Hamiltonian quantum computing with superconducting qubits

Ciani, Alessandro; Terhal, Barbara M.; DiVincenzo, David P.

doi:10.1088/2058-9565/ab18dd

Cited by 9 publications

(10 citation statements)

References 60 publications

(156 reference statements)

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“…In Refs. [16,58] two physical qubits represent a site in a lattice, which can host a mobile logical qubit. The state |00 represents a vacant site, while the states |01 and |10 represent the two internal states of a present logical qubit.…”

Section: Discussionmentioning

confidence: 99%

Native three-body interaction in superconducting circuits

Pedersen

Christensen²,

Zinner

2019

Phys. Rev. Research

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We show how a superconducting circuit consisting of three identical, non-linear oscillators in series considered in terms of its electrical modes can implement a strong, native three-body interaction among qubits. Because of strong interactions, part of the qubit-subspace is coupled to higher levels. The remaining qubit states can be used to implement a restricted Fredkin gate, which in turn implements a CNOT-gate or a spin transistor. Including non-symmetric contributions from couplings to ground and external control we alter the circuit slightly to compensate, and find average fidelities for our implementation of the above gates above 99.5% with operation times on the order of a nanosecond. Additionally we show how to analytically include all orders of the cosine contributions from Josephson junctions to the Hamiltonian of a superconducting circuit.

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Section: Discussionmentioning

confidence: 99%

Native three-body interaction in superconducting circuits

Pedersen

Christensen²,

Zinner

2019

Phys. Rev. Research

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“…First, computing correlators up to constant additive errors on ground states of quasi-local Hamiltonians is -hard by the Feynman–Kitaev construction ( 38 ). Furthermore this remains true for several classes of local observables and local Hamiltonians, including one-local observables measured on ground states of nearest-neighbor two-local Hamiltonians on qubits ( 39 , 40 ) and two-local observables measured on ground states of translation invariant nearest-neighbor two-local Hamiltonians with local dimension three ( 41 ).…”

Section: On the Computational Complexity Of The Dsfmentioning

confidence: 99%

Dynamical structure factors of dynamical quantum simulators

Baez

Goihl²,

Haferkamp³

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors and, hence, offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are bounded-error quantum polynomial time (BQP)-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate-scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.

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“…First, computing correlators up to constant additive errors on ground states of quasi-local Hamiltonians is BQP-hard by the Feynman-Kitaev construction [47]. Furthermore this remains true for several classes of local observables and local Hamiltonians, including one-local observables measured on ground states of nearest-neighbour two-local Hamiltonians on qubits [48,49], and two-local observables measured on ground states of translation invariant nearest-neighbour two-local Hamiltonians with local dimension three [50].…”

Section: A Hardness For Estimating Correlators On Ground Statesmentioning

confidence: 99%

Dynamical structure factors of dynamical quantum simulators

Baez,

Goihl,

Haferkamp

et al. 2019

Preprint

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The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors; and hence offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are BQP-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available, measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.

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Hamiltonian quantum computing with superconducting qubits

Cited by 9 publications

References 60 publications

Native three-body interaction in superconducting circuits

Native three-body interaction in superconducting circuits

Dynamical structure factors of dynamical quantum simulators

Dynamical structure factors of dynamical quantum simulators

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