Optical Coherence And Quantum Optics Pdf
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- Optical Coherence and Quantum Optics
- Optics Express
- Coherence (physics)
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I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding.
Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed. These problems have applications in public key cryptosystems and modeling of quantum systems such as high energy physics and condensed matter systems.
Another important application of quantum algorithms is in the understanding of models of quantum chemistry, which would lead to efficient design of drugs and the analysis of their effects. All of these applications rely on efficient quantum algorithms and, in fact, represent problems for which no efficient classical algorithms exist.
There are several other problems for which quantum systems provide a more modest advantage than an exponential speed-up. These problems include collision finding, which is applicable in secure hashing, solving differential equations using the finite element method [ 9 ], and search on graphs for marked vertices [ 10 ]. All these examples provide evidence that this model of computing is potentially more powerful than classical computing.
However, it should also be pointed out that there is currently no evidence that quantum computers can solve NP-hard problems in polynomial time. The class NP stands for nondeterministic polynomial time defined more explicitly in the next section and consists of problems whose solution can be checked polynomial time by deterministic classical computers.
The importance of this class stems from the fact that several practical problems lie in this class. Despite the lack of evidence of an exponential quantum speed-up for problems in this class, there are a lot of examples where one has a polynomial speed-up such as a square-root speed-up for several problems in this class see, for example, [ 11 ]. This speed-up over conventional digital computers has led to numerous proposals to implement quantum computers.
Some of the proposed implementations are on superconducting qubits [ 12 ], ion traps [ 13 ], quantum dots [ 14 ], and quantum optics [ 15 ].
Each implementation scheme has its relative advantages as well as drawbacks. Most of these implementations focus on a model of quantum computing known as the circuit model. This model is closest to classical digital computers in the sense that the information is encoded in bits or qubits in the quantum case.
Quantum logic gates corresponding to a quantum circuit are applied to the qubits to get the desired output. Many of the quantum algorithms for which there is an exponential speed-up over classical algorithms are designed in this model. There are, however, several other quantum computing models. Some of the well-known ones include the cluster state model which is relevant to optical quantum computing , the adiabatic model, and the quantum walk model.
It can be shown that these models are equivalent to each other, which implies that any algorithm in one model can be converted to an algorithm in the other with a polynomial overhead. Optical implementation of quantum gates is important for several reasons. First, communicating over quantum channels, such as the bosonic channel, requires one to implement quantum optical gates. In fact, optimal decoding of the communication codes usually involves quite general quantum circuits [ 16 ].
Second, quantum key distribution QKD over long distances needs optics. QKD [ 17 ] is a scheme in which two parties can exchange secret keys that can be used in several cryptographic primitives. Long-distance QKD requires the use of repeaters, which are devices with quantum memory that can implement quantum gates, especially the so-called Bell measurement which is a measurement that can be used to generate entanglement between two parties.
However, the deployment of such schemes has been hampered by low rates and the high cost of infrastructure in the form of quantum memories, reliable single photon, and entangled sources. Recently, in [ 18 ], schemes that relax the requirements on the sources have been proposed.
The tradeoff is that in this scheme, the detectors need to be more sophisticated and need to resolve multiple photons. However, this is considered a more plausible requirement by experimentalists. Several schemes for such repeaters exist using rare earth atoms [ 19 ], [ 20 ], ion traps [ 21 ], and optical repeaters [ 22 ].
All of these would require implementing optical gates for quantum information processing even though they may not be universal quantum computers.
In all of these schemes, one needs a reliable on-demand quantum memory and the ability to produce high-quality entangled states. In fact, these capabilities also allow one to do arbitrary quantum computation as well. Third, even for computing applications, optics becomes important when other schemes run out of resources.
For example, since superconducting qubits are required to be stored at milli-Kelvin temperatures, this way of implementing quantum computers is fundamentally limited by the number of qubits that can be stored in a dilution refrigerator or a server of qubits. When one refrigerator runs of space, one can use several servers; however, they must be connected to each other in order to transport quantum information without measuring.
This can be done using quantum optics, and it leads to the challenging problem of transferring quantum information from the superconducting device to an optical state.
It also points to the need to develop high-fidelity quantum optical gates. These quantum optical interconnects can help increase the number of qubits used in computation by combining several servers.
Indeed, there has been tremendous experimental progress in demonstrating various quantum computing models over a small number of modes and photons, but a detailed discussion of this progress and challenges in scaling up is outside the scope of this review. However, we provide a short review of experimental progress in Section 6. In this review article, we focus on the optical implementation of some quantum computing models.
Specifically, we focus on schemes to implement the circuit model, the adiabatic model, as well as some models believed to be intermediate between classical computing and quantum computing.
In Section 2, we briefly review the necessary complexity theory. In Section 3, we discuss optical implementations of digital quantum computation. In Section 4, we discuss other models that are easier to implement using optics and are not as powerful as universal quantum computers but that have quantum computational power greater than classical computers do assuming standard conjectures in complexity theory. Then in Section 5, we discuss analog models of quantum computation and some recent work in implementing them in optics.
Section 6 discusses some of the experimental progress in building these models. Finally, in Section 7, we present some conclusions and outlook. In this subsection, we explain some core concepts of computational complexity that are useful to understand the power of various models of optical computing. The main reason for introducing complexity theory is that it is the right framework to discuss the computational power of various models. Rather than use the formal definitions from computer science literature, we will present somewhat informal but, hopefully, more intuitive definitions.
The reason for this choice is to make contact with the kinds of problems one hopes to solve using these models. For detailed definitions, see [ 23 ]. In all of the definitions, we will refer to n as the input size and all scalings are in terms of this quantity.
In fact, rather than using the solution itself in the definition, one can define this class with respect to a more general witness which is a function of the problem instance such that it is easy to check from the witness that a given string is a solution. While it may seem at first sight that being able to check might give enough power to find the solution, there is overwhelming evidence to suggest that this is not true. It is the class of decision problems that can be solved in polynomial time on a quantum computer.
The relationship between these classes is depicted in Figure 1. This overhead is needed to convert the solution of one problem to the solution of the other. Most problems that we encounter in practice are not decision problems since we would like to know the solutions or at least some properties of the solutions.
The description here is adapted from [ 24 ]. It can be defined from the point of view of CSPs. This means that when V is given, the problem instance i.
Building in this way, we can construct infinitely many levels, which do not collapse onto the first or, indeed, we do not expect them to collapse at any level. Since we do not expect the hierarchy to collapse at any level, this gives evidence of the power of these quantum models. Put another way, this is evidence that classical computers cannot simulate these quantum models in polynomial time.
Similar to the polynomial hierarchy, there is another hierarchy called the exponential hierarchy. One might hope that this change in the definition of the problem might make it easier to find a polynomial time algorithm or make it possible for it to exist. This is essentially the content of a famous theorem in computer science called probabilistically checkable proofs; i. Despite these seemingly negative results, approximation algorithms can provide the best possible solutions to NP-hard problems for suitable approximation ratios.
For approximation ratios where the problem is NP-hard, polynomial or constant factor speed-up is still possible with quantum algorithms. One might wonder how often these occur in practical situations or, more precisely, if one picks instances at random from some reasonable distribution, then it may turn out that with high probability, a given instance can be solved efficiently. However, this turns out to be false as well. There are several types of speed-up over the state-of-the-art SOA that one can aim for and that will still make it worthwhile to develop the model.
These are explained below. Although these are important types of speed-up, they are by no means exhaustive. Indeed, there are infinitely many types of speed-up as one can obtain any function of the run-time of the SOA as the run-time of the algorithm of interest. This is the speed-up obtained when the algorithm of interest is exponentially better than the run-time scaling of the SOA algorithm.
This kind of speed-up can be thought of as the next best one, although in practice, it can be just as good. It is defined as follows. The next one we would like to describe is a polynomial speed-up, which means that the run-times of the SOA and the new algorithm are related by a polynomial, i. Constant factor. The last one we would like to mention is, in a sense, the least interesting but which nevertheless can be substantial in some cases. This kind of speed-up can be substantial if the constant c 2 is large.
In complexity theory, these are usually ignored as one is only interested in functions growing as n. There are several more that one can construct that are in between exponential and polynomial.
These different classes of computational advantages point to the fact that models can be useful even if they do not lead to an exponential speed-up. An exponential cost solution in a particular model may not improve in scaling over the SOA but could lead to a substantial improvement via a large constant factor advantage.
