A quantum computer has been created in a diamond. The Fian have developed two methods for creating invisible marks marking diamonds Nv centers in a diamond

The joint laboratory of FIAN and the Russian Quantum Center (RQC) has created a model of a quantum computer based on diamond.

Quantum mechanics is one of the main pillars of modern physical research. Elementary particles and microelectronics have long lived according to the quantum laws of the world. Quantum mechanics begins to work at an action size comparable to Planck's constant. The so-called new sciences at the intersection of quantum mechanics and informatics, such as quantum information theory and informatics. Classical information is represented in bits of the form 0 and 1. In quantum information theory, a memory cell is a qubit that stores a superposition of states 0 and 1.

Sergey Kudryashov, Alexei Levchenko, Leonid Seleznev, and Dmitry Sinitsyn, members of the Laboratory of Gas Lasers of the Lebedev Physical Institute, managed to create an increased concentration of vacancies (defects in the diamond lattice, where there are no carbon atoms) by exposing a diamond to femtosecond laser radiation. FIAN researcher comments Alexey Levchenko:

« Usually, vacancies are created using electron beams or beams of any high-energy particles. This method gives a uniform concentration of vacancies throughout the entire volume of the sample. With the help of a femtosecond laser, on the contrary, it is possible to achieve a similar but local effect - to draw the required “picture” with small clusters of vacancies.”

Then these vacancies can contact impurity nitrogen atoms, which are usually present in significant concentrations in the volume of diamond, and form the so-called NV center (nitrogen-vacancy center) - a defect that is very “useful” for diamond marking. The fact is that when irradiated with visible light, the NV centers begin to characteristically fluoresce, and the application of an external microwave field can also change the intensity of this fluorescence.

« There may be other impurities in the diamond that glow under the influence of external radiation (pink, yellow, blue diamonds), therefore, by turning on the microwave field, we can see our changing signal against the background of all these noises. If we create an invisible microcluster of NV centers - due to sharp focusing in volume literally up to a micron, then later we can read the mark of our diamond by fluorescence in the microwave field – Alexey Levchenko.

The joint laboratory of FIAN and the Russian Quantum Center is studying diamond color centers, NV centers. But what is an NV center? Let's consider a matrix of carbon (diamond) in which instead of one carbon in an atom, a nitrogen atom is substituted (yellow diamonds are yellow due to the admixture of nitrogen), and the neighboring atom is absent. The resulting system is called the NV center or color center. Accordingly, N is nitrogen, and V is a vacancy. This color center has an axis. The electron spin projection on this axis is conserved and can serve as a qubit. This spin is the total spin of all electrons involved in this insert. Accordingly, we can use this spin as a quantum memory.

Powerful laser facility "PIKO" for research on the interaction of nanosecond and picosecond laser radiation with matter. From left to right: Mikhailov Yu.A. Kutsenko A.V.

« You can create a state with a projection of zero, with a projection of one on this axis, or a superposition of "zero plus one", while zero and one will be represented in a superposition with some weight. By the glow of the NV center, you can determine its state. If it is in the zero state, it glows more brightly. If it is in the state of one, then it is less bright. We have the ability to determine where he was, just by the brightness. As if you had two bulbs zero and one” – commented on the work of a senior researcher at the Lebedev Physical Institute, head of the RQC Quantum Simulators and Integrated Photonics Group, Candidate of Physical and Mathematical Sciences Alexey Akimov.

In addition, we have the ability to manipulate the state with the help of a radio frequency field. Between two states zero and one, applying an impulse, you can organize intermediate states, or a complete transition from one state to another. It all depends on the duration of the pulse, usually this duration is of the order of tens of nanoseconds. Thus, we can prepare quantum states very quickly, faster than the relaxation times of our centers. That is, we can always prepare the state we need by shining a green light on it and then applying a radio frequency field.

« But it wouldn't be so interesting if we couldn't use nuclear spin. Due to the fact that the color center and the nuclear spin 13 C can be nearby, a magnetic interaction arises between them, which allows you to rewrite information from electronic to nuclear spin and vice versa. Since the nuclear spin interacts much less with the outside world, it is a more isolated, more long-term memory. In the nuclear spin, information can be stored much longer, as long as this time is reduced to a few seconds."- tells Alexey Akimov

The ability to perform calculations according to the laws of quantum mechanics opens up a huge field of new opportunities for mathematicians, physicists and programmers. But new calculation algorithms introduce new rules of the game into our lives, for example, the RSA encryption algorithm, which is resistant from a classical point of view, becomes vulnerable to Shor's quantum algorithm. Shor's algorithm is able to factorize a prime number much faster than classical algorithms, in a time comparable to the multiplication of these very prime numbers. And one of the most common and secure RSA encryption methods is based on the use of prime factorization. The model of a quantum computer created at FIAN, consisting of several qubits on diamond color centers, is designed to show the possibility of such quantum algorithms.

B. Massalimov, API "FIAN-inform"

Well, I, in turn, really hope that the readers of the SUN, thanks to this article, will guess what a magic staff is, the one that Santa Claus, the monarch, and the ordinary wizard have, and how it works.

MICROELECTRONICS, 2012, Volume 41, No. 2, p. 104-119

QUANTUM COMPUTERS:

NV-CENTERS IN DIAMOND. PART I. GENERAL INFORMATION, MANUFACTURING TECHNOLOGY, SPECTRUM STRUCTURE

A. V. Tsukanov © 2012

Institute of Physics and Technology of the Russian Academy of Sciences E-mail: [email protected] Received March 31, 2011

A quantum system is considered in detail, which is one of the most popular and promising in experimental quantum informatics - the NV center in diamond. We focus the reader's attention on the results obtained over the past few years and covering a wide range of issues related to the fabrication, control, measurement of NV centers and their use as elementary carriers of quantum information. The problem of building a full-scale quantum computer is discussed.

1. INTRODUCTION

The idea of ​​quantum information processing originated at the end of the 20th century and by now has become one of the most attractive and intriguing for many researchers working in various fields of science. With the development of the experimental and technological base, the creation of a quantum computer has ceased to be only speculative theoretical problem, transforming into a complex but interesting practical problem.

As an elementary cell of a quantum computer - a quantum bit or a qubit - a two-level system is chosen, the state of which can be effectively controlled. It is assumed that the system representing a qubit has a number of specific properties. These include a) high discreteness of the energy spectrum, which makes it possible to single out two logical states 10) and 11 qubits from the complete Hilbert state space of the system, b) the existence of physical mechanisms that provide initialization, control and measurement of the state of the qubit, and c) large times of relaxation and dephasing of logical states. The construction of a full-scale quantum computer, consisting of a large number of qubits operating synchronously, also implies the possibility of controlling the interaction between two arbitrary qubits. It is generally accepted that an increase in the number of qubits to a practically useful value (of the order of several thousand) will most likely be implemented in solid-state structures. There are several promising areas that consider such quantum systems (superconducting elements, semiconductor quantum dots, implanted

bath atoms) as qubits. All of them satisfy the above requirements only at very low (<100 мК) температурах, когда энергия размерного квантования системы значительно больше, чем энергия тепловых флуктуаций. Указанное обстоятельство накладывает жесткие ограничения на дизайн и качество контроля кубита. В этой связи представляется крайне важным ослабление данного требования за счет выбора такой системы, которая сохраняла бы когерентность, необходимую для квантовых операций, при более высокой (желательно - комнатной) температуре. На сегодняшний день известны две такие системы. Первая из них, раствор молекул некоторых органических веществ (например, раствор ацетона в хлороформе), представляет собой объект, на котором в 1998 году были продемонстрированы принципы квантовых вычислений . Однако количество кубитов - ядерных спинов атомов водорода, углерода и др., входящих в структуру молекулы, ограничено числом атомов в молекуле. Вторая система, являющаяся предметом нашего рассмотрения, есть дефект кристаллической решетки алмаза, который состоит из соседних атома азота (Ы) и вакансии (V). Принятое обозначение такого дефекта - NV - указывает на структурный состав, а название - "NV-центр" - говорит о том, что он представляет собой так называемый центр окраски по отношению к чистому алмазному субстрату. Принципиальное преимущество данной твердотельной системы - возможность создания упорядоченных двумерных массивов, содержащих произвольное количество одиночных NV-центров, т.е. возможность масштабирования.

