The Quantum IO Monad - School of Computer Science
... Haskell is a pure functional programming language, treating computations as the evaluation of pure mathematical functions. A function is said to be pure if it always returns the same result when given the same arguments, and in producing that result has not caused any side-effects to occur within th ...
... Haskell is a pure functional programming language, treating computations as the evaluation of pure mathematical functions. A function is said to be pure if it always returns the same result when given the same arguments, and in producing that result has not caused any side-effects to occur within th ...
Lecture 8
... Claim: For every Boolean function there is a unique multilinear polynomial, which represents f exactly, i.e. f(x)= p(x) for all Boolean x. Proof: Assume f(x)=p(x)=q(x) for alle Boolean x, yet pq Then p-q is a multilinear polynomial for g(x)=0, and p-q is not the zero polynomial Take a minimum ...
... Claim: For every Boolean function there is a unique multilinear polynomial, which represents f exactly, i.e. f(x)= p(x) for all Boolean x. Proof: Assume f(x)=p(x)=q(x) for alle Boolean x, yet pq Then p-q is a multilinear polynomial for g(x)=0, and p-q is not the zero polynomial Take a minimum ...
On the Topological Origin of Entanglement in Ising Spin Glasses
... number invariants. This property is exactly like the corresponding property of the Borromean rings which, however, are known to be distinguished from a disjoint union of unlinked rings by a higher order topological invariant, namely the Massey triple product.27 An Abelian topological theory cannot p ...
... number invariants. This property is exactly like the corresponding property of the Borromean rings which, however, are known to be distinguished from a disjoint union of unlinked rings by a higher order topological invariant, namely the Massey triple product.27 An Abelian topological theory cannot p ...
Entanglement for Pedestrians
... work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on.” ...
... work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on.” ...
Synthesising arbitrary quantum states in a
... of such superposed states, and their subsequent use, is the basis for quantum computation and simulation1 . Creating these complex superpositions in harmonic systems, such as the motional state of trapped ions2 , microwave resonators3–5 or optical cavities6 , has presented a significant challenge, b ...
... of such superposed states, and their subsequent use, is the basis for quantum computation and simulation1 . Creating these complex superpositions in harmonic systems, such as the motional state of trapped ions2 , microwave resonators3–5 or optical cavities6 , has presented a significant challenge, b ...
Determination of Enzymatic Reaction Pathways Using QM/MM
... small molecules) are described by quantum mechanics, whereas the solvent (water, methanol, etc.) is described by molecular mechanics using polarizable or nonpolarizable [15, 32] force fields. There, the delineation between the quantum and classic parts is clearly defined as a molecule is exclusively i ...
... small molecules) are described by quantum mechanics, whereas the solvent (water, methanol, etc.) is described by molecular mechanics using polarizable or nonpolarizable [15, 32] force fields. There, the delineation between the quantum and classic parts is clearly defined as a molecule is exclusively i ...
Phys. Rev. Lett. 103, 025301 (2009).
... Fig. 2, it keeps the ratio =s small in a large temperature regime, where it approaches the value of Eq. (1). As was shown recently, cold atoms with diverging scattering length are materials which also come close to the value (1) [15,16]. Our result shows that, interestingly, graphene has an even sm ...
... Fig. 2, it keeps the ratio =s small in a large temperature regime, where it approaches the value of Eq. (1). As was shown recently, cold atoms with diverging scattering length are materials which also come close to the value (1) [15,16]. Our result shows that, interestingly, graphene has an even sm ...
Computation in a Topological Quantum Field Theory
... a Topological Quantum Field Theory. We ask two basic questions: i) how does the computational power of these excitations change as a function of the genus of a fixed 2-dimensional space-time? and ii) independent of any particular space-time, what structural properties of a TQFT govern its computatio ...
... a Topological Quantum Field Theory. We ask two basic questions: i) how does the computational power of these excitations change as a function of the genus of a fixed 2-dimensional space-time? and ii) independent of any particular space-time, what structural properties of a TQFT govern its computatio ...
3. Generation of the Quantum Fault Table
... literature including [3, 4, 5] presents errorcorrecting codes, and these codes help the system recover from errors of phase-shift and rotations, and it is often mentioned [3, 4, 5, 1, 2] that Qubits can become entangled with the environment causing errors to occur[4, 5, 6, 2]. [18] Presents a study ...
... literature including [3, 4, 5] presents errorcorrecting codes, and these codes help the system recover from errors of phase-shift and rotations, and it is often mentioned [3, 4, 5, 1, 2] that Qubits can become entangled with the environment causing errors to occur[4, 5, 6, 2]. [18] Presents a study ...
001 Introduction to Quantum Mechanics, Probability Amplitudes and
... Of course quantum mechanics has a very funny way of looking at the world. That’s part of the problem. And it’s by constant practice and experience that you’ll deepen that understanding. Okay, so. Einstein, as everybody knows, didn’t like quantum mechanics. But I think the reason why he didn’t like q ...
... Of course quantum mechanics has a very funny way of looking at the world. That’s part of the problem. And it’s by constant practice and experience that you’ll deepen that understanding. Okay, so. Einstein, as everybody knows, didn’t like quantum mechanics. But I think the reason why he didn’t like q ...
Modal Approaches in Metaphysics and Quantum Mechanics1
... At the heart of the Feynman path integral is a geometric model of a summation of rotating arrows that symbolise probability amplitude of virtual or possible trajectories of quantum particles. It was found that the probability of quantum events can be found not only by solving the Schrödinger equatio ...
... At the heart of the Feynman path integral is a geometric model of a summation of rotating arrows that symbolise probability amplitude of virtual or possible trajectories of quantum particles. It was found that the probability of quantum events can be found not only by solving the Schrödinger equatio ...
Spin Squeezing on an Atomic Clock Transition.
... individual particles constitutes a fundamental source of noise that limits the precision of the measurement7–9 at the standard quantum limit (SQL). The SQL is the fundamental limit for measurements with ensembles of uncorrelated particles. However, quantum mechanics allows one to redistribute the qu ...
... individual particles constitutes a fundamental source of noise that limits the precision of the measurement7–9 at the standard quantum limit (SQL). The SQL is the fundamental limit for measurements with ensembles of uncorrelated particles. However, quantum mechanics allows one to redistribute the qu ...
Quantum key distribution
Quantum key distribution (QKD) uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. It is often incorrectly called quantum cryptography, as it is the most well known example of the group of quantum cryptographic tasks.An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold, a key can be produced that is guaranteed to be secure (i.e. the eavesdropper has no information about it), otherwise no secure key is possible and communication is aborted.The security of encryption that uses quantum key distribution relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography which relies on the computational difficulty of certain mathematical functions, and cannot provide any indication of eavesdropping at any point in the communication process, or any mathematical proof as to the actual complexity of reversing the one-way functions used. QKD has provable security based on information theory, and forward secrecy.Quantum key distribution is only used to produce and distribute a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel. The algorithm most commonly associated with QKD is the one-time pad, as it is provably secure when used with a secret, random key. In real world situations, it is often also used with encryption using symmetric key algorithms like the Advanced Encryption Standard algorithm. In the case of QKD this comparison is based on the assumption of perfect single-photon sources and detectors, that cannot be easily implemented.