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Book ; Online: Phase transitions in sampling and error correction in local Brownian circuits

Sahu, Subhayan / Jian, Shao-Kai

2023

Abstract: We study the emergence of anticoncentration and approximate unitary design behavior in local Brownian circuits. The dynamics of circuit averaged moments of the probability distribution and entropies of the output state can be represented as imaginary ... ...

Abstract	We study the emergence of anticoncentration and approximate unitary design behavior in local Brownian circuits. The dynamics of circuit averaged moments of the probability distribution and entropies of the output state can be represented as imaginary time evolution with an effective local Hamiltonian in the replica space. This facilitates large scale numerical simulation of the dynamics in $1+1d$ of such circuit-averaged quantities using tensor network tools, as well as identifying the various regimes of the Brownian circuit as distinct thermodynamic phases. In particular, we identify the emergence of anticoncentration as a sharp transition in the collision probability at $\log N$ timescale, where $N$ is the number of qubits. We also show that a specific classical approximation algorithm has a computational hardness transition at the same timescale. In the presence of noise, we show there is a noise-induced first order phase transition in the linear cross entropy benchmark when the noise rate is scaled down as $1/N$. At longer times, the Brownian circuits approximate a unitary 2-design in $O(N)$ time. We directly probe the feasibility of quantum error correction by such circuits, and identify a first order transition at $O(N)$ timescales. The scaling behaviors for all these phase transitions are obtained from the large scale numerics, and corroborated by analyzing the spectrum of the effective replica Hamiltonian. Comment: 17+3 pages, 10 figures
Keywords	Quantum Physics ; Condensed Matter - Statistical Mechanics
Subject code	612
Publishing date	2023-07-09
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Entanglement structure and information protection in noisy hybrid quantum circuits

Liu, Shuo / Li, Ming-Rui / Zhang, Shi-Xin / Jian, Shao-Kai

2024

Abstract: In the context of measurement-induced entanglement phase transitions, the influence of quantum noises, which are inherent in real physical systems, is of great importance and experimental relevance. In this Letter, we present a comprehensive theoretical ... ...

Abstract	In the context of measurement-induced entanglement phase transitions, the influence of quantum noises, which are inherent in real physical systems, is of great importance and experimental relevance. In this Letter, we present a comprehensive theoretical analysis of the effects of both temporally uncorrelated and correlated quantum noises on entanglement generation and information protection. This investigation reveals that entanglement within the system follows $q^{-1/3}$ scaling for both types of quantum noises, where $q$ represents the noise probability. The scaling arises from the Kardar-Parisi-Zhang fluctuation with effective length scale $L_{\text{eff}} \sim q^{-1}$. Moreover, the timescales of information protection are explored and shown to follow $q^{-1/2}$ and $q^{-2/3}$ scaling for temporally uncorrelated and correlated noises, respectively. The former scaling can be interpreted as a Hayden-Preskill protocol, while the latter is a direct consequence of Kardar-Parisi-Zhang fluctuations. We conduct extensive numerical simulations using stabilizer formalism to support the theoretical understanding. This Letter not only contributes to a deeper understanding of the interplay between quantum noises and measurement-induced phase transition but also provides a new perspective to understand the effects of Markovian and non-Markovian noises on quantum computation. Comment: 4.5 pages, 3 figures, and Supplemental Materials
Keywords	Quantum Physics ; Condensed Matter - Disordered Systems and Neural Networks ; Condensed Matter - Statistical Mechanics
Subject code	612 ; 190
Publishing date	2024-01-03
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Nonequilibrium Dynamics of Deconfined Quantum Critical Point in Imaginary Time.

Shu, Yu-Rong / Jian, Shao-Kai / Yin, Shuai

Physical review letters

2022 Volume 128, Issue 2, Page(s) 20601

Abstract: Deconfined quantum critical point (DQCP) characterizes a kind of exotic phase transition beyond the usual Landau-Ginzburg-Wilson paradigm. Here we study the nonequilibrium imaginary-time dynamics of the DQCP in the two-dimensional J-Q_{3} model. We ... ...

