Measurement of many-body chaos using a quantum clock

Zhu, Guanyu; Hafezi, Mohammad; Grover, Tarun

doi:10.1103/physreva.94.062329

Cited by 173 publications

(176 citation statements)

References 68 publications

(158 reference statements)

Supporting

Mentioning

176

Contrasting

Order By: Relevance

“…One can also investigate quantum quenches as a possible probe of SYK physics by disconnecting or reconnecting the dot and wires to effectively freeze the zero modes or restore their coupling. Finally, much work has been done regarding measuring out-of-time-order correlators in cold atoms and qubit systems (see, e.g., [60][61][62][63]). Our setup offers the exciting prospect of exploiting Majorana hardware and topological quantum information ideas to measure such quantities in pursuit of the SYK model's hallmark maximal chaos.…”

Section: Let Us Now Examine a General T -Invariant Four-fermion Intermentioning

confidence: 99%

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

2017

View full text Add to dashboard Cite

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random-matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures. DOI: 10.1103/PhysRevB.96.121119 Introduction. Majorana fermions provide building blocks for many novel phenomena. As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.The SYK Hamiltonian reads

show abstract

Section: Let Us Now Examine a General T -Invariant Four-fermion Intermentioning

confidence: 99%

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

2017

View full text Add to dashboard Cite

show abstract

“…Experimental measurements of F (t) are possible for certain platforms in certain regimes [15][16][17][18][19]. Theorem 1 expands the set of platforms and regimes.…”

Section: Discussionmentioning

confidence: 99%

“…The absence of time reversal has been regarded as beneficial in OTOC-measurement schemes [16,17], as time reversal can be difficult to implement.…”

Section: Interference-based Measurement Ofã ρmentioning

confidence: 99%

“…Let S denote a quantum system associated with a Hilbert space H of dimensionality d. The simple example of a spin chain [16][17][18][19] [43].…”

Section: Setupmentioning

confidence: 99%

“…In the context of quantum channels, F (t) is related to the tripartite information [14]. Experiments have been proposed [15][16][17] and performed [18,19] to measure F (t) with cold atoms and ions, with cavity quantum electrodynamics, and with nuclear-magnetic-resonance quantum simulators.F (t) quantifies sensitivity to initial conditions, a signature of chaