CS286.2 Lectures 5-6: Introduction to Hamiltonian Complexity, QMA
... Theorem 11. (Kempe-Kitaev-Regev) 2 − LHa,b is QMA-complete for some a = 2− poly(n) and b = 1/ poly(n). The first result along these lines came from Kitaev, who showed that 5 − LH is QMA-complete. We shall show a slightly weaker version of the theorem, which will contain all the key ideas: Theorem 12 ...
... Theorem 11. (Kempe-Kitaev-Regev) 2 − LHa,b is QMA-complete for some a = 2− poly(n) and b = 1/ poly(n). The first result along these lines came from Kitaev, who showed that 5 − LH is QMA-complete. We shall show a slightly weaker version of the theorem, which will contain all the key ideas: Theorem 12 ...
Gentzen-Like Methods in Quantum Logic*
... sense, quantum logic has a logical status similar to other non-classical logics like, say, intuitionistic logic or minimal logic, independent of its physical heritage. Let us recall that an orthomodular lattice is a Boolean lattice in which the distributive laws are no longer stipulated, and in whic ...
... sense, quantum logic has a logical status similar to other non-classical logics like, say, intuitionistic logic or minimal logic, independent of its physical heritage. Let us recall that an orthomodular lattice is a Boolean lattice in which the distributive laws are no longer stipulated, and in whic ...
PDF
... Advances in programming languages are often driven by advances in compiler design, and vice versa. In the case of quantum computation, the situation is complicated by the fact that no practical quantum hardware exists yet, and not much is known about the detailed architecture of any future quantum h ...
... Advances in programming languages are often driven by advances in compiler design, and vice versa. In the case of quantum computation, the situation is complicated by the fact that no practical quantum hardware exists yet, and not much is known about the detailed architecture of any future quantum h ...
Computing prime factors with a Josephson phase qubit quantum
... this algorithm involves the challenge of combining both single- and coupled-qubit gates in a meaningful sequence. We constructed the full factoring sequence by first performing automatic calibration of the individual gates and then combined them, without additional tuning, so as to factor the compos ...
... this algorithm involves the challenge of combining both single- and coupled-qubit gates in a meaningful sequence. We constructed the full factoring sequence by first performing automatic calibration of the individual gates and then combined them, without additional tuning, so as to factor the compos ...
EnvCalc_Output_Variable_Description
... Description of EnvCalc Output Variables The following brief descriptions of variables are intended for quick reference, not necessarily to tell you everything you need to know to understand how a variable is calculated. The logic of the calculation of environmental variables is detailed in Chapter 4 ...
... Description of EnvCalc Output Variables The following brief descriptions of variables are intended for quick reference, not necessarily to tell you everything you need to know to understand how a variable is calculated. The logic of the calculation of environmental variables is detailed in Chapter 4 ...
Why physics does not preclude free will
... opposed to standard QM: that is not possible, since they both yield exactly the same observable predictions. (Argument from simplicity is unreliable; specifics given later if time allows.) Note that I don’t claim that any particular experiment (at the nonrelativistic level*) corroborates TI, since a ...
... opposed to standard QM: that is not possible, since they both yield exactly the same observable predictions. (Argument from simplicity is unreliable; specifics given later if time allows.) Note that I don’t claim that any particular experiment (at the nonrelativistic level*) corroborates TI, since a ...
Single photon nonlinear optics in photonic crystals
... The structure consists of a linear three-hole defect cavity in a triangular photonic crystal lattice, as shown in Fig.1(a). It is fabricated in GaAs and contains a central layer of InAs quantum dots and has a quality factor Q = 104 . The temperature of the structure is scanned by a heating laser.14 ...
... The structure consists of a linear three-hole defect cavity in a triangular photonic crystal lattice, as shown in Fig.1(a). It is fabricated in GaAs and contains a central layer of InAs quantum dots and has a quality factor Q = 104 . The temperature of the structure is scanned by a heating laser.14 ...
propagation methods for quantum molecular dynamics
... space, such as the potential, are calculated on the grid points while nonlocal operators, such as the kinetic energy operator, are calculated in the functional space (27). They are then recast into the same grid points. The discretization schemedetermines the domainof values of the operator I~. For ...
... space, such as the potential, are calculated on the grid points while nonlocal operators, such as the kinetic energy operator, are calculated in the functional space (27). They are then recast into the same grid points. The discretization schemedetermines the domainof values of the operator I~. For ...
coherent states in quantum mechanics
... In classical physics the properties of a certain system can be described using its position x and mass m. With these variables it is possible to determine the velocity v(=dx/dt), the momentum p(=mv) and any other dynamical variable of interest. Quantum mechanics describes the time evolution of physi ...
... In classical physics the properties of a certain system can be described using its position x and mass m. With these variables it is possible to determine the velocity v(=dx/dt), the momentum p(=mv) and any other dynamical variable of interest. Quantum mechanics describes the time evolution of physi ...
6 Wave equation in spherical polar coordinates
... This is another example of a BC (periodic in this case) quantising a separation constant. In principle m can take any integer value between −∞ and ∞. It turns out in Quantum Mechanics that m is the integer magnetic quantum number and −l ≤ m ≤ l for the z-component of angular momentum. In that contex ...
... This is another example of a BC (periodic in this case) quantising a separation constant. In principle m can take any integer value between −∞ and ∞. It turns out in Quantum Mechanics that m is the integer magnetic quantum number and −l ≤ m ≤ l for the z-component of angular momentum. In that contex ...
“Mind the gap” Solving optimization problems with a
... Quantum computer: qubit: linear superposition of 0 and 1. N qubits: linear superposition of 2N basis states Actions on the quantum state act on all 2N basis states Quantum Parallelism ...
... Quantum computer: qubit: linear superposition of 0 and 1. N qubits: linear superposition of 2N basis states Actions on the quantum state act on all 2N basis states Quantum Parallelism ...
