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We study the quantum computational power of a generic class of anisotropic solid state Hamiltonians. A universal set of encoded logic operations are found which do away with difficult-to-implement single-qubit gates in a number of quantum computer proposals, e.g., quantum dots and donor atom spins with anisotropic exchange coupling, quantum Hall systems, and electrons floating on helium.We show how to make the corresponding Hamiltonians universal by encoding one qubit into two physical qubits, and by controlling nearest neighbor interactions.
We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of multiple patte
For superconducting qubits, microwave pulses drive rotations around the Bloch sphere. The phase of these drives can be used to generate zero-duration arbitrary virtual Z-gates which, combined with two $X_{pi/2}$ gates, can generate any SU(2) gate. He
Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class--number-phase codes--which inclu
We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of weak pair