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arXiv:0811.4245 · Physical Review A

Globally controlled universal quantum computation with arbitrary subsystem dimension

Gerardo A. Paz-Silva, Gavin K. Brennen, Jason Twamley

Published Nov 12, 2009• 5 citations
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Abstract

We present a scheme to perform universal quantum computation using global control with an arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array, using only mirror-symmetric logical encoding, global pulses for single subsystem operations, uniform Ising-type interaction, and an all zero initial pure state. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.

DOI
10.1103/physreva.80.052318

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We present a scheme to perform universal quantum computation using global control with an arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension NNN-element array, using only mirror-symmetric logical encoding, global pulses for single subsystem operations, uniform Ising-type interaction, and an all zero initial pure state. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.
We describe a new design for a q wire with perfect transmission using a uniformly coupled Ising spin chain subject to global pulses. In addition to allowing for the perfect transport of single qubits, the design also yields the perfect "mirroring" of multiply encoded qubits within the wire. We further utilize this global-pulse generated perfect mirror operation as a "clock cycle" to perform universal quantum computation on these multiply encoded qubits where the interior of the q wire serves as the quantum memory while the q-wire ends perform one- and two-qubit gates.
We develop a model for quantum computation with Rydberg atom arrays, which only relies on global driving, without the need of local addressing of the qubits: any circuit is executed by a sequence of global, resonant laser pulses on a static atomic arrangement. We present two constructions: for the first, the circuit is imprinted in the trap positions of the atoms and executed by the pulses; for the second, the atom arrangement is circuit-independent, and the algorithm is entirely encoded in the global driving sequence. Our results show in particular that a quadratic overhead in atom number is sufficient to eliminate the need for local control to realize a universal quantum processor. We give explicit protocols for all steps of an arbitrary quantum computation, and discuss strategies for error suppression specific to our model. Our scheme is based on dual-species processors with atoms subjected to Rydberg blockade constraints, but it might be transposed to other setups as well.
We characterize a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and ancillary qubits. No additional access is required to the computational register and the dynamics of both the register and ancilla are unitary. This scheme is inspired by the measurement-based ancilla-driven quantum computation of Anders et al. [Phys. Rev. A 82, 020301(R) (2010)], but does not require measurements of the ancillas, and in this respect is similar to the original gate-based model of quantum computation. We consider what possible forms this ancilla-register interaction can take, with a proof that the interaction is necessarily locally equivalent to swap combined with an entangling controlled gate. We further show which Hamiltonians can create such interactions and discuss two examples; the two-qubit XY Hamiltonian and a particular case of the XXZ Hamiltonian. We then give an example of a simple, finite, and fault-tolerant gate set for universal quantum computation in this model.
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally applied transformations. Here we demonstrate the minimum physical requirements for such an approach: a one-dimensional array composed of two alternating ``types'' of two-state system. Each system need be sensitive only to the net state of its nearest neighbors, i.e. the number in state $``\ensuremath{\uparrow}''$ minus the number in $``\ensuremath{\downarrow}.''$ Additionally, we show that all such arrays can perform quite general parallel operations. A broad range of physical systems and interactions is suitable: we highlight two examples.
We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spin-orbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single-qubit rotations or controlled-Not gates scales as the inverse of a dimensionless measure of the degree of control of spin-orbit coupling.