Experimental Realization of a Compressed Quantum Simulation of a 32-Spin Ising Chain

Li, Zhaokai; Zhou, Hui; Ju, Chenyong; Chen, Hongwei; Zheng, Wenqiang; Lu, Dawei; Rong, Xing; Duan, Chang‐Kui; Peng, Xinhua; Du, Jiangfeng

doi:10.1103/physrevlett.112.220501

Cited by 40 publications

(40 citation statements)

References 26 publications

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“…Now we turn to the experimental implementation of the quantum algorithm for OCR. The widely utilized nuclear magnetic resonance (NMR) technique [20][21][22][23][24] is employed to realize the four-qubit quantum processor. The experi ments are carried out on a Bruker AV-400 spectrometer at 306 K. The sample used is the l3C-iodotrifluroethylene (C2F3I) dissolved in t/-chloroform, which consists of a 13C nuclear spin and three 19F nuclear spins.…”

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confidence: 99%

Experimental Realization of a Quantum Support Vector Machine

et al. 2015

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The fundamental principle of artificial intelligence is the ability of machines to learn from previous experience and do future work accordingly. In the age of big data, classical learning machines often require huge computational resources in many practical cases. Quantum machine learning algorithms, on the other hand, could be exponentially faster than their classical counterparts by utilizing quantum parallelism. Here, we demonstrate a quantum machine learning algorithm to implement handwriting recognition on a four-qubit NMR test bench. The quantum machine learns standard character fonts and then recognizes handwritten characters from a set with two candidates. Because of the wide spread importance of artificial intelligence and its tremendous consumption of computational resources, quantum speedup would be extremely attractive against the challenges of big data.

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Section: )mentioning

confidence: 99%

Experimental Realization of a Quantum Support Vector Machine

et al. 2015

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“…Said differently, the KZM can be extended to account for the full distribution of topological defects.The quantum Ising model in a transverse field.-As a paradigmatic model of a quantum phase transition we consider the one dimensional quantum Ising model [25,26]. The Hamiltonian of a chain of N spins in a transverse magnetic field g reads,Its experimental study is amenable via quantum simulation that has been reported in a variety of platforms including trapped ions, [27,28], superconducting circuits [29,30], Rydberg gases [31], and NMR experiments [32]. We consider periodic boundary conditions σ N+1 = σ 1 with even N, for simplicity.…”

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confidence: 99%

Universal Statistics of Topological Defects Formed in a Quantum Phase Transition

Campo

2018

Phys. Rev. Lett.

104

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When a quantum phase transition is crossed in finite time, critical slowing down leads to the breakdown of adiabatic dynamics and the formation of topological defects. The average density of defects scales with the quench rate following a universal power-law predicted by the Kibble-Zurek mechanism. We analyze the full counting statistics of kinks and report the exact kink number distribution in the transverse-field quantum Ising model. Kink statistics is described by the Poisson binomial distribution with all cumulants exhibiting a universal power-law scaling with the quench rate. In the absence of finite-size effects, the distribution approaches a normal one, a feature that is expected to apply broadly in systems described by the Kibble-Zurek mechanism.Across a quantum phase transition, the equilibrium relaxation time diverges. This phenomenon, known as critical slowing down, is responsible for the nonadiabatic character of critical dynamics. Preparing the ground state of the brokensymmetry phase, an ubiquitous task in quantum science and technology, is thus intrinsically challenging: traversing the phase transition in finite time leads to the formation of topological defects. The Kibble-Zurek mechanism (KZM) is the paradigmatic theory to describe this scenario [1][2][3]. Its origins are found in the pioneering insight by Kibble on the role of causality in structure formation in the early universe [4,5]. Soon after, it was pointed out by Zurek that condensed-matter systems offer a test-bed to study the dynamics of symmetry breaking [6][7][8]. The key prediction of the KZM is that the average density d of the resulting topological defects scales with the quench time τ Q in which the phase transition is crossed as a universal power-law, d ∝ τ −α Q . The power-law exponent α = Dν/(1 + νz) is set by a combination of the dimensionality of the system D, and the dynamic and correlation-length (equilibrium) critical exponents denoted by z and ν, respectively.The validity of the KZM is however not restricted to the classical domain. The paradigmatic Landau-Zener formula, describing excitation formation in two-level systems, was shown to capture the KZM for long quench times [9,10]. As a result, paradigmatic models exhibiting quantum phase transitions, such as the 1D Ising chain, could be shown to obey the KZM, establishing the validity of the mechanism in the quantum domain for thermally isolated systems [9][10][11][12]. Due to its broad applicability, the KZM stands out as a result in statistical mechanics describing nonequilibrium properties (density of defects) in terms of equilibrium quantities (critical exponents). On the applied side, it suggest the need to pursue adiabatic strategies in quantum simulations as well as in quantum annealing, where the mechanism provides useful heuristics.Under unitary dynamics the state of the system following the crossing of the phase transition is characterized by collective and coherent quantum excitations. One can thus expect that even for isolated quantum systems, the order para...

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“…Eq. (46) is valid in the time scale in which we neglect internal relaxation in the ground state subspace. This is possible since we have a separation of the time scales: the prefactor κ(E j ) in W (j,0 1 )→g and W (j,0 1 )→0 is ruled by the gap κ(E j ) κ(E gap ) and, at the same time, the overlap factor χ ± (j,0 1 ) involves a delocalized, extended state in the chain with one localized state at the end.…”

Section: Results For the Transverse Ising Modelmentioning

confidence: 99%

Decoherence and relaxation of topological states in extended quantum Ising models

2019

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We study the decoherence and the relaxation dynamics of topological states in an extended class of quantum Ising chains which can present a multidimensional ground state subspace. The leading interaction of the spins with the environment is assumed to be the local fluctuations of the transverse magnetic field. By deriving the Lindblad equation using the many-body states, we investigate the relation between decoherence, energy relaxation and topology. In particular, in the topological phase and at low temperature, we analyze the dephasing rates between the different degenerate ground states.

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Experimental Realization of a Compressed Quantum Simulation of a 32-Spin Ising Chain

Cited by 40 publications

References 26 publications

Experimental Realization of a Quantum Support Vector Machine

Experimental Realization of a Quantum Support Vector Machine

Universal Statistics of Topological Defects Formed in a Quantum Phase Transition

Decoherence and relaxation of topological states in extended quantum Ising models

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