Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator(OTOC) generically behaves differently at long times, while, it may show similar early growth in one-b...Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator(OTOC) generically behaves differently at long times, while, it may show similar early growth in one-body systems. In this paper, by means of numerical simulations, it is shown that OTOC has similar early growth in two quantum many-body systems, one integrable and one chaotic.展开更多
We study the behavior of information spreading in the XY model, using out-of-time-order correlators(OTOCs). The effects of anisotropic parameter γ and external magnetic field λon OTOCs are studied in detail within t...We study the behavior of information spreading in the XY model, using out-of-time-order correlators(OTOCs). The effects of anisotropic parameter γ and external magnetic field λon OTOCs are studied in detail within thermodynamical limits. The universal form which characterizes the wavefront of information spreading still holds in the XY model. The butterfly speed vBdepends on(γ, λ). At a fixed location, the early-time evolution behavior of OTOCs agrees with the results of the Hausdorff–Baker–Campbell expansion. For long-time evolution,OTOCs with local operators decay as for power law t^-1, but those with nonlocal operators show different and nontrivial power law behaviors. We also observe temperature dependence for OTOCs when(γ=0, λ=1). At low temperature, the OTOCs with nonlocal operators show divergence over time.展开更多
Performance of a scalable quantum processor critically relies on minimizing crosstalk and unwanted interactions within the system,as it is vital for parallel controlled operations on qubits.We present a protocol not o...Performance of a scalable quantum processor critically relies on minimizing crosstalk and unwanted interactions within the system,as it is vital for parallel controlled operations on qubits.We present a protocol not only to provide information about residual coupling but also to effectively discriminate it from the influence of classical crosstalk.Our approach utilizes out-of-time-order correlators(OTOCs)as a signal of quantum crosstalk,making it applicable to various coupling forms and scalable architectures.To demonstrate the effectiveness of our protocol,we provide a theoretical analysis and simulate its implementation in coupled superconducting qubits.展开更多
In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law i...In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.展开更多
A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the H...A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the Hawking temperature.Motivated by this,we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction.Numerically,we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field.They are mainly contributed by the bound states near the horizon and lie below the chaos bound.展开更多
We study a simplified version of the Sachdev-Ye-Kitaev(SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be ...We study a simplified version of the Sachdev-Ye-Kitaev(SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be chosen from discrete values with a finite separation. A quantum phase transition from a chaotic state to an integrable state is observed by increasing the discrete separation. Below the critical value, the discrete model can well reproduce various physical quantities of the original SYK model,including the volume law of the ground-state entanglement, level distribution, thermodynamic entropy,and out-of-time-order correlation(OTOC) functions. For systems of size up to N=20, we find that the transition point increases with system size, indicating that a relatively weak randomness of interaction can stabilize the chaotic phase. Our findings significantly relax the stringent conditions for the realization of SYK model, and can reduce the complexity of various experimental proposals down to realistic ranges.展开更多
The physical world is inherently out of equilibrium,and understanding the non-equilibrium behavior of quantum many-body systems remains a key open challenge in condensed matter physics.Recent advances in quantum compu...The physical world is inherently out of equilibrium,and understanding the non-equilibrium behavior of quantum many-body systems remains a key open challenge in condensed matter physics.Recent advances in quantum computing platforms,such as Rydberg atoms and superconducting qubits,have opened promising avenues for studying non-equilibrium dynamics of many-particle systems using quantum simulators.In this work,we propose a benchmark scheme for validating the dynamical evolution outcomes of future large-scale qubit systems,which far exceeds the capability of classical numerical benchmark.Based on the J_(1)–J_(2)Heisenberg model,we provide tunable analytical results including quantum walk dynamics,the out-of-time-ordered correlator(OTOC),and the butterfly velocity.Furthermore,taking IBM’s programmable quantum platform as an example,we design a scheme for simulating quantum walk dynamics and experimentally demonstrate the feasibility of benchmarking with our proposed dynamical observables.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11535011 and 11775210
文摘Previous studies show that, in quantum chaotic and integrable systems, the so-called out-of-time-ordered correlator(OTOC) generically behaves differently at long times, while, it may show similar early growth in one-body systems. In this paper, by means of numerical simulations, it is shown that OTOC has similar early growth in two quantum many-body systems, one integrable and one chaotic.
