Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits called qubits, between physically separated quantum processors. A quantum processor is a small quantum computer being able to perform quantum logic gates on a certain number of qubits. Quantum networks work in a similar way to classical networks; the main difference, as will be detailed more in paragraphs, is that quantum networking like quantum computing is better at solving certain problems, such as modeling quantum systems. Networked quantum computing or distributed quantum computing works by linking multiple quantum processors through a quantum network by sending qubits in-between them. Doing this creates a quantum computing cluster and therefore creates more computing potential. Less powerful computers can be linked in this way to create one more powerful processor; this is analogous to connecting several classical computers to form a computer cluster in classical computing.
Like classical computing this system is scale-able by adding more and more quantum computers to the network. Quantum processors are only separated by short distances. In the realm of quantum communication, one wants to send qubits from one quantum processor to another over long distances; this way local quantum networks can be intra connected into a quantum internet. A quantum internet supports many applications, which derive their power from the fact that by creating quantum entangled qubits, information can be transmitted between the remote quantum processors. Most applications of a quantum internet require only modest quantum processors. For most quantum internet protocols, such as quantum key distribution in quantum cryptography, it is sufficient if these processors are capable of preparing and measuring only a single qubit at a time; this is in contrast to quantum computing where interesting applications can only be realized if the quantum processors can simulate more qubits than a classical computer.
Quantum internet applications require only small quantum processors just a single qubit, because quantum entanglement can be realized between just two qubits. A simulation of an entangled quantum system on a classical computer can not provide the same security and speed; the basic structure of a quantum network and more a quantum internet is analogous to a classical network. First, we have end nodes on which applications are run; these end nodes are quantum processors of at least one qubit. Some applications of a quantum internet require quantum processors of several qubits as well as a quantum memory at the end nodes. Second, to transport qubits from one node to another, we need communication lines. For the purpose of quantum communication, standard telecom fibers can be used. For networked quantum computing, in which quantum processors are linked at short distances, different wavelengths are chosen depending on the exact hardware platform of the quantum processor. Third, to make maximum use of communication infrastructure, one requires optical switches capable of delivering qubits to the intended quantum processor.
These switches need to preserve quantum coherence, which makes them more challenging to realize than standard optical switches. One requires a quantum repeater to transport qubits over long distances. Repeaters appear in-between end nodes. Since qubits cannot be copied, classical signal amplification is not possible. By necessity, a quantum repeater works in a fundamentally different way than a classical repeater. End nodes can both emit information. Telecommunication lasers and parametric down-conversion combined with photodetectors can be used for quantum key distribution. In this case, the end nodes can in many cases be simple devices consisting only of beamsplitters and photodetectors. However, for many protocols more sophisticated end nodes are desirable; these systems provide advanced processing capabilities and can be used as quantum repeaters. Their chief advantage is that they can store and retransmit quantum information without disrupting the underlying quantum state; the quantum state being stored can either be the relative spin of an electron in a magnetic field or the energy state of an electron.
They can perform quantum logic gates. One way of realizing such end nodes is by using color centers in diamond, such as the nitrogen-vacancy center; this system forms a small quantum processor featuring several qubits. NV centers can be utilized at room temperatures. Small scale quantum algorithms and quantum error correction has been demonstrated in this system, as well as the ability to entangle two remote quantum processors, perform deterministic quantum teleportation. Another possible platform are quantum processors based on Ion traps, which utilize radio-frequency magnetic fields and lasers. In a multispecies trapped-ion node network, photons entangled with a parent atom are used to entangle different nodes. Cavity quantum electrodynamics is one possible method of doing this. In Cavity QED, photonic quantum states can be transferred to and from atomic quantum states stored in single atoms contained in optical cavities; this allows for the transfer of quantum states between single atoms using optical fiber in addition to the creation of remote entanglement between distant atoms.
Over long distances, the primary method of operating quantum networks is to use optical networks and photon-based qubits. This is due to optical networks having a reduced chance of decoherence. Optical networks have the advantage of being able to re-use existing optical fiber. Alternately, free space networks can be implemented that transmit quantum informati
Quantum simulators permit the study of quantum systems that are difficult to study in the laboratory and impossible to model with a supercomputer. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems. A universal quantum simulator is a quantum computer proposed by Yuri Manin in 1980 and Richard Feynman in 1982. Feynman showed that a classical Turing machine would experience an exponential slowdown when simulating quantum phenomena, while his hypothetical universal quantum simulator would not. David Deutsch in 1985, described a universal quantum computer. In 1996, Seth Lloyd showed that a standard quantum computer can be programmed to simulate any local quantum system efficiently. A quantum system of many particles is described by a Hilbert space whose dimension is exponentially large in the number of particles. Therefore, the obvious approach to simulate such a system requires exponential time on a classical computer. However, it is conceivable that a quantum system of many particles could be simulated by a quantum computer using a number of quantum bits similar to the number of particles in the original system.
