Defects in Quantum Computers

Gardas, Bartłomiej; Dziarmaga, Jacek; Zurek, Wojciech H.; Zwolak, Michael

doi:10.1038/s41598-018-22763-2

Cited by 96 publications

(80 citation statements)

References 20 publications

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“…By studying the growth of spatial correlations while crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) [7-9] for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models [10,11], providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories [12,13] and applications to quantum optimization [14,15].The celebrated Kibble-Zurek mechanism [2, 3] describes nonequilibrium dynamics and the formation of topological defects in a second-order phase transition driven by thermal fluctuations, and has been experimentally verified in a wide variety of physical systems [4,5]. Recently, the concepts underlying the Kibble-Zurek description have been extended to the quantum regime [7][8][9].…”

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confidence: 99%

“…By studying the growth of spatial correlations while crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) [7][8][9] for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models [10,11], providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories [12,13] and applications to quantum optimization [14,15].…”

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confidence: 99%

“…While QKZM has many important implications, e.g. in quantum information science [14], its experimental verification is challenging due to the coupling of many-body systems to the environment [15]. Recently, experimental control over isolated quantum systems enabled the observation of scaling behavior across quantum phase transitions described by mean-field theories [16,17].…”

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confidence: 99%

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Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Keesling

Omran

Levine

et al. 2019

Nature

489

379

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Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations [1]. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. While time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early universe to Bose Einstein Condensates [2-5], understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is an outstanding challenge [6]. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) [7-9] for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models [10,11], providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories [12,13] and applications to quantum optimization [14,15].The celebrated Kibble-Zurek mechanism [2, 3] describes nonequilibrium dynamics and the formation of topological defects in a second-order phase transition driven by thermal fluctuations, and has been experimentally verified in a wide variety of physical systems [4,5]. Recently, the concepts underlying the Kibble-Zurek description have been extended to the quantum regime [7][8][9]. Here, the typical size of the correlated regions, ξ, after a dynamical sweep across the QPT scales as a power-law Critical point gc Control parameter g Correlation length » Phase 1 Phase 2 » » jg ¡ gcj ¡º Time ¿ » jg ¡ gcj ¡zº Fast ramp Slow ramp 0 1 2 3 4 5 Detuning ¢= 1 2 3 4 Interaction range RB=a ²±²±²±²±²±²±² ²±±²±±²±±²±±² ²±±±²±±±²±±±² ℤ2 ℤ3 ℤ4 t ¢ -0.05 0 0.05 -0.1 0 0.1 Density-density correlator G(r) 0 4 8 12 16 20 Distance r (sites) -0.2 -0.1 0 0.1 a b c d Ω Ω FIG. 1: Quantum Kibble-Zurek mechanism (QKZM) and phase diagram. a, Illustration of the QKZM. As the control parameter approaches its critical value, the response time, τ , given by the inverse energy gap of the system, diverges. When the temporal distance to the critical point becomes equal to the response time, as marked by red crosses, the correlation length, b, stops growing due to nonadiabatic excitations. c, Numerically calculated ground-state phase diagram. Circles (diamonds) denote numerically obtained points along the phase boundaries calculated using (infinite-size) Density-Matrix Renormalization Group techniques (Methods). The shaded regions are a guide to the eye. Dashed lines show the experimental trajectories across the phase transitions determined by the pulse diagram shown...

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Keesling

Omran

Levine

et al. 2019

Nature

489

379

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“…For this purpose, it may be particularly fruitful to implement simple, uniform model Hamiltonians to avoid distractions of not fully understood random couplings [60]. Such a study was already carried out with the one-dimensional transverse-field Ising model (TFIM) coded on a D-Wave device [59], but the results did not exhibit any obvious scaling behavior.In this Letter, we report success of a scaling approach for a two-dimensional (2D) Ising model, with data generated on the D-Wave DW_2000Q_2_1 solver (DWQ) [23]. We observe how the improved adiabaticity with lowered FIG.…”

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confidence: 99%

Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device

et al. 2020

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We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on L × L lattices with L ≤ 32. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal L dependent annealing rate v for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of v and L-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when v is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.The prospect of simulating theoretical quantum manybody Hamiltonians with controllable engineered systems is now an important motivation for atomic and quantum device physics [1-3]. Systems explored for creating such "synthetic quantum matter" include ultracold gases [4][5][6][7][8][9], photonic devices [10][11][12][13][14], polaritons [15], and trapped ions [16][17][18][19][20][21][22]. Another emerging simulation platform is large arrays of superconducting qubits [23][24][25][26][27][28][29], which were originally envisioned in the context of quantum annealing (QA) as efficient solvers of classical optimization problems mapped to Ising like Hamiltonians [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. To reach the classical ground state (the problem solution) in a QA process, strong quantum fluctuations are initially induced by applying a transverse field, which is quasi-adiabatically reduced to zero. QA devices operating according to this principle have entered industrial production and applications beyond the academic setting [23], motivated by the hope of more efficient solutions of NP-hard problems [33,44] and, more recently, quantum enhanced machine learning [45,46]. It is still unclear what systems (classes of optimization problems) are amenable to significant speedup, and to what extent QA can be realized in actual devices [41,[47][48][49][50][51][52][53][54][55].While the question of quantum speedups is essential, the potential of using QA devices as generic quantum many-body emulators motivates a broader range of investigations into the devices and how they can be exploited for probing various quantum phenomena. As an example, recently a QA device produced by D-Wave Systems was used in an impressive study of a quantum phase transition of a quantum spin glass [29]. An important question in applications of QA devices, for optimization or quantum simulation, is whether the desired adiabatic evolution is sufficiently realized in the presence of noise (the environment) and finite annealing time. This question motivates studies of the dependence of measured properties on the annealing time [27,[57][58][59], which also impacts the effects of noise. For this...

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“…The quality of a quantum computation/annealing can be measured in various ways [47]. For instance, one may try to count defects [26], estimate fluctuations [27], calculate the fidelity between the final state, |ψ(τ) , and the true ground state of the problem Hamiltonian [48], |φ , or simply determine the difference between their corresponding energies, δ E = ψ(τ)|Ĥ |ψ(τ) − φ |Ĥ |φ [24].…”

Section: Resultsmentioning

confidence: 99%

Disorder-assisted graph coloring on quantum annealers

2019

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We are at the verge of a new era, which will be dominated by Noisy Intermediate-Scale Quantum Devices. Prototypical examples for these new technologies are present-day quantum annealers. In the present work, we investigate to what extent static disorder generated by an external source of noise does not have to be detrimental, but can actually assist quantum annealers in achieving better performance. In particular, we analyze the graph coloring problem that can be solved on a sparse topology (i.e. chimera graph) via suitable embedding. We show that specifically tailored disorder can enhance the fidelity of the annealing process and thus increase the overall performance of the annealer.

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Defects in Quantum Computers

Cited by 96 publications

References 20 publications

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device

Disorder-assisted graph coloring on quantum annealers

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