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King EC, Kriel JN, Kastner M. Universal Cooling Dynamics toward a Quantum Critical Point. PHYSICAL REVIEW LETTERS 2023; 130:050401. [PMID: 36800445 DOI: 10.1103/physrevlett.130.050401] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
We investigate the loss of adiabaticity when cooling a many-body quantum system from an initial thermal state toward a quantum critical point. The excitation density, which quantifies the degree of adiabaticity of the dynamics, is found to obey scaling laws in the cooling velocity as well as in the initial and final temperatures of the cooling protocol. The scaling laws are universal, governed by the critical exponents of the quantum phase transition. The validity of these statements is shown analytically for a Kitaev quantum wire coupled to Markovian baths and argued to be valid under rather general conditions. Our results establish that quantum critical properties can be probed dynamically at finite temperature, without even varying the control parameter of the quantum phase transition.
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Affiliation(s)
- Emma C King
- Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa
| | - Johannes N Kriel
- Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa
| | - Michael Kastner
- Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa
- Hanse-Wissenschaftskolleg, Lehmkuhlenbusch 4, 27753 Delmenhorst, Germany
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Klassert R, Baumbach A, Petrovici MA, Gärttner M. Variational learning of quantum ground states on spiking neuromorphic hardware. iScience 2022; 25:104707. [PMID: 35992070 PMCID: PMC9386107 DOI: 10.1016/j.isci.2022.104707] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Revised: 05/05/2022] [Accepted: 06/28/2022] [Indexed: 11/26/2022] Open
Abstract
Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a challenging computational bottleneck. Compared to conventional neural networks, physical model devices offer a fast, efficient and inherently parallel substrate capable of related forms of Markov chain Monte Carlo sampling. Here, we demonstrate the ability of a neuromorphic chip to represent the ground states of quantum spin models by variational energy minimization. We develop a training algorithm and apply it to the transverse field Ising model, showing good performance at moderate system sizes (N≤10). A systematic hyperparameter study shows that performance depends on sample quality, which is limited by temporal parameter variations on the analog neuromorphic chip. Our work thus provides an important step towards harnessing the capabilities of neuromorphic hardware for tackling the curse of dimensionality in quantum many-body problems. Variational scheme for representing quantum ground states with neuromorphic hardware Accelerated physical system yields system-size independent sample generation time Accurate learning of ground states across a quantum phase transition Detailed analysis of algorithmic and technical limitations
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Titum P, Iosue JT, Garrison JR, Gorshkov AV, Gong ZX. Probing Ground-State Phase Transitions through Quench Dynamics. PHYSICAL REVIEW LETTERS 2019; 123:115701. [PMID: 31573251 DOI: 10.1103/physrevlett.123.115701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Indexed: 06/10/2023]
Abstract
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
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Affiliation(s)
- Paraj Titum
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Joseph T Iosue
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James R Garrison
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Zhe-Xuan Gong
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
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