realization of a magnetic- \nbased quantum device, i.e. the control of a qubit state and entanglement generation. In particular, we have \ndeveloped it focusing on magnetic one-dimensional systems, i.e. spin chains, as channels connecting one or \nmore qubits to some external control apparatus. \nThis choice follows from the observation that classical spin chains are non-linear systems which enumerate \nsolitons among their dynamical configurations which are solutions of their equations of motion. In fact, \nsolitons are those particular solutions of non-linear systems which show space-time localization and shape- \ninvariant evolution and are celebrated for their impressive properties of robustness against scattering and \nexternal disturbances. These properties make them suitable candidates for practical purposes. \nWe have considered systems made by one-dimensional discrete lattices hosting, at each lattice site, one \nclassical spin (classical spin chain) or a large-S spin, i.e. a quantum spin characterized by a S-value large \nenough for the spin to be well described by a semi-classical behaviour (large-S spin chain). \nA classical, or a large-S, spin chain (with its solitons) can play the role of the robust partner while \nthe role of the fragile quantum system is played by the qubit, which is the agent of the relevant quantum \noperations in our hybrid quantum device.We have first introduced a method for generating solitons on discrete, classical Heisenberg chains by \napplying a time-dependent magnetic field to one of the chain extremities. The method has been numerically \nchecked, revealing the actual possibility of producing soliton-like dynamical configurations running on the \nspin chain, which resemble the known analytical solitons of the continuous chain if their typical width is \nlarge with respect to the chain spacing. The robustness of the generated solitons has been also tested with \nrespect to thermal noise present in the system. \nWe have then proposed a set-up where the generated soliton acts as a magnetic signal that travels along \nthe chain and eventually reaches a qubit and changes its quantum state. Since any unitary action on a single \nqubit can be represented in terms of a Zeeman interaction lasting for a precise time interval, qubit state \ncontrol is usually assumed to be obtained by applying suitable sequences of external magnetic fields. Indeed, \nfor this particular application, the spin chain needs not to be quantum and the suitable magnetic field is \nprovided by the moving deformation of the uniform chain represented by the magnetic soliton travelling \nalong the chain. Numerical results confirm that solitons are suitable for this task, giving the possibility to \nremotely control the qubit state by an appropriate choice of soliton shape and qubit-chain coupling. \nWe have finally addressed the problem of generating entanglement between distant qubits by introducing \na model where two qubits, distant and non-interacting, are locally coupled with a large-S Heisenberg chain, \nwhose dynamics is assumed to be characterized by the presence of solitons. The aim of this study was to \nverify if, by properly choosing the state of the spin chain, the evolution of such a robust semi-classical system \ncan bring the two qubits from a separable initial state to a non-separable state after a certain amount of \ntime, i.e., if a semi-classical channel could generate entanglement between the two qubits. \nAt variance with the previous application, the spin chain must here be considered, and consequently \ntreated, as a quantum system in order to allow for entanglement generation/transfer, but a suitable approximation \nis needed to solve the chain dynamics, as accounting for the exact evolution of large-S spin chain \nis out of reach, even numerically. This leads us to introduce a particular set of chain states built as product \nof single-spin coherent states which are in one-to-one correspondence with the configurations of the classical \nspin chain and are thus referred to as the semi-classical states of the chain. Being able to solve the evolution \nof the coherent state products, allow us to complete the hybrid scheme for entanglement generation: in \nfact, it is shown that, choosing the chain initial state as a semi-classical state corresponding to a soliton \nconfiguration, the correlations, generated between one qubit and the corresponding spin-S, are efficiently \ntransferred along the chain up to the other qubit, finally leaving the two qubits in an entangled state. \nThe results about the proposed hybrid schemes, showing their effectiveness for remotely controlling qubit \nstates and generating entanglement between distant qubits, encourage further studies opening also new \nperspectives for the realization of novel quantum devices based on the exploitation of the robustness features \nof semi-classical systems.
