POLYNOMIAL-TIME ALGORITHMS FOR PRIME FACTORIZATION
... is a basis vector of the Hilbert space. If the machine is measured (with respect to this basis) at any particular step, the probability of seeing basis state jSi i is jaij2; however, measuring the state of the machine projects this state to the observed basis vector jSi i. Thus, looking at the machi ...
... is a basis vector of the Hilbert space. If the machine is measured (with respect to this basis) at any particular step, the probability of seeing basis state jSi i is jaij2; however, measuring the state of the machine projects this state to the observed basis vector jSi i. Thus, looking at the machi ...
REDUCED AND EXTENDED WEAK COUPLING LIMIT
... Thus one can obtain a Markov c.p. semigroup by reducing a single unitary dynamics, without invoking a family of dynamics and taking its limit. However, the generator of a quantum Langevin dynamics equals i[Z, ·] where Z is a self-adjoint operator that does not look like a physically realistic Hamilt ...
... Thus one can obtain a Markov c.p. semigroup by reducing a single unitary dynamics, without invoking a family of dynamics and taking its limit. However, the generator of a quantum Langevin dynamics equals i[Z, ·] where Z is a self-adjoint operator that does not look like a physically realistic Hamilt ...
Fractionalization, Topological Order, and
... Fractionalization of quantum numbers has been a focus of condensed matter physics in recent years. It refers to the emergence of a collective excitation having fractional quantum numbers with respect to the elementary particles (such as electrons), in a strongly correlated system. The notion of frac ...
... Fractionalization of quantum numbers has been a focus of condensed matter physics in recent years. It refers to the emergence of a collective excitation having fractional quantum numbers with respect to the elementary particles (such as electrons), in a strongly correlated system. The notion of frac ...
Ch 8 – Oscillation
... from its equilibrium position. It moves as far on one side as it does on the other. • The time that it takes to make one complete repetition or cycle is called the period of the motion. We will usually measure the period in seconds. • Frequency is the number of cycles per second that an oscillator g ...
... from its equilibrium position. It moves as far on one side as it does on the other. • The time that it takes to make one complete repetition or cycle is called the period of the motion. We will usually measure the period in seconds. • Frequency is the number of cycles per second that an oscillator g ...
Pedestrian notes on quantum mechanics
... conversion of the physical interactions into real numbers. As regarding computers, there should be a continuous effort to study their rate of producing numbers which is not depending only on the used algorithm, and to have more involved definitions of computable numbers (so-called Turing Problem [5] ...
... conversion of the physical interactions into real numbers. As regarding computers, there should be a continuous effort to study their rate of producing numbers which is not depending only on the used algorithm, and to have more involved definitions of computable numbers (so-called Turing Problem [5] ...
An Introduction to Quantum Cosmology
... Quantum cosmology does not pertain to provide a complete, fundamental description of the universe, but rather provide a predictive guide for theories that do. It is a framework, based on quantized Einstein gravity or quantum geometrodynamics, in which the universe may be described as a closed quantu ...
... Quantum cosmology does not pertain to provide a complete, fundamental description of the universe, but rather provide a predictive guide for theories that do. It is a framework, based on quantized Einstein gravity or quantum geometrodynamics, in which the universe may be described as a closed quantu ...
and quantum properties - Hal-SHS
... various eigenvalues corresponding to the system's state function, each with the probability for this state. Such a formulation avoids (and even rejects) the association of a definite physical quantity to a given system, except for quantities obeying a superselection condition (corresponding to one u ...
... various eigenvalues corresponding to the system's state function, each with the probability for this state. Such a formulation avoids (and even rejects) the association of a definite physical quantity to a given system, except for quantities obeying a superselection condition (corresponding to one u ...
Many Oscillators
... The unitary counterpart: a strong coupling can struggle the effects of a weaker one, realizing the partitioning of the Hilbert space: ...
... The unitary counterpart: a strong coupling can struggle the effects of a weaker one, realizing the partitioning of the Hilbert space: ...
Cryogenic Control Architecture for Large
... Realizing the classical control and readout system of a quantum computer is a formidable scientific and engineering challenge in its own right, likely requiring the invention of a suite of new devices with tailored physical properties. Already under way for this purpose is the development of near-qu ...