As shown by Lloyd, this is true for a class of quantum systems known as local quantum systems. This has been extended to much larger classes of quantum systems. Quantum simulators have been realized on a number of experimental platforms, including systems of ultracold quantum gases, trapped ions, photonic systems and superconducting circuits. A trapped-ion simulator, built by a team that included the NIST and reported in April 2012, can engineer and control interactions among hundreds of quantum bits. Previous endeavors were unable to go beyond 30 quantum bits; as described in the scientific journal Nature, the capability of this simulator is 10 times more than previous devices. It has passed a series of important benchmarking tests that indicate a capability to solve problems in material science that are impossible to model on conventional computers. Furthermore, many important problems in physics low-temperature physics, remain poorly understood because the underlying quantum mechanics is vastly complex.
Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles. Better computational tools are needed to understand and rationally design materials, whose properties are believed to depend on the collective quantum behavior of hundreds of particles; the trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of beryllium ions, less than 1 millimeter in diameter, hovering inside a device called a Penning trap. The outermost electron of each ion acts as a tiny quantum magnet and is used as a qubit, the quantum equivalent of a “1” or a “0” in a conventional computer. In the benchmarking experiment, physicists used. Timed microwave and laser pulses caused the qubits to interact, mimicking the quantum behavior of materials otherwise difficult to study in the laboratory. Although the two systems may outwardly appear dissimilar, their behavior is engineered to be mathematically identical. In this way, simulators allow researchers to vary parameters that couldn’t be changed in natural solids, such as atomic lattice spacing and geometry.
Friedenauer et al. adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states. Kim et al. extended the trapped ion quantum simulator to 3 spins, with global antiferromagnetic Ising interactions featuring frustration and showing the link between frustration and entanglement and Islam et al. used adiabatic quantum simulation to demonstrate the sharpening of a phase transition between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9. Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir and Lanyon et al. demonstrated digital quantum simulation with up to 6 ions. Islam, et al. demonstrated adiabatic quantum simulation of the transverse Ising model with variable range interactions with up to 18 trapped ion spins, showing control of the level of spin frustration by adjusting the antiferromagnetic interaction range. Britton, et al. from NIST has experimentally benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism.
Pagano, et al. reported a new cryogenic ion trapping system designed for long time storage of large ion chains demonstrating coherent one and two-qubit operations for chains of up to 44 ions. Simulators exploit a property of quantum mechanics called superposition, wherein a quantum particle is made to be in two distinct states at the same time, for example and anti-aligned with an external magnetic field. Crucially, the simulator can engineer a second quantum property called entanglement between the qubits, so that physically well separated particles may be made interconnected. Quantum Turing machine Deutsch's 1985 paper Online Web-based Quantum Computer Simulator
Quantum annealing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions, by a process using quantum fluctuations. Quantum annealing is used for problems where the search space is discrete with many local minima, it was formulated in its present form by T. Kadowaki and H. Nishimori in "Quantum annealing in the transverse Ising model" though a proposal in a different form had been made by A. B. Finilla, M. A. Gomez, C. Sebenik and J. D. Doll, in "Quantum annealing: A new method for minimizing multidimensional functions". Quantum annealing starts from a quantum-mechanical superposition of all possible states with equal weights; the system evolves following the time-dependent Schrödinger equation, a natural quantum-mechanical evolution of physical systems. The amplitudes of all candidate states keep changing, realizing a quantum parallelism, according to the time-dependent strength of the transverse field, which causes quantum tunneling between states.
If the rate of change of the transverse field is slow enough, the system stays close to the ground state of the instantaneous Hamiltonian. If the rate of change of the transverse field is accelerated, the system may leave the ground state temporarily but produce a higher likelihood of concluding in the ground state of the final problem Hamiltonian, i.e. diabatic quantum computation. The transverse field is switched off, the system is expected to have reached the ground state of the classical Ising model that corresponds to the solution to the original optimization problem. An experimental demonstration of the success of quantum annealing for random magnets was reported after the initial theoretical proposal. An introduction to combinatorial optimization problems, the general structure of quantum annealing-based algorithms and two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems together with an overview of the quantum annealing systems manufactured by D-Wave Systems are presented in.
