Analytic pulse-sequence construction for exchange-only quantum computation

Zeuch, Daniel; Cipri, Robert; Bonesteel, N. E.

doi:10.1103/physrevb.90.045306

Cited by 12 publications

(44 citation statements)

References 32 publications

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“…Ultimately, a three electron-spin encoding allows for full qubit control without any magnetic fields and without relying on the spin-orbit coupling, but with the electrically controllable exchange interaction only [15][16][17][18] . The exchange-only scheme requires the exchange coupling between pairs of spins to be switched on only for a short period of time.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric resonant exchange qubit under the influence of electrical noise

Russ

Burkard

2015

Phys. Rev. B

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We investigate the influence of electrical charge noise on a resonant exchange (RX) qubit in a triple quantum dot. This RX qubit is a variation of the exchange-only spin qubit which responds to a narrow-band resonant frequency. Our noise model includes uncorrelated charge noise in each quantum dot giving rise to two independent (noisy) bias parameters ε and ∆. We calculate the energy splitting of the two qubit states as a function of these two bias detuning parameters to find "sweet spots", where the qubit is least susceptible to noise. Our investigation shows that such sweet spots exist within the low bias regime, in which the bias detuning parameters have the same magnitude as the hopping parameters. The location of the sweet spots in the (ε, ∆) plane depends on the hopping strength and asymmetry between the quantum dots. In the regime of weak charge noise, we identify a new favorable operating regime for the RX qubit based on these sweet spots.

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Section: Introductionmentioning

confidence: 99%

Asymmetric resonant exchange qubit under the influence of electrical noise

Russ

Burkard

2015

Phys. Rev. B

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“…It should be noted that all sequences were discovered using a numerical minimization algorithm due to the very large Hilbert space for six spins-1 2 (dimension 2 6 = 64). A full understanding and analytical derivation of the path through the Hilbert space associated with the exact cnot gate has subsequently been found [13,231].…”

Section: Using Short-ranged Exchangementioning

confidence: 99%

“…Both of these interaction types can be expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses [2,11,12,13,14,15], while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances [16,17]. The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection of the qubit to several sources of noise [2,18,10,19].…”

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confidence: 99%

Three-electron spin qubits

Russ

Burkard

2017

J. Phys.: Condens. Matter

102

117

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The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the exchange-only qubit (Bacon et al 2000 Phys. Rev. Lett. 85 1758-61, DiVincenzo et al 2000 Nature 408 339) and its derived versions, e.g. the resonant exchange (RX) qubit, but we also discuss other qubit implementations using three electron spins. For each three-spin qubit we describe the qubit model, the envisioned physical realization, the implementations of single-qubit operations, as well as the read-out and initialization schemes. Two-qubit gates and decoherence properties are discussed for the RX qubit and the exchange-only qubit, thereby completing the list of requirements for quantum computation for a viable candidate qubit implementation. We start by describing the full system of three electrons in a triple quantum dot, then discuss the charge-stability diagram, restricting ourselves to the relevant subsystem, introduce the qubit states, and discuss important transitions to other charge states (Russ et al 2016 Phys. Rev. B 94 165411). Introducing the various qubit implementations, we begin with the exchange-only qubit (DiVincenzo et al 2000 Nature 408 339, Laird et al 2010 Phys. Rev. B 82 075403), followed by the RX qubit (Medford et al 2013 Phys. Rev. Lett. 111 050501, Taylor et al 2013 Phys. Rev. Lett. 111 050502), the spin-charge qubit (Kyriakidis and Burkard 2007 Phys. Rev. B 75 115324), and the hybrid qubit (Shi et al 2012 Phys. Rev. Lett. 108 140503, Koh et al 2012 Phys. Rev. Lett. 109 250503, Cao et al 2016 Phys. Rev. Lett. 116 086801, Thorgrimsson et al 2016 arXiv:1611.04945). The main focus will be on the exchange-only qubit and its modification, the RX qubit, whose single-qubit operations are realized by driving the qubit at its resonant frequency in the microwave range similar to electron spin resonance. Two different types of two-qubit operations are presented for the exchange-only qubits which can be divided into short-ranged and long-ranged interactions. Both of these interaction types are expected to be necessary in a large-scale quantum computer. The short-ranged interactions use the exchange coupling by placing qubits next to each other and applying exchange-pulses (DiVincenzo et al 2000 Nature 408 339, Fong and Wandzura 2011 Quantum Inf. Comput. 11 1003, Setiawan et al 2014 Phys. Rev. B 89 085314, Zeuch et al 2014 Phys. Rev. B 90 045306, Doherty and Wardrop 2013 Phys. Rev. Lett. 111 050503, Shim and Tahan 2016 Phys. Rev. B 93 121410), while the long-ranged interactions use the photons of a superconducting microwave cavity as a mediator in order to couple two qubits over long distances (Russ and Burkard 2015 Phys. Rev. B 92 205412, Srinivasa et al 2016 Phys. Rev. B 94 205421). The nature of the three-electron qubit states each having the same total spin and total spin in z-direction (same Zeeman energy) provides a natural protection against several sources of noise (DiVincenzo et al 2000 Nature 408 339, Taylor et al 2013 Phys. R...

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“…Returning to symmetric group irreps, and henceforth overloading Young diagrams to denote symmetric group irreps directly, notice that irrep has one extra dimension and irrep has five extra dimensions outside of the images of representation ⊗ under the intertwiners of Eqs. (18)(19). The extra dimension in irrep and one of the extra dimensions in irrep each correspond to the image of representation ⊗ under the respective intertwiner implied by Theorem 1 for λ = µ = , which is associated with states for which each block has total spin 3/2.…”

Section: Representation Theorymentioning

confidence: 99%

“…Surprisingly this exact spin-independent solution was simpler, in terms of the number of exchange gates and their analytic coefficients, than that of the original spin-dependent solutions. Since then several other spin-independent, exchange-only CNOT gates have been found [17,18].…”

Section: Introductionmentioning

confidence: 99%

Approximate exchange-only entangling gates for the three-spin-1/2decoherence-free subsystem

Meter

Knill

2019

Phys. Rev. A

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The three-spin-1/2 decoherence-free subsystem defines a logical qubit protected from collective noise and supports exchange-only universal gates. Such logical qubits are well-suited for implementation with electrically-defined quantum dots. Exact exchange-only entangling logical gates exist but are challenging to construct and understand. We use a decoupling strategy to obtain straightforward approximate entangling gates. A benefit of the strategy is that if the physical spins are aligned, then it can implement evolution under entangling Hamiltonians. Hamiltonians expressible as linear combinations of logical Pauli products not involving σ y can be implemented directly. Self-inverse gates that are constructible from these Hamiltonians, such as the CNOT, can be implemented without the assumption on the physical spins. We compare the control complexity of implementing CNOT to previous methods and find that the complexity for fault-tolerant fidelities is competitive.

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Analytic pulse-sequence construction for exchange-only quantum computation

Cited by 12 publications

References 32 publications

Asymmetric resonant exchange qubit under the influence of electrical noise

Asymmetric resonant exchange qubit under the influence of electrical noise

Three-electron spin qubits

Approximate exchange-only entangling gates for the three-spin-1/2decoherence-free subsystem

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