It was Richard Feynman who first proposed, in 1982, the far-reaching concept of \na ”quantum computer”—a device more powerful than classical computers. The idea \nof a quantum computer is to employ the fascinating and often counterintuitive \nlaws of quantum mechanics to process information. It is far from obvious that \nthe proposed concept of a quantum computer is more powerful than its classical \ncounterpart, it was only in 1994 when Peter Shor theoretically demonstrated the \nexistence of a quantum algorithm for factorizing integers into prime factors \nthat runs in polynomial time unlike its classical counterpart which works in \nsub-exponential time. The factorization of integers into prime factors is the \nbasis of asymmetric cryptography. These early theoretical results lunched an \nimmense interest of the scientific community. Already during ’90s, the first \nproposals for the physical implementation of quantum computation emerged. Ever \nsince, many experimental groups around the world pursued different physical \nimplementations of quantum bits (qubits). The first decade of the new century \nsaw a steady improvement in the control and decoherence time (the time over \nwhich the information carried by the qubit is lost) for various qubits by many \norders of magnitude. The natural next step in this context is to answer the \nquestion of how to scale the system up to include many qubits and thus build a \nquantum computer? One of the main parts of this thesis addresses exactly this \nquestion, namely the question of architecture and scalability of future quantum \ncomputer. \n \nAmong various different physical realizations of qubits, the idea of using \nelectron spins trapped in electrostatic semiconductor quantum dots as the \nbuilding blocks of a quantum computer (the so-called spin qubits), put forward \nby Daniel Loss and David DiVincenzo in 1997, triggered tremendous interest in \nscientific community. Nevertheless, the implementation of the original \nLoss-DiVincenzo proposal posed a considerable technical challenge. It used \nquantum tunneling between qubits to enable their communication with each other, \nand thus required that the qubits to be placed very close to each other. This \nrequirement not only leaves little \nspace for the placement of the vast amount of gates and wirings needed to define \nthe electrostatic quantum dots, but also makes it challenging to control the \nlocal magnetic field needed for single-qubit operations. For these reasons, no \nsystem with more than a couple of spin qubits has been \nsuccessfully implemented thus far. In the first part of this thesis, we leap \nover this long-standing problem with an entirely different strategy of using \nmetallic floating gates or ferromagnets to couple together qubits that are \nseparated over a long distance. Our scheme works for any type of \nspin qubits, including the qubits based on nitrogen-vacancy center (NV-center) \nin diamond and technologically very important silicon qubits. \n \nThe main topic of this thesis is related to quantum computer. Still, quite \nunexpectedly, some of the ideas we employed in order to tackle the problem of \nquantum computer scalability can be utilized in a completely different field of \nresearch, namely, in the field of magnetic field sensing. Qubit are not only a \nnecessary ingredient of quantum computer but they also provide a way to measure \nvery accurately magnetic fields. The magnetometer build upon the qubit based on \nNV-center, so-called NV-magnetometer, emerged in recent years as most sensitive \nmagnetic moment sensor. These magnetometers are able to detect about hundred \nnuclear spins within a minute of acquisition time. In the second part of this \nthesis, we propose an entirely novel experimental realization of \nNV-magnetometers which increases present NV-center sensitivities by four orders \nof magnitude at room temperature. This unprecedented amplification of \nsensitivity will render magnetometers capable of detecting individual nuclear \nspins. This amplification is achieved by introducing a ferromagnetic particle \nbetween the nuclear spin that needs to be detected and the NV-magnetometer. Our \nsetup, in contrast to existing schemes, is particularly advantageous because, \ndue to the large amplification of sensitivity, the nuclear spin need not lie \nwithin a few nanometers of the surface but rather can be detectable at a \ndistance of 30 nm. With these novelties, our scheme provides chemically \nsensitive spin detection under ambient conditions allowing nanoscale resolution \nof nuclear magnetic moments in biological systems—the holy grail of nuclear \nmagneticresonance. \n \nIn the last part of the thesis we focus our attention to a new direction in \nquantum computer implementation that deals with topological quantum computer \nintroduced by Alexei Kitaev in 1997; in this approach the idea is to use \nquasiparticles with ”fractional” statistics and to perform the single- and \ntwo-qubit gates by merely exchanging these quasiparticles. Additionally, \ninformation in this system is stored non-locally thus it mitigates the problem \nof decoherence caused by local noise from the environment. Majorana fermions are \none of the most well known examples of such excitations. We analyze transport \nsignatures of different topological states in one-dimensional systems, like \nMajorana fermions and fractionally charged states. We envision an Aharonov-Bohm \nsetup wherein conductance measurement provides a clear signature of presence of \nfractionally charged fermionic states, since oscillations with double period \nemerge in this case. Additionally, we propose a very simple setup that enables \nexistence of degenerate mid-gap states, so-called Tamm-Shockley states that are \ncharacterized by fractional charge and discuss possible ways of detecting these \nstates experimentally. \n
The recently emerged field of quantum technology is aiming to employ quantum coherence and entanglement for realization of next generation sensors, standards, imaging systems, secure communication and computers.Although applications of quantum technologies cover a broad spectrum and their development stage varies from early demonstrations to commercially available devices, many challenges have been identified.The first includes tailoring materials for quantum technologies, which is playing an essential role in technological applications of quantum science.Solid state systems allowing long coherence time are essential for quantum computation and quantum sensing.Ultrapure materials with tailored isotopic content are important for reaching long coherence time of spin qubits (Awschalom et al., 2013).The ability to place single dopants with high precision and form spin qubits at desired location is essential for both quantum computing and quantum sensing applications (McCallum et al., 2012;Smith et al., 2019).The performance of different types of qubits is usually benchmarked in terms of controllability and coherence time.Usually solid-state systems allow fast control, but exhibit fast decoherence owing to complex environment.It is therefore important to search for new types of qubits combining isolation from environment and access via fast coherent control and readout.Novel approaches combining different quantum systems into build hybrid quantum devices for optimal performance is a promising avenue.Examples of such hybrid approaches are spin systems coupled to superconducting qubits (Kubo et al., 2011) and hybrid nuclear-electronic qubits (Morley et al., 2013).Optimal protocols for quantum technologies requires extension of coherence time of qubits beyond the coherence time of the isolated quantum system.The efficient protection toolkit includes dynamical decoupling (Yang et al., 2011) and quantum error correction (Terhal, 2015) based techniques.Although general principles of qubits protection were developed and tested experimentally in different model environments, it is essential to adapt them to realistic environmental noise.In the field of quantum sensing, it is also essential to combine protections against noise with non-reduced sensing performance.Experimental imperfections can be addressed using optimal control tools (Glaser et al., 2015).The development of efficient quantum algorithms is another growing field belonging to quantum software area.On one hand, it is essential to find problems where a quantum computer can outperform classical computers.On the other hand, it is essential to develop an application scenario for a limited number of qubits (Montanaro, 2016).In addition, in order to develop new algorithms, future work must include discoveries of application scenarios of already known algorithms.Application of quantum Fourier transform for sensing is a promising example of such new applications (Vorobyov et al., 2021).Signal processing is another field of quantum software that is becoming essential in applications.Advanced signal analysis protocols, like quantum compressed sensing, can be employed to quantify entanglement in large quantum devices via efficient quantum tomography (Riofrío et al., 2017).