The main goal of this paper is a brief, but as complete as possible, acquaintance of the reader with the NII centers, their structure and physical properties, as well as the position that they

occupy in modern experimental physics of low-dimensional structures. Focusing on a fairly detailed discussion of the results directly related to quantum computing, we, nevertheless, will pay attention to other close directions related to coherent manipulations on the state of ME centers. In the first part of the review, we consider the main properties of ME centers, their fabrication technology, and group-theoretic analysis of the spectrum. The second part will be devoted to the control of both the orbital and spin states of the center, elementary quantum operations, initialization, measurements and suppression of quantum errors. The third part will present quantum algorithms, hybrid systems and possible options for scaling a quantum computer at MU centers. In addition, we will discuss the prospects for their practical use as single-photon sources and magnetometers.

2. MU-CENTERS IN DIAMOND: GENERAL

DETAILS AND MAIN FEATURES

The structure of an MU center in diamond is shown in Fig. . 1a. As can be seen, the nitrogen atom and the vacancy lie on one of the main diagonals ((111)) of the face-centered cubic diamond lattice, which in this case is also the symmetry axis of our center (z axis). This means that there are four possible orientations of the MU center relative to the crystal lattice of the substrate. When a tetravalent carbon atom is replaced by pentavalent nitrogen, an additional electron appears in the lattice, and when a neighboring vacancy is formed, four more electrons are released - three from nearby carbon atoms lying at the vertices of an equilateral triangle in the xy plane, through the center of which the z axis passes, and one from the atom nitrogen. The corresponding four unpaired ^-orbitals are oriented towards the formed vacancy. In addition, experiments convincingly show that often a sixth electron is added to these five electrons associated with the center, apparently from another nitrogen atom. This means that the center can be either neutral (MU0, about 30% of their total number) or negatively charged (MU-, about 70%). The isotopic composition of the MU center depends on the relative concentrations of various nitrogen and carbon isotopes in a given crystal. Usually, the 14M nitrogen isotope with nuclear spin I = 1 prevails in natural diamond, while the fraction of the 15M isotope with nuclear spin I = 1/2 is only 0.37%. The spinless carbon isotope 12C also dominates, while the 13C isotope with

nuclear spin I = 1/2 occurs in the crystal lattice with a probability of 1%.

The physical properties of an MU center are determined by its structure. We briefly list the most important of them. As follows from the results of numerous experiments, the spin wave function in the ground orbital state is concentrated in the vacancy region. In this case, the paramagnetic ground state of the center with a strong polarization of the electron spin (w = 1, w, = 0, +1, -1) is inherent only in the MU- form. The center actively absorbs green light at a wavelength X = 532 nm and exhibits stable fluorescence in the red wavelength range X ~ 630–800 nm with a zero phonon line peak at X = 637 nm. Spectroscopic measurements indicate long times of spin relaxation (t1 ~ 1 ms) and dephasing (t2 ~ 10 μs) at room temperature. A very important circumstance is the spin-dependent nature of fluorescence, which makes it possible to measure and initialize the electron spin by excitation of optical transitions. The theoretical explanation of these and other properties of the MU center, which requires a detailed analysis of its structure, will be given below. We add that fluorescence from single centers can be observed visually using a conventional optical confocal microscope. The first such observation dates back to 1997 (see Fig. 1b).

The data accumulated to date allow us to state that MU centers satisfy the above requirements and can be considered as qubits. Thus, the paramagnetism of a negatively charged center means the splitting of the spin multiplet in the absence of an external magnetic field and makes it possible to single out sublevels with w, = 0 and w, = -1 (or +1) into a logical subspace. The splitting value for the ground orbital state is = 2.87 GHz, which makes it possible to carry out transitions \m5 = 0 ^ \m5 = -1 (+1)) between logical states, that is, perform one-qubit quantum operations by acting on the MU center with a resonant microwave impulse. Long lifetimes of the spin state of the center at room temperature provide a large number of such elementary quantum operations. All these facts give grounds to consider MU centers as very promising solid-state qubits.

Let us present the main experimental results obtained with the use of MU centers and focused on the processing of quantum information. Currently, intensive research is being carried out with the aim of creating an ordered matrix of single centers as a basis for full-scale quantum regions.

Rice. 1. Fragment of the crystal lattice of diamond (a) containing a N^ center and the electronic structure of the valence shells of carbon and nitrogen; (b) - the first photographic image of fluorescing N^ centers in diamond.

str. Further, coherent operations with single spins (both electronic and nuclear) were demonstrated at room temperature, as well as two- and three-qubit operations on a single N2 center involving the electron spin and the nuclear spins of nitrogen and carbon. Of the simplest quantum algorithms, we should mention the recently implemented Deutsch-Jossa algorithm, as well as schemes for generating entangled spin states. Quantum error correction is achieved by using refocusing techniques adapted from EPR spectroscopy and

Tsukanov A.V. - 2015

13:07 17.10.2013

The specialists of the Laboratory of Gas Lasers of the Lebedev Physical Institute managed to develop two methods for precision microscale marking of diamonds. As reported on the institute's website, marks invisible to the naked eye are created here using femtosecond laser radiation.

Sergei Kudryashov, Leonid Seleznev, Alexei Levchenko and Dmitry Sinitsyn have developed a way to create a kind of "quality marks". The diamond is exposed to femtosecond laser radiation, which creates an increased concentration of vacancies in it (defects in the diamond lattice in which there are no carbon atoms).

The use of a femtosecond laser instead of electron beams or beams of any high-energy particles (uniform concentration of vacancies throughout the volume) makes it possible to achieve a local effect - to draw the required “picture” with small clusters of vacancies.

These vacancies can then bind to impurity nitrogen atoms, which, as a rule, are present in significant concentrations in diamond, and form an NV center (nitrogen-vacancy center), which is very useful for diamond defect marking: when irradiated with visible light, such NV- the centers begin to fluoresce, and the application of an external microwave field can change the fluorescence intensity.

According to Alexei Levchenko, diamonds can also contain other impurities that glow under the action of external radiation. Turning on the microwave field, you can see our changing signal against the background of all these noises, and if you create an invisible microcluster of NV centers, this will allow you to read the diamond mark by fluorescence in the microwave field.

The second way of marking gemstones also uses femtosecond laser radiation, however, unlike the first one, here, instead of creating vacancies, inclusions of an amorphous carbon phase are formed.

Test lines of glassy carbon formed under the action of highly focused femtosecond laser radiation. (A) on the diamond surface, line width - 3 µm; (B) in its volume, the width of the thin line is about 1 μm. Photo from fian-inform.ru

Sergey Kudryashov notes that femtosecond laser radiation can be focused at different depths inside transparent materials, and therefore this technology allows creating a unique three-dimensional marking. In the experiments performed, volumetric microscale marks were successfully formed on artificial and natural diamonds.

Under normal conditions, the mark is not visible even under a microscope, it does not reduce the value of the stone, under the influence of laser radiation it begins to fluoresce brightly. The mark is created inside the diamond and cannot be polished or filed. Photo from fian-inform.ru