... Realizing the classical control and readout system of a quantum computer is a formidable scientific and engineering challenge in its own right, likely requiring the invention of a suite of new devices with tailored physical properties. Already under way for this purpose is the development of near-qu ...
generalized numerical ranges and quantum error correction
... Evidently, ( a1 , . . . , am ) ∈ Λk (A) if and only if there exists an n × k matrix U such that U ∗ U = Ik , and U ∗ A j U = a j Ik for j = 1, . . . , m. Let x, y ∈ Cn . Denote by hAx, yi the vector (h A1 x, yi, . . . , h Am x, yi) ∈ Cm . Then a ∈ Λk (A) if and only if there exists an orthonormal se ...
... Evidently, ( a1 , . . . , am ) ∈ Λk (A) if and only if there exists an n × k matrix U such that U ∗ U = Ik , and U ∗ A j U = a j Ik for j = 1, . . . , m. Let x, y ∈ Cn . Denote by hAx, yi the vector (h A1 x, yi, . . . , h Am x, yi) ∈ Cm . Then a ∈ Λk (A) if and only if there exists an orthonormal se ...
Equivalence of Topological Codes and Fast Decoding
... corollaries of our mapping. In addition, our mapping provides a method to decode any 2D TSC code, while only a handful of special cases previously had solutions [10, 11, 19]. Secondly, the local mapping can be used to change encoding during a quantum computation. Because the mapping is local, this c ...
... corollaries of our mapping. In addition, our mapping provides a method to decode any 2D TSC code, while only a handful of special cases previously had solutions [10, 11, 19]. Secondly, the local mapping can be used to change encoding during a quantum computation. Because the mapping is local, this c ...
Spintronics and Quantum Dots for Quantum Computing and
... between the two if there are strong spin-orbit effects, but our intention is that conditions and materials should be chosen such that these effects are weak. Under these circumstances the spin coherence times (the time over which the phase of a superposition of spin-up and spin-down states is well-d ...
... between the two if there are strong spin-orbit effects, but our intention is that conditions and materials should be chosen such that these effects are weak. Under these circumstances the spin coherence times (the time over which the phase of a superposition of spin-up and spin-down states is well-d ...
Feynman Diagrams in Quantum Mechanics
... Now that we have explained how to calculate with Feynman Diagrams, we will proceed to explain why these calculations should be correct. In this section we introduce some of the terminology that will be used through the rest of the paper. The objects in this section are of particular importance when ...
... Now that we have explained how to calculate with Feynman Diagrams, we will proceed to explain why these calculations should be correct. In this section we introduce some of the terminology that will be used through the rest of the paper. The objects in this section are of particular importance when ...
Fully nonlocal quantum correlations
... (a ,x ) ∈ Dy . Now, since {Max } is in one-to-one correspondence with the projectors {zi }, vA can then be thought of as a valid noncontextual deterministic assignment map for {zi }. This, however, is prohibited because {zi } is a KS proof. Thus, one concludes that βL βNS − 1. The desired B ...
... (a ,x ) ∈ Dy . Now, since {Max } is in one-to-one correspondence with the projectors {zi }, vA can then be thought of as a valid noncontextual deterministic assignment map for {zi }. This, however, is prohibited because {zi } is a KS proof. Thus, one concludes that βL βNS − 1. The desired B ...
Quantum Copy-Protection and Quantum Money
... In classical physics, any information that can be read can be copied an unlimited number of times— which is why the makers of software, music CDs, and so on have met such severe difficulties enforcing “digital rights management” on their products (see Halderman [15] for example). Quantum states, on ...
... In classical physics, any information that can be read can be copied an unlimited number of times— which is why the makers of software, music CDs, and so on have met such severe difficulties enforcing “digital rights management” on their products (see Halderman [15] for example). Quantum states, on ...
Exponential algorithmic speedup by quantum walk Andrew M. Childs, Richard Cleve, Enrico Deotto,
... a universal quantum computer. Our goal is to simulate the unitary evolution e−iHt with H given by (5). We want to do this with the graph given to us in the form of an oracle. However, in the oracular setting, we have only been able to implement the quantum walk on a general graph using additional st ...
... a universal quantum computer. Our goal is to simulate the unitary evolution e−iHt with H given by (5). We want to do this with the graph given to us in the form of an oracle. However, in the oracular setting, we have only been able to implement the quantum walk on a general graph using additional st ...