Quantum annealing can be compared to simulated annealing, whose "temperature" parameter plays a similar role to QA's tunneling field strength. In simulated annealing, the temperature determines the probability of moving to a state of higher "energy" from a single current state. In quantum annealing, the strength of transverse field determines the quantum-mechanical probability to change the amplitudes of all states in parallel. Analytical and numerical evidence suggests that quantum annealing outperforms simulated annealing under certain conditions; the tunneling field is a kinetic energy term that does not commute with the classical potential energy part of the original glass. The whole process can be simulated in a computer using quantum Monte Carlo, thus obtain a heuristic algorithm for finding the ground state of the classical glass. In the case of annealing a purely mathematical objective function, one may consider the variables in the problem to be classical degrees of freedom, the cost functions to be the potential energy function.
A suitable term consisting of non-commuting variable has to be introduced artificially in the Hamiltonian to play the role of the tunneling field. One may carry out the simulation with the quantum Hamiltonian thus constructed just as described above. Here, there is a choice in selecting the non-commuting term and the efficiency of annealing may depend on that, it has been demonstrated experimentally as well as theoretically, that quantum annealing can indeed outperform thermal annealing in certain cases where the potential energy landscape consists of high but thin barriers surrounding shallow local minima. Since thermal transition probabilities depend only on the height Δ of the barriers, for high barriers, it is difficult for thermal fluctuations to get the system out from such local minima. However, as argued earlier in 1989 by Ray, Chakrabarti & Chakrabarti, the quantum tunneling probability through the same barrier depends not only on the height Δ of the barrier, but on its width w and is given by e − Δ w Γ, where Γ is the tunneling field.
If the barriers are thin enough, quantum fluctuations can bring the system out of the shallow local minima. For N -spin glasses, Δ is proportional to N, with a linear annealing schedule for the transverse field, one gets τ proportional to e N for the annealing time (instead of
International Standard Serial Number
An International Standard Serial Number is an eight-digit serial number used to uniquely identify a serial publication, such as a magazine. The ISSN is helpful in distinguishing between serials with the same title. ISSN are used in ordering, interlibrary loans, other practices in connection with serial literature; the ISSN system was first drafted as an International Organization for Standardization international standard in 1971 and published as ISO 3297 in 1975. ISO subcommittee TC 46/SC 9 is responsible for maintaining the standard; when a serial with the same content is published in more than one media type, a different ISSN is assigned to each media type. For example, many serials are published both in electronic media; the ISSN system refers to these types as electronic ISSN, respectively. Conversely, as defined in ISO 3297:2007, every serial in the ISSN system is assigned a linking ISSN the same as the ISSN assigned to the serial in its first published medium, which links together all ISSNs assigned to the serial in every medium.
The format of the ISSN is an eight digit code, divided by a hyphen into two four-digit numbers. As an integer number, it can be represented by the first seven digits; the last code digit, which may be 0-9 or an X, is a check digit. Formally, the general form of the ISSN code can be expressed as follows: NNNN-NNNC where N is in the set, a digit character, C is in; the ISSN of the journal Hearing Research, for example, is 0378-5955, where the final 5 is the check digit, C=5. To calculate the check digit, the following algorithm may be used: Calculate the sum of the first seven digits of the ISSN multiplied by its position in the number, counting from the right—that is, 8, 7, 6, 5, 4, 3, 2, respectively: 0 ⋅ 8 + 3 ⋅ 7 + 7 ⋅ 6 + 8 ⋅ 5 + 5 ⋅ 4 + 9 ⋅ 3 + 5 ⋅ 2 = 0 + 21 + 42 + 40 + 20 + 27 + 10 = 160 The modulus 11 of this sum is calculated. For calculations, an upper case X in the check digit position indicates a check digit of 10. To confirm the check digit, calculate the sum of all eight digits of the ISSN multiplied by its position in the number, counting from the right.