基金funded by the China Postdoctoral Science Foundationsupported by NSFC Grant No.11947067。
文摘We study the behavior of information spreading in the XY model, using out-of-time-order correlators(OTOCs). The effects of anisotropic parameter γ and external magnetic field λon OTOCs are studied in detail within thermodynamical limits. The universal form which characterizes the wavefront of information spreading still holds in the XY model. The butterfly speed vBdepends on(γ, λ). At a fixed location, the early-time evolution behavior of OTOCs agrees with the results of the Hausdorff–Baker–Campbell expansion. For long-time evolution,OTOCs with local operators decay as for power law t^-1, but those with nonlocal operators show different and nontrivial power law behaviors. We also observe temperature dependence for OTOCs when(γ=0, λ=1). At low temperature, the OTOCs with nonlocal operators show divergence over time.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12074179 and U21A20436)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301702)+1 种基金the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BE2021015-1 and BK20232002)the Natural Science Foundation of Shandong Province(Grant No.ZR2023LZH002).
文摘Performance of a scalable quantum processor critically relies on minimizing crosstalk and unwanted interactions within the system,as it is vital for parallel controlled operations on qubits.We present a protocol not only to provide information about residual coupling but also to effectively discriminate it from the influence of classical crosstalk.Our approach utilizes out-of-time-order correlators(OTOCs)as a signal of quantum crosstalk,making it applicable to various coupling forms and scalable architectures.To demonstrate the effectiveness of our protocol,we provide a theoretical analysis and simulate its implementation in coupled superconducting qubits.
基金supported by the National Key Research and Development Plan (2016YFA0301600)the National Natural Science Foundation of China (11325418)Tsinghua University Initiative Scientific Research Program
文摘In this paper we first compute the out-of-time-order correlators （OTOC） for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Renyi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.
基金supported by the National Natural Science Foundation of China with Grants No.12174067 and No.11804223。
文摘A semiclassical particle moving near the horizon of a Schwarzschild black hole is chaotic,and its Lyapunov exponent saturates the chaos bound proposed by Maldacena,Shenker,and Stanford,with the temperature being the Hawking temperature.Motivated by this,we consider the Lyapunov exponents of scalar and spinor fields in Schwarzschild spacetime by calculating their out-of-time-ordered commutators along the radial direction.Numerically,we find that the Lyapunov exponent of the scalar field is smaller than that of the spinor field.They are mainly contributed by the bound states near the horizon and lie below the chaos bound.
基金This work was supported by the National Natural Science Foundation of China(11434011,11522436,11774425,11704029)the National Key R&D Program of China(2018YFA0306501)+1 种基金the Beijing Natural Science Foundation(Z180013)the Research Funds of Renmin University of China(16XNLQ03 and 18XNLQ15)。
文摘We study a simplified version of the Sachdev-Ye-Kitaev(SYK) model with real interactions by exact diagonalization. Instead of satisfying a continuous Gaussian distribution, the interaction strengths are assumed to be chosen from discrete values with a finite separation. A quantum phase transition from a chaotic state to an integrable state is observed by increasing the discrete separation. Below the critical value, the discrete model can well reproduce various physical quantities of the original SYK model,including the volume law of the ground-state entanglement, level distribution, thermodynamic entropy,and out-of-time-order correlation(OTOC) functions. For systems of size up to N=20, we find that the transition point increases with system size, indicating that a relatively weak randomness of interaction can stabilize the chaotic phase. Our findings significantly relax the stringent conditions for the realization of SYK model, and can reduce the complexity of various experimental proposals down to realistic ranges.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFA1405300)Guangdong Provincial Quantum Science Strategic Initiative(Grant No.GDZX2204003)+4 种基金Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301700)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2021A1515012350)Guangdong Provincial Quantum Science Strategic Initiative(Grants No.GDZX2304002 and GDZX2404001)the Open Fund of Key Laboratory of Atomic and Subatomic Structure and Quantum Control(Ministry of Education)the National Natural Science Foundation of China(Grant No.12405034).
文摘The physical world is inherently out of equilibrium,and understanding the non-equilibrium behavior of quantum many-body systems remains a key open challenge in condensed matter physics.Recent advances in quantum computing platforms,such as Rydberg atoms and superconducting qubits,have opened promising avenues for studying non-equilibrium dynamics of many-particle systems using quantum simulators.In this work,we propose a benchmark scheme for validating the dynamical evolution outcomes of future large-scale qubit systems,which far exceeds the capability of classical numerical benchmark.Based on the J_(1)–J_(2)Heisenberg model,we provide tunable analytical results including quantum walk dynamics,the out-of-time-ordered correlator(OTOC),and the butterfly velocity.Furthermore,taking IBM’s programmable quantum platform as an example,we design a scheme for simulating quantum walk dynamics and experimentally demonstrate the feasibility of benchmarking with our proposed dynamical observables.