In this section, we survey various schemes to perform quantum computation digitally, i. For any computation classical or quantum, there is a notion of a universal gate set. For quantum computation, one needs to append this with other gates. One standard gate set used in quantum computing consists of the CNOT gate; Hadamard gate denoted as H ; phase gate, sometimes denoted as S ; and its square-root, denoted T.
Optical Coherence and Quantum Optics
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Mandel and E. Mandel , E.
This book presents a systematic treatment of a broad area of modern optical physics dealing with coherence and fluctuations of light. It is a field that has largely developed since the first lasers became available in the s. The first three chapters cover various mathematical techniques that are needed later. A systematic account is then presented of optical coherence theory within the framework of classical optics, and this is applied to subjects that have not been treated systematically before, such as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, coherence theory of laser modes and scattering of partially coherent light by random media. A semiclassical description of photoelectron detection precedes the treatment of field quantization and of the coherent suites, and this is followed by a discussion of photon statistics, the quantum theory of photoelectric detection and applications to thermal light.
In physics , two wave sources are perfectly coherent if their frequency and waveform are identical and their phase difference is constant. Coherence is an ideal property of waves that enables stationary i. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics.
I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.
ГЛАВА 63 Новообретенная веспа Дэвида Беккера преодолевала последние метры до Aeropuerto de Sevilla. Костяшки его пальцев, всю дорогу судорожно сжимавших руль, побелели. Часы показывали два часа с минутами по местному времени. Возле главного здания аэровокзала Беккер въехал на тротуар и соскочил с мотоцикла, когда тот еще двигался.
Если Танкадо - Северная Дакота, выходит, он посылал электронную почту самому себе… а это значит, что никакой Северной Дакоты не существует. Партнер Танкадо - призрак. Северная Дакота - призрак, сказала она. Сплошная мистификация. Блестящий замысел. Выходит, Стратмор был зрителем теннисного матча, следящим за мячом лишь на одной половине корта. Поскольку мяч возвращался, он решил, что с другой стороны находится второй игрок.
This is a useful book for many, though it is too brief and not sufficiently detailed to be used as a text. Undergraduates in physics and astrophysics should read it.
- Лживый негодяй. Вы промыли ей мозги. Вы рассказываете ей только то, что считаете нужным. Знает ли она, что именно вы собираетесь сделать с Цифровой крепостью. - И что .
Однажды вечером на университетском представлении Щелкунчика Сьюзан предложила Дэвиду вскрыть шифр, который можно было отнести к числу базовых. Весь антракт он просидел с ручкой в руке, ломая голову над посланием из одиннадцати букв: HL FKZC VD LDS В конце концов, когда уже гасли огни перед началом второго акта, его осенило. Шифруя послание, Сьюзан просто заменила в нем каждую букву на предшествующую ей алфавите.
Он подошел ближе. - Я опытный диагност. К тому же умираю от любопытства узнать, какая диагностика могла заставить Сьюзан Флетчер выйти на работу в субботний день.
Вас подбросить в аэропорт? - предложил лейтенант - Мой Мото Гуччи стоит у подъезда. - Спасибо, не стоит. Я возьму такси.
ГЛАВА 7 Мозг Сьюзан лихорадочно работал: Энсей Танкадо написал программу, с помощью которой можно создавать шифры, не поддающиеся взлому. Она никак не могла свыкнуться с этой мыслью. - Цифровая крепость, - сказал Стратмор. - Так назвал ее Танкадо.
Плутоний впервые был открыт… - Число, - напомнил Джабба. - Нам нужно число. Сьюзан еще раз перечитала послание Танкадо. Главная разница между элементами… разница между… нужно найти число… - Подождите! - сказала .
Я хотел лично сказать Росио, какое удовольствие получил от общения с ней несколько дней. Но я уезжаю сегодня вечером. Пожалуй, я все же оставлю ей записку. - И он положил конверт на стойку.
На экране промелькнула внутренняя часть мини-автобуса, и перед глазами присутствующих предстали два безжизненных тела у задней двери. Один из мужчин был крупного телосложения, в очках в тонкой металлической оправе с разбитыми стеклами. Второй - молодой темноволосый, в окровавленной рубашке.