Many proposals for quantum devices are based on qubits that are physically realized by the spin magnetic moment of some quantum object. In this case, one of the most often adopted strategies for manipulating qubits is that of using external magnetic fields. However, selectively applying a field just to one qubit may be a practically unattainable goal, as it is, for instance, in most solid-state based setups. In this work, we present a proposal for using nonlinear excitations of solitonic type to accomplish the above task. Our scheme entails the generation of a dynamical soliton in a classical spin-chain which is locally coupled with one qubit: as the soliton runs through, the qubit behaves, due to its interaction with the chain, as if it were subject to a magnetic field with a time dependence that follows from the soliton's features. We here present results for the time evolution of the qubit density-matrix induced by the overall dynamics of the above scheme.
We are still at the very beginnings of physical implementations of quantum computers. The devices listed below have been used successfully to entangle two qubits (at most!), except for NMR which has gone up to 7 qubits. It is still premature to try to predict which device will prove most effective for building a quantum computer capable of dealing with several hundred qubits (if such a computer someday exists); perhaps it will be something new, not on this list at all. In any case, it would be as foolish to predict that such a computer will not be available by 2050 as to predict the contrary. The storage and processing of quantum information requires physical systems possessing the following properties (di Vincenzo criteria): (i) they must be scalable, that is, capable of being extended to a sufficient number of qubits, with well defined qubits; (ii) they must have qubits which can be initialized in the state |0〉; (iii) they must have qubits which are carried by physical states of sufficiently long lifetime, so as to ensure that the quantum states remain coherent throughout the calculation; (iv) they must possess a set of universal quantum gates: unitary transformations on individual qubits and a cNOT gate, which are obtained by controlled manipulations; (v) there must be an efficient procedure for measuring the state of the qubits at the end of the calculation ( readout of the results).
Propagation of soliton-like excitations along spin chains has been proposed as a possible way for transmitting both classical and quantum information between two distant parties with negligible dispersion and dissipation. In this work, a somewhat different use of solitons is considered. Solitons propagating along a spin chain realize an effective magnetic field, well localized in space and time, which can be exploited as a means to manipulate the state of an external spin (i.e., a qubit) that is weakly coupled to the chain. We have investigated different couplings between the qubit and the chain, as well as different soliton shapes, according to a Heisenberg chain model. It is found that symmetry properties strongly affect the effectiveness of the proposed scheme, and the most suitable setups for implementing single qubit quantum gates are singled out.
Quantum computers have gained widespread interest as they can potentially solve problems that are intractable even for today’s supercomputers, such as the simulation of quantum systems as initially proposed by Feynman. To achieve such tremendous progress, a quantum computer relies on processing the information stored in quantum bits (qubits), the fundamental units of quantum computation, similar to the bits in a classical (i.e., non-quantum) processor. In general, a quantum processor comprising several qubits is connected through a quantum-to-classical interface consisting of classical electrical circuits for manipulating and reading out their quantum state. The accuracy of an operation on a qubit is characterized using the fidelity, which is 100 % in case of a perfect operation. In practice, a fidelity between 99 % and 99.9 % is typically achieved in today’s experiments with less than 100 qubits, limited by non-idealities in the control signals and by the implementation of the physical qubit itself. Since such qubit fidelities are too low to execute relevant quantum algorithms, quantum error correction schemes have been developed which rely on a much larger number of qubits to correct for possible errors, resulting in the need for quantum processors with thousands or millions of qubits. Solid-state qubits promise the largescale integration required to scale to millions of qubits, as they exploit the lithographic fabrication techniques borrowed from the semiconductor industry. However, state-of-theart solid-state qubits, such as transmons and single-electron spin qubits, must be typically cooled to cryogenic temperatures in a dilution refrigerator to exhibit quantum behavior. Because of the limited number of qubits (< 100) in state-of-theart solid-state quantum processors, the classical controller is currently implemented by general-purpose instruments or by tailor-made controllers operating at room temperature connected via several wires to the qubits in the cryogenic chamber. However, these systems must scale to support millions of qubits. While scaling up the underlying quantum processor is already exceptionally challenging, building the electronics required to interface such a large-scale processor is just as relevant and arduous.