Abstract	Deconfined quantum critical point (DQCP) characterizes a kind of exotic phase transition beyond the usual Landau-Ginzburg-Wilson paradigm. Here we study the nonequilibrium imaginary-time dynamics of the DQCP in the two-dimensional J-Q_{3} model. We explicitly show the deconfinement dynamic process and identify that it is the spinon confinement length, rather than the usual correlation length, that increases proportionally to the time. Moreover, we find that, in the relaxation process, the order parameters of the Néel and the valence-bond-solid orders can be controlled by different length scales, although they satisfy the same equilibrium scaling forms. A dual dynamic scaling theory is then proposed. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems. Possible realizations in foreseeable quantum computers are also discussed.
Language	English
Publishing date	2022-01-28
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.128.020601
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Article ; Online: Charge-4e Superconductivity from Nematic Superconductors in Two and Three Dimensions.

Jian, Shao-Kai / Huang, Yingyi / Yao, Hong

Physical review letters

2021 Volume 127, Issue 22, Page(s) 227001

Abstract: Charge-4e superconductivity as a novel phase of matter remains elusive so far. Here, we show that charge-4e phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. ... ...

Abstract	Charge-4e superconductivity as a novel phase of matter remains elusive so far. Here, we show that charge-4e phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect-nematic vortex-is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-4e phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-Landau theory of the nematic superconductors has two distinct decoupling channels to either charge-4e orders or nematic orders; by analyzing the competition between the effective mass of the charge-4e order and the cubic potential of the nematic order, we find a sizable regime where the charge-4e order is favored. These two analyses consistently show that nematic superconductors can provide a promising route to realize charge-4e phases, which may apply to candidate nematic superconductors such as PbTaSe_{2} and twisted bilayer graphene.
Language	English
Publishing date	2021-12-10
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.127.227001
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Article ; Online: Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model.

Winer, Michael / Jian, Shao-Kai / Swingle, Brian

Physical review letters

2021 Volume 125, Issue 25, Page(s) 250602

Abstract: A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. ... ...

Abstract	A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.
Language	English
Publishing date	2021-01-08
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.125.250602
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Book ; Online: Noise-induced phase transitions in hybrid quantum circuits

Liu, Shuo / Li, Ming-Rui / Zhang, Shi-Xin / Jian, Shao-Kai / Yao, Hong

2024

Abstract: The presence of quantum noises inherent to real physical systems can strongly impact the physics in quantum hybrid circuits with local random unitaries and mid-circuit measurements. For example, an infinitesimal size-independent noise probability can ... ...

Abstract	The presence of quantum noises inherent to real physical systems can strongly impact the physics in quantum hybrid circuits with local random unitaries and mid-circuit measurements. For example, an infinitesimal size-independent noise probability can lead to the disappearance of measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this Letter, we investigate the effects of quantum noises with size-dependent probabilities $q=p/L^{\alpha}$ where $\alpha$ represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements as $p$ increases when $\alpha=1.0$. With the help of an effective statistical model, we find that this transition is a first-order phase transition and shares the same analytical understanding as the noise-induced coding transition. We also discuss the differences between the effect of size-dependent noise and the boundary noise in the phase transitions. We validate our analytical predictions with extensive numerical results from stabilizer circuit simulations. Comment: 4.3 pages, 4 figures, and Supplemental Materials
Keywords	Quantum Physics ; Condensed Matter - Disordered Systems and Neural Networks ; Condensed Matter - Statistical Mechanics ; Condensed Matter - Strongly Correlated Electrons
Subject code	612
Publishing date	2024-01-29
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Equilibration of Topological Defects at the Deconfined Quantum Critical Point

Shu, Yu-Rong / Jian, Shao-Kai / Sandvik, Anders W. / Yin, Shuai

2023

Abstract: Deconfined quantum criticality (DQC) arises from fractionalization of quasi-particles and leads to fascinating behaviors beyond the Landau-Ginzburg-Wilson (LGW) description of phase transitions. The unusual aspects of DQC in equilibrium also suggest ... ...

Abstract	Deconfined quantum criticality (DQC) arises from fractionalization of quasi-particles and leads to fascinating behaviors beyond the Landau-Ginzburg-Wilson (LGW) description of phase transitions. The unusual aspects of DQC in equilibrium also suggest exotic phenomena out of equilibrium, which are still largely unexplored. Here we study manifestations of DQC when driving (quantum annealing) a two-dimensional quantum magnet through a critical point separating antiferromagnetic and spontaneously dimerized ground states. Numerical simulations show that the celebrated Kibble-Zurek scaling (KZS) mechanism is inadequate for describing the annealing process. To explain our results, we introduce the concept of dual asymmetric KZS, where a deconfinement time enters in addition to the conventional relaxation time and the scaling also depends on the direction in which the system is driven through the critical point according to a duality principle connecting the topological defects in the two phases. These defects -- spinons in the dimerized phase and space-time hedgehogs in the antiferromagnetic phase -- require a much longer time scale for equilibration than the amplitude of the order parameter. Beyond the new insights into DQC, our scaling approach provides a new window into out-of-equilibrium criticality with multiple length and time scales. Comment: 15 pages, 9 figures
Keywords	Condensed Matter - Strongly Correlated Electrons ; Condensed Matter - Statistical Mechanics
Subject code	612
Publishing date	2023-05-08
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Chiral topological superconductivity in Josephson junction

Jian, Shao-Kai / Yin, Shuai

2020

Abstract: We consider a heterostructure of semiconductor layers sandwiched between two superconductors, forming a two-dimensional Josephson junction. Applying a Zeeman field perpendicular to the junction can render a topological superconducting phase with chiral ... ...

Abstract	We consider a heterostructure of semiconductor layers sandwiched between two superconductors, forming a two-dimensional Josephson junction. Applying a Zeeman field perpendicular to the junction can render a topological superconducting phase with chiral Majorana edge mode. We show that the phase difference between two superconductors can efficiently reduce the magnetic field required to achieve the chiral topological superconductivity, providing an experimentally feasible setup to realize chiral Majorana edge modes. We also construct a lattice Hamiltonian of the setup to demonstrate the chiral Majorana edge mode and the Majorana bound state localized in vortices. Comment: 10 pages, 6 figures
Keywords	Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Materials Science
Publishing date	2020-09-04
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Solvable Sachdev-Ye-Kitaev Models in Higher Dimensions: From Diffusion to Many-Body Localization.

Jian, Shao-Kai / Yao, Hong

Physical review letters

2017 Volume 119, Issue 20, Page(s) 206602

Abstract: Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition. The model on a bipartite lattice has N ... ...

Abstract	Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition. The model on a bipartite lattice has N Majorana fermions with SYK interactions on each site of the A sublattice and M free Majorana fermions on each site of the B sublattice, where N and M are large and finite. For r≡M/N<r_{c}=1, it describes a diffusive metal exhibiting maximal chaos. Remarkably, its diffusive constant D vanishes [D∝(r_{c}-r)^{1/2}] as r→r_{c}, implying a dynamical transition to a MBL phase. It is further supported by numerical calculations of level statistics which changes from Wigner-Dyson (r<r_{c}) to Poisson (r>r_{c}) distributions. Note that no subdiffusive phase intervenes between diffusive and MBL phases. Moreover, the critical exponent ν=0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions.
Language	English
Publishing date	2017-11-17
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.119.206602
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Book ; Online: Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution

Shu, Yu-Rong / Jian, Shao-Kai / Yin, Shuai

2021

Abstract: As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of ... ...

Abstract	As proposed to describe putative continuous phase transitions between two ordered phases, the deconfined quantum critical point (DQCP) goes beyond the prevalent Landau-Ginzburg-Wilson (LGW) paradigm since its critical theory is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent symmetry. So far, great efforts have been spent on its equilibrium properties, but the nonequilibrium properties therein are largely unknown. Here we study the nonequilibrium dynamics of the DQCP via the imaginary-time evolution in the two-dimensional (2D) J-Q$_3$ model. We discover fascinating nonequilibrium scaling behaviors hinging on the process of fractionization and the dynamics of emergent symmetry associated with two length scales. Our findings not only constitute a new realm of nonequilibrium criticality in DQCP, but also offer a controllable knob by which to investigate the dynamics in strongly correlated systems. Comment: 19 pages, 14 figures
Keywords	Condensed Matter - Strongly Correlated Electrons ; Condensed Matter - Statistical Mechanics ; High Energy Physics - Lattice
Subject code	612
Publishing date	2021-02-08
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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