Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

Dodd, Jennifer L.; Nielsen, Michael A.; Bremner, Michael J.; Thew, Rob

doi:10.1103/physreva.65.040301

Cited by 121 publications

(196 citation statements)

References 16 publications

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“…We propose a number of axioms that such measures might be expected to satisfy and investigate some implications of these axioms. 8 The structure we adopt is first to describe ͑in Sec. III B 1͒ the fundamental axioms that we expect any strength measure should satisfy.…”

Section: B Axiomatic Approachmentioning

confidence: 99%

Quantum dynamics as a physical resource

et al. 2003

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How useful is a quantum dynamical operation for quantum information processing? Motivated by this question, we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of such strength measures, based on axiomatic considerations independent of state-based resources. The power of this theory is demonstrated with applications to quantum communication complexity, quantum computational complexity, and entanglement generation by unitary operations.

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Section: B Axiomatic Approachmentioning

confidence: 99%

Quantum dynamics as a physical resource

et al. 2003

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“…Concerning gates, i.e., discrete time unitary evolutions, it has been shown in the early days of quantum information theory that almost any two-qubit gate is universal [8]. Similarly, any fixed entangling two-body interaction was shown to be capable of simulating any other two-body Hamiltonian when supplemented by the set of all local unitaries [9]. The many-body analogue of this problem was solved in [10] and the efficiency of quantum simulations was studied in various contexts (cf.…”

Section: Introductionmentioning

confidence: 99%

Quantum simulations under translational symmetry

2007

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We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those that can not be simulated. Whereas for general spin systems no finite universal set of generating interactions is shown to exist, universality turns out to be generic for quadratic bosonic and fermionic nearest-neighbor interactions when supplemented by all translationally invariant onsite Hamiltonians.

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“…Repeating this procedure N times, we then get the transformation e −i(σ x q 1 σ x i 1 +σ y q 1 σ y i 1 )π/4 , which is a swap gate between q 1 and i 1 (and multiplication by −i when their states are different) [9]. In order to reduce the error, the number of repetition N can be quite large [15], therefore many local gates (44N in total) are needed. The interaction time needed is π/2J xy .…”

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confidence: 99%

Quantum Computation with Untunable Couplings

et al. 2002

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Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme to remove the necessity of switching the couplings between qubits for two bit gates, which are more costly in many cases. Our strategy is to compute in and out of carefully designed interaction free subspaces analogous to decoherence free subspaces, which allows us to effectively turn off and turn on the interactions between the encoded qubits. We give two examples to show how universal quantum computation is realized in our scheme with local manipulations to physical qubits only, for both diagonal and off diagonal interactions. Quantum computation is generally formulated in terms of a collection of qubits subject to a sequence of single and two bit operations [1]. This implies that the effective local fields applied to individual qubits, and the couplings between the qubits, are variable functions subject to external control. In many cases, two bit operations, whose implementation depends on certain interactions between qubits, are more difficult than single bit gates. They can require more sophisticated manipulations, therefore may take a longer time and cause stronger decoherence. This usually results from the requirement to vary (in the simplest case just switch on and off) the couplings between qubits, which is not always possible, or easy to realize. One such example is quantum computing with Josephson junction devices, both charge and flux type [2,3,4,5,6]. In this case, the coupling between qubits is most naturally realized with a hard wired capacitor or inductor, whose value is fixed by the fabrication and cannot be tuned during the computation. The superconducting quantum computing community has been working hard to devise variable coupling schemes [5,7,8,9], but it is generally agreed that none of these proposed switches is completely satisfactory [9]. Most of them [5,7] require external controls, thus are likely to be major decoherence sources. Others were designed to avoid such external controls, but may suffer other problems, for instance the number of qubits that can be incorporated into the system can be limited [8,9], which is at odd with the supposed scalability of a solid state quantum computer.An always on and un-tunable coupling causes certain problems for quantum computation, depending on the particular form of the interaction. If the interaction Hamiltonian is diagonal in the computational basis, each qubit state will gain additional phases depending on the states of the qubits to which it is coupled, even in the idle mode. It is then necessary to keep track of these phases, or suppress them by repeated refocusing pulses like those used in NMR, which requires high precisions and complicates the operation [8,9]. The situation is more serious in the case of off diagonal interactions, because these interactions will cause the states of the qubits to propaga...

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Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

Cited by 121 publications

References 16 publications

Quantum dynamics as a physical resource

Quantum dynamics as a physical resource

Quantum simulations under translational symmetry

Quantum Computation with Untunable Couplings

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