The modulus 11 of the sum must be 0. There is an online ISSN checker. ISSN codes are assigned by a network of ISSN National Centres located at national libraries and coordinated by the ISSN International Centre based in Paris; the International Centre is an intergovernmental organization created in 1974 through an agreement between UNESCO and the French government. The International Centre maintains a database of all ISSNs assigned worldwide, the ISDS Register otherwise known as the ISSN Register. At the end of 2016, the ISSN Register contained records for 1,943,572 items. ISSN and ISBN codes are similar in concept. An ISBN might be assigned for particular issues of a serial, in addition to the ISSN code for the serial as a whole. An ISSN, unlike the ISBN code, is an anonymous identifier associated with a serial title, containing no information as to the publisher or its location. For this reason a new ISSN is assigned to a serial each time it undergoes a major title change. Since the ISSN applies to an entire serial a new identifier, the Serial Item and Contribution Identifier, was built on top of it to allow references to specific volumes, articles, or other identifiable components.
Separate ISSNs are needed for serials in different media. Thus, the print and electronic media versions of a serial need separate ISSNs. A CD-ROM version and a web version of a serial require different ISSNs since two different media are involved. However, the same ISSN can be used for different file formats of the same online serial; this "media-oriented identification" of serials made sense in the 1970s. In the 1990s and onward, with personal computers, better screens, the Web, it makes sense to consider only content, independent of media; this "content-oriented identification" of serials was a repressed demand during a decade, but no ISSN update or initiative occurred. A natural extension for ISSN, the unique-identification of the articles in the serials, was the main demand application. An alternative serials' contents model arrived with the indecs Content Model and its application, the digital object identifier, as ISSN-independent initiative, consolidated in the 2000s. Only in 2007, ISSN-L was defined in the
In quantum information theory, superdense coding is a quantum communication protocol to transmit two classical bits of information from a sender to a receiver, by sending only one qubit from Alice to Bob, under the assumption of Alice and Bob pre-sharing an entangled state. This protocol was first proposed by Bennett and Weisner in 1992 and experimentally actualized in 1996 by Mattel, Weinfurter and Zeilinger using entangled photon pairs. By performing one of four quantum gate operations on the qubit she possesses, Alice can prearrange the measurement Bob makes. After receiving Alice's qubit, operating on the pair and measuring both, Bob has two classical bits of information. If Alice and Bob do not share entanglement before the protocol begins it is impossible to send two classical bits using 1 qubit, as this would violate Holevo's theorem. Superdense coding is the underlying principle of secure quantum secret coding; the necessity of having both qubits to decode the information being sent eliminates the risk of eavesdroppers intercepting messages.
It can be thought of as the opposite of quantum teleportation, in which one transfers one qubit from Alice to Bob by communicating two classical bits, as long as Alice and Bob have a pre-shared Bell pair. Suppose Alice wants to send two classical bits of information to Bob using qubits. To do this, an entangled state is prepared using gate by Charlie, a third person. Charlie sends one of these qubits to Alice and the other to Bob. Once Alice obtains her qubit in the entangled state, she applies a certain quantum gate to her qubit depending on which two-bit message she wants to send to Bob, her entangled qubit is sent to Bob who, after applying the appropriate quantum gate and making a measurement, can retrieve the classical two-bit message. Alice must tell Bob which gate to apply after he receives the entangled qubit in order to obtain the correct classical bits; the protocol can be split into five different steps: preparation, encoding and decoding. The protocol starts with the preparation of an entangled state, shared between Alice and Bob.
Suppose the following Bell state | Φ + ⟩ = 1 2 where ⊗ denotes the tensor product, is prepared. Note: we can omit the tensor product symbol ⊗ and write the Bell state as | Φ + ⟩ = 1 2. After the preparation of the Bell state | Φ + ⟩, the qubit denoted by subscript A is sent to Alice and the qubit denoted by subscript B is sent to Bob. At this point and Bob may be in different locations. There may be a long period of time between the preparation and sharing of the entangled state | Φ + ⟩ and the rest of the steps in the procedure. By applying a quantum gate to her qubit locally, Alice can transform the entangled state | Φ + ⟩ into any of the four Bell states. Note that this process cannot "break" the entanglement between the two qubits. Let's now describe which operations Alice needs to perform on her entangled qubit, depending on which classical two-bit message she wants to send to Bob. We'll see why these specific operations are performed. There are four cases, which correspond to the four possible two-bit strings that Alice may want to send.
