Quantum Rotations: A Case Study in Static and Dynamic Machine
... a qubit. The initial state s1 rotates θ radians about the Z-axis. The resultant state, s2 , maintains the same superposition but has a phase shifted by θ. act on a single qubit. An accessible example is the quantum NOT gate which performs a 180 degree rotation about the X- axis. When applied to a cl ...
... a qubit. The initial state s1 rotates θ radians about the Z-axis. The resultant state, s2 , maintains the same superposition but has a phase shifted by θ. act on a single qubit. An accessible example is the quantum NOT gate which performs a 180 degree rotation about the X- axis. When applied to a cl ...
Quantum information processing by nuclear magnetic resonance
... by taking advantage of the very ensemble nature of the system which gave rise to it in the first place. Namely, we define a ‘‘pseudopure’’ ensemble to be one in which the sum of the nuclear magnetic moments over all the molecules present in the sample yields a system of moments proportional to that ...
... by taking advantage of the very ensemble nature of the system which gave rise to it in the first place. Namely, we define a ‘‘pseudopure’’ ensemble to be one in which the sum of the nuclear magnetic moments over all the molecules present in the sample yields a system of moments proportional to that ...
Quantum Computer Compilers - Computer Science, Columbia
... The Future of Quantum Hardware • The future does not necessarily belong to the ion trappers: for example, electron spins in quantum dots, superconducting qubits, ultracold neutral atoms are all making impressive progress. • But ion traps have a head start, and some serious effort has been devoted t ...
... The Future of Quantum Hardware • The future does not necessarily belong to the ion trappers: for example, electron spins in quantum dots, superconducting qubits, ultracold neutral atoms are all making impressive progress. • But ion traps have a head start, and some serious effort has been devoted t ...
Quantum Chaos
... the energy levels and eigenstates of the (bound) system? For an open system, in the decay rates, in the Smatrix, in the transport properties? (lectures 1 and 2) What kind of semiclassical approximations can be used? (lecture 2) What is the longtime behaviour of a quantum system? (lecture 3) For a ...
... the energy levels and eigenstates of the (bound) system? For an open system, in the decay rates, in the Smatrix, in the transport properties? (lectures 1 and 2) What kind of semiclassical approximations can be used? (lecture 2) What is the longtime behaviour of a quantum system? (lecture 3) For a ...
How Many Query Superpositions Are Needed to Learn?
... corresponds a subset of Bn so-called consistent set and denoted by σqa . Functions in σqa are said to be consistent with tuple (q, a). In the learning game defined by protocol P , answer a to query q provides the information that the target function belongs to σqa . We also denote by Σq the set of ...
... corresponds a subset of Bn so-called consistent set and denoted by σqa . Functions in σqa are said to be consistent with tuple (q, a). In the learning game defined by protocol P , answer a to query q provides the information that the target function belongs to σqa . We also denote by Σq the set of ...
Quantum Communications in the Maritime Environment
... of classical information processing systems. These efforts in quantum information science have produced a variety of promising theoretical and experimental results with a considerable impact on the development of perfectly secure quantum communications. In this regard, “perfectly secure” communicati ...
... of classical information processing systems. These efforts in quantum information science have produced a variety of promising theoretical and experimental results with a considerable impact on the development of perfectly secure quantum communications. In this regard, “perfectly secure” communicati ...
Solutions of the Equations of Motion in Classical and Quantum
... a fixed time and it is best suited for the formulation of the quantum theory in the Schrodinger picture. The Heisenberg picture is obtained usually from the Schrodinger picture by applying the time-dependent unitary automorphism to the operator algebra. The Schrodinger picture description is not ver ...
... a fixed time and it is best suited for the formulation of the quantum theory in the Schrodinger picture. The Heisenberg picture is obtained usually from the Schrodinger picture by applying the time-dependent unitary automorphism to the operator algebra. The Schrodinger picture description is not ver ...
... that depends explicitly on the time (see Sec. 3.1, below). The aim of this paper is to show that, with an appropriate definition of the invariance of a Hamiltonian [that generalizes Eq. (2)], any conserved operator is associated with a group of unitary transformations that leave the Hamiltonian inva ...
Quantum graphs and the integer quantum Hall effect
... Quantum graphs have been the focus of much interest during the last thirty years [1–3]. These models which describe the propagation of a quantum wave within an arbitrary complex object are extremely versatile allowing the study of various interesting quantum phenomena. Quantum graphs appear in vario ...
... Quantum graphs have been the focus of much interest during the last thirty years [1–3]. These models which describe the propagation of a quantum wave within an arbitrary complex object are extremely versatile allowing the study of various interesting quantum phenomena. Quantum graphs appear in vario ...
Ground State Structure in Supersymmetric Quantum Mechanics* Qv
... A zero mode of Q is defined as an element of the kernel of Q, namely an eigenvector of H with energy zero. The index (1.8) is the number of linearly independent bosonic zero modes n + , minus the number of linearly independent fermionic zero modes n _ . Clearly i(Q + ) # 0 is a sufficient condition ...
... A zero mode of Q is defined as an element of the kernel of Q, namely an eigenvector of H with energy zero. The index (1.8) is the number of linearly independent bosonic zero modes n + , minus the number of linearly independent fermionic zero modes n _ . Clearly i(Q + ) # 0 is a sufficient condition ...
Classification of Topologically ordered Phases
... in finding and classifying the SPT phase via MPS/TPS. A key observation is that preserving symmetry in the QSRG allows us to study fix points of symmetry protected topological phases We have consider the 1- and 2-dimensional AKLT phases as the examples. ...
... in finding and classifying the SPT phase via MPS/TPS. A key observation is that preserving symmetry in the QSRG allows us to study fix points of symmetry protected topological phases We have consider the 1- and 2-dimensional AKLT phases as the examples. ...
1 = A
... J2 is the Casimir operator, which commutes with unit operator. In general case several Casimir operators may be constructed from group generators. Usually Casimir operators explicitly enter the Hamiltonian. In particular, one may use J2 instead of Δ . In some special cases Casimir operators do not e ...
... J2 is the Casimir operator, which commutes with unit operator. In general case several Casimir operators may be constructed from group generators. Usually Casimir operators explicitly enter the Hamiltonian. In particular, one may use J2 instead of Δ . In some special cases Casimir operators do not e ...
Quantum Computer - Physics, Computer Science and Engineering
... computation. i.e. we can perform any quantum computation by connecting just 1-qubit rotation gates and controlled-NOT gates (cf. any classical computation can be realized using just AND and ...
... computation. i.e. we can perform any quantum computation by connecting just 1-qubit rotation gates and controlled-NOT gates (cf. any classical computation can be realized using just AND and ...
