Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

Goto, Hayato

doi:10.1038/srep21686

Cited by 196 publications

(310 citation statements)

References 35 publications

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“…In the studies by Goto ( 30 , 31 ), a system of N KPOs coupled via a term of the form

\sum_{italicn italicm} J_{italicn italicm} a_{n}^{†} a_{m}

was considered. It was shown, using perturbation theory, that as the two-photon drive strength of each KPO is varied from ε = 0 to ε ≫ |Δ|, the multimode vacuum

false| 0_{1}, 0_{2}, \dots, 0_{N} 〉

is adiabatically connected to a multimode cat state of the form

\frac{1}{\sqrt{2}} false(false| s_{1} normalα, s_{2} normalα, \dots, s_{N} normalα true〉 + false| - s_{1} normalα, - s_{2} normalα, \dots, - s_{N} normalα true〉 false)

where s 1 , …, s N ∈ {−1,1} are such that the Ising energy − ∑ n , m J nm s n s m is minimized.…”

Section: Resultsmentioning

confidence: 99%

Robust quantum optimizer with full connectivity

2017

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“…In the studies by Goto ( 30 , 31 ), a system of N KPOs coupled via a term of the form

\sum_{italicn italicm} J_{italicn italicm} a_{n}^{†} a_{m}

was considered. It was shown, using perturbation theory, that as the two-photon drive strength of each KPO is varied from ε = 0 to ε ≫ |Δ|, the multimode vacuum

false| 0_{1}, 0_{2}, \dots, 0_{N} 〉

is adiabatically connected to a multimode cat state of the form

\frac{1}{\sqrt{2}} false(false| s_{1} normalα, s_{2} normalα, \dots, s_{N} normalα true〉 + false| - s_{1} normalα, - s_{2} normalα, \dots, - s_{N} normalα true〉 false)

where s 1 , …, s N ∈ {−1,1} are such that the Ising energy − ∑ n , m J nm s n s m is minimized.…”

Section: Resultsmentioning

confidence: 99%

Robust quantum optimizer with full connectivity

2017

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“…(13) with an (a † a) 2 term [66], known as the cavity self-Kerr. There is interest in using networks of such nonlinear cavities to perform quantum computation [67,68].…”

Section: Stabilisation Of Cat Statesmentioning

confidence: 99%

Applications of the Fokker-Planck equation in circuit quantum electrodynamics

Elliott

Ginossar

2016

Phys. Rev. A

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We study exact solutions of the steady state behaviour of several non-linear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planck equations in the generalised P -representation we investigate the analytical solutions of two fundamental models. First, we solve for the steady-state response of a linear cavity that is coupled to an approximate transmon qubit and use this solution to study both the weak and strong driving regimes, using analytical expressions for the moments of both cavity and transmon fields, along with the Husimi Q-function for the transmon. Second, we revisit exact solutions of quantum Duffing oscillator which is driven both coherently and parametrically while also experiencing decoherence by the loss of single and pairs of photons. We use this solution to discuss both stabilisation of Schrödinger cat states and the generation of squeezed states in parametric amplifiers, in addition to studying the Q-functions of the different phases of the quantum system. The field of superconducting circuits, with its strong nonlinearities and couplings, has provided access to new parameter regimes in which returning to these exact quantum optics methods can provide valuable insights.

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“…Several aspects of the dynamics of a parametric oscillator in the quantum regime have been studied theoretically, cf. [14][15][16][17][18][19][20][21], and in experiments, cf. [22][23][24].…”

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confidence: 99%

Time-translation-symmetry breaking in a driven oscillator: From the quantum coherent to the incoherent regime

et al. 2017

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We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. Such systems are intermediate between large closed systems and small dissipative systems, which both display the symmetry breaking, but have qualitatively different dynamics. As a nontrivial example we consider period tripling in a quantum nonlinear oscillator. We show that, for moderately strong driving, the period tripling is robust on an exponentially long time scale, which is further extended by an even weak decoherence.The breaking of translation symmetry in time, first proposed by Wilczek [1], has been attracting much attention recently. Such symmetry breaking can occur only away from thermal equilibrium [2]. It is of particular interest for periodically driven systems, which have a discrete time-translation symmetry imposed by the driving. Here, the time symmetry breaking is manifested in the onset of oscillations with a period that is a multiple of the driving period t F . Oscillations with period 2t F due to simultaneously initialized protected boundary states were studied in photonic quantum walks [3]; period-two oscillations can also be expected from the coexistence of Floquet Majorana fermions with quasienergies 0 and π/t F in a cold-atom system [4]. The onset of periodtwo phases was predicted and analyzed [5][6][7][8][9][10] in Floquet many-body localized systems, and the first observations of oscillations at multiples of the driving period in disordered systems were reported [11,12].In systems coupled to a thermal bath, on the other hand, the effect of period doubling has been well-known. A textbook example is a classical oscillator modulated close to twice its eigenfrequency and displaying vibrations with period 2t F [13]. The oscillator has two states of such vibrations; they have opposite phases, reminiscent of a ferromagnet with two orientations of the magnetization. Several aspects of the dynamics of a parametric oscillator in the quantum regime have been studied theoretically, cf. [14][15][16][17][18][19][20][21], and in experiments, cf. [22][23][24]. For a sufficiently strong driving field, a quantum dissipative oscillator, like a classical oscillator, mostly performs vibrations with period 2t F . The interplay of quantum fluctuations and dissipation leads to transitions between the period-two vibrational states, but the rate of these transitions is exponentially small [18].The goal of this paper is to study time symmetry breaking in isolated or almost isolated driven quantum systems with a few degrees of freedom. They are intermediate between large closed systems and dissipative systems, where the nature of the symmetry breaking is very different. To this end, we analyze a driven nonlinear quantum oscillator. Time symmetry breaking in this system should not be limited to period doubling. As an illustration of a behavior qualitatively different from period doubling, we consider period tripling and find the conditions where it occurs. We also address the role of decoherence and the co...

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Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

Cited by 196 publications

References 35 publications

Robust quantum optimizer with full connectivity

Robust quantum optimizer with full connectivity

Applications of the Fokker-Planck equation in circuit quantum electrodynamics

Time-translation-symmetry breaking in a driven oscillator: From the quantum coherent to the incoherent regime

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