1. If Alice wants to send the classical two-bit string 00 to Bob she applies the identity quantum gate, I =, to her qubit, so that it remains unchanged; the resultant entangled state is | Φ + ⟩:= | B 00 ⟩ = 1 2 In other words, the entangled state shared between Alice and Bob has not changed, i.e. it is still | Φ + ⟩. The notation | B 00 ⟩ is used to r
John Watrous (computer scientist)
John Harrison Watrous is a professor of computer science at the David R. Cheriton School of Computer Science at the University of Waterloo, a member of the Institute for Quantum Computing, an affiliate member of the Perimeter Institute for Theoretical Physics and a Fellow of the Canadian Institute for Advanced Research, he was a faculty member in the Department of Computer Science at the University of Calgary from 2002 to 2006 where he held a Canada Research Chair in quantum computing. He is an editor of the journal Theory of Computing and former editor for the journal Quantum Information & Computation, his research interests include quantum quantum computation. He is well known for his work on quantum interactive proofs, the quantum analogue of the celebrated result IP equals PSPACE, QIP equals PSPACE; this was preceded by a series of results, showing QIP can be constrained to 3 messages, QIP is contained in EXP, the 2-message version of QIP is in PSPACE. He has published important papers on quantum finite automata and quantum cellular automata.
With Scott Aaronson, he showed that certain forms of time travel can make quantum and classical computation equivalent: together, the authors showed that quantum effects do not offer advantages for computation if computers can send information to the past through a type of closed timelike curve proposed by the physicist David Deutsch. He obtained his Ph. D. in 1998 at the University of Wisconsin–Madison under the supervision of Eric Bach
Computational complexity theory
Computational complexity theory focuses on classifying computational problems according to their inherent difficulty, relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used; the theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e. the amount of resources needed to solve them, such as time and storage. Other measures of complexity are used, such as the amount of communication, the number of gates in a circuit and the number of processors. One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do; the P versus NP problem, one of the seven Millennium Prize Problems, is dedicated to the field of computational complexity.
Related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More computational complexity theory tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically. A computational problem can be viewed as an infinite collection of instances together with a solution for every instance; the input string for a computational problem is referred to as a problem instance, should not be confused with the problem itself.
In computational complexity theory, a problem refers to the abstract question to be solved. In contrast, an instance of this problem is a rather concrete utterance, which can serve as the input for a decision problem. For example, consider the problem of primality testing; the instance is a number and the solution is "yes" if the number is prime and "no" otherwise. Stated another way, the instance is a particular input to the problem, the solution is the output corresponding to the given input. To further highlight the difference between a problem and an instance, consider the following instance of the decision version of the traveling salesman problem: Is there a route of at most 2000 kilometres passing through all of Germany's 15 largest cities? The quantitative answer to this particular problem instance is of little use for solving other instances of the problem, such as asking for a round trip through all sites in Milan whose total length is at most 10 km. For this reason, complexity theory addresses computational problems and not particular problem instances.
When considering computational problems, a problem instance is a string over an alphabet. The alphabet is taken to be the binary alphabet, thus the strings are bitstrings; as in a real-world computer, mathematical objects other than bitstrings must be suitably encoded. For example, integers can be represented in binary notation, graphs can be encoded directly via their adjacency matrices, or by encoding their adjacency lists in binary. Though some proofs of complexity-theoretic theorems assume some concrete choice of input encoding, one tries to keep the discussion abstract enough to be independent of the choice of encoding; this can be achieved by ensuring that different representations can be transformed into each other efficiently. Decision problems are one of the central objects of study in computational complexity theory. A decision problem is a special type of computational problem whose answer is either yes or no, or alternately either 1 or 0. A decision problem can be viewed as a formal language, where the members of the language are instances whose output is yes, the non-members are those instances whose output is no.
The objective is to decide, with the aid of an algorithm, whether a given input string is a member of the formal language under consideration. If the algorithm deciding this problem returns the answer yes, the algorithm is said to accept the input string, otherwise it is said to reject the input. An example of a decision problem is the following; the input is an arbitrary graph. The problem consists in deciding; the formal language associated with this decision problem is the set of all connected graphs — to obtain a precise definition of this language, one has to decide how graphs are encoded as binary strings. A function problem is a computational problem where a single output is expected for every input, but the output is more complex than that of a decision problem—that is, the output isn't just yes or no. Notable examples include the integer factorization problem, it is tempting to think that the notion of function problems is much richer than the notion of decision problems. However, this is not the case, since function problems can be recast as decision problems.
For example, the multiplication of two integers can be expressed as the set of triples such that the relation a × b = c holds. Deciding whether a given triple is a member of this set corresponds to solving