Quantum gates with controlled adiabatic evolutions

Hen, Itay

doi:10.1103/physreva.91.022309

Cited by 32 publications

(50 citation statements)

References 29 publications

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“…The target subsystem will be evolved by a complete set {P k } of orthogonal projectors over T , which satisfy P k P m = δ km P k and k P k = 1. In a controlled adiabatic dynamics, the composite system T A will be governed by a Hamiltonian in the form [63] H…”

Section: Adiabatic and Counter-diabatic Controlled Quantum Dynamicsmentioning

confidence: 99%

“…Let us begin by considering T as a single qubit and a single-qubit gate as an arbitrary rotation of angle φ around a directionn over the Bloch sphere. Under this consideration, the Hamiltonian that adiabatically implements such a single-qubit gate for an arbitrary input state |ψ = a|0 + b|1 , with a, b ∈ C, is given by [63] H sg (s) = P + ⊗ H 0 (s)…”

Section: Quantum Computation Via Adiabatic Controlled Evolutionsmentioning

confidence: 99%

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Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

Santos¹,

Sarandy²

2017

J. Phys. A: Math. Theor.

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Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counterdiabatic evolutions, higher speed comes at higher energy cost. Here, the counterdiabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.

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Section: Adiabatic and Counter-diabatic Controlled Quantum Dynamicsmentioning

confidence: 99%

Section: Quantum Computation Via Adiabatic Controlled Evolutionsmentioning

confidence: 99%

Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

Santos¹,

Sarandy²

2017

J. Phys. A: Math. Theor.

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“…As a second application, we have studied adiabatic and counter-diabatic implementations of single-qubit quantum gates in NMR. By using a generalized approach for TQD, we have addressed the problem of the feasibility of the shortcuts to adiabaticity, as provided by TQD protocols, in the context of quantum computation via controlled evolutions [7,24]. By using the generalized TQD Hamiltonian [29], we have presented the optimal solution in terms of pulse sequence and resources to implement fast quantum gates red through counter-diabatic (transitionless) quantum computation with high fidelity, as shown in Fig.…”

Section: Discussionmentioning

confidence: 99%

Optimizing NMR quantum information processing via generalized transitionless quantum driving

Santos

Nicotina

Souza

et al. 2020

EPL

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High performance quantum information processing requires efficient control of undesired decohering effects, which are present in realistic quantum dynamics. To deal with this issue, a powerful strategy is to employ transitionless quantum driving (TQD), where additional fields are added to speed up the evolution of the quantum system, achieving a desired state in a short time in comparison with the natural decoherence time scales. In this paper, we provide an experimental investigation of the performance of a generalized approach for TQD to implement shortcuts to adiabaticity in nuclear magnetic resonance (NMR). As a first discussion, we consider a single nuclear spin-1 2 system in a time-dependent rotating magnetic field. While the adiabatic dynamics is violated at a resonance situation, the TQD Hamiltonian is shown to be robust against resonance, allowing us to mimic the adiabatic behavior in a fast evolution even under the resonant configurations of the original (adiabatic) Hamiltonian. Moreover, we show that the generalized TQD theory requires less energy resources, with the strength of the magnetic field less than that required by standard TQD. As a second discussion, we analyze the experimental implementation of shortcuts to single-qubit adiabatic gates. By adopting generalized TQD, we can provide feasible time-independent driving Hamiltonians, which are optimized in terms of the number of pulses used to implement the quantum dynamics. The robustness of adiabatic and generalized TQD evolutions against typical decoherence processes in NMR is also analyzed.

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“…And the initial states for both algorithms are eigenstates of the controlled Hamiltonians, respectively. The difference is that our algorithm is based on a resonance mechanism to obtain the ground state of a system, it starts from the target Hamiltonian directly; while the algorithm in [27], the desired quantum state is reached through a controlled adiabatic evolution.…”

Section: Discussionmentioning

confidence: 99%

Quantum algorithm for preparing the ground state of a system via resonance transition

Wang

2017

Sci Rep

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Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary qubit, by introducing a resonance mechanism between the ancilla qubit and the system, and combined with measurements performed on the ancilla qubit, the system can be evolved to monotonically converge to its ground state through an iterative procedure. We have simulated the application of this algorithm for the Afflect-Kennedy-Lieb-Tasaki model, whose ground state can be used as resource state in one-way quantum computation.

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Quantum gates with controlled adiabatic evolutions

Cited by 32 publications

References 29 publications

Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

Generalized shortcuts to adiabaticity and enhanced robustness against decoherence

Optimizing NMR quantum information processing via generalized transitionless quantum driving

Quantum algorithm for preparing the ground state of a system via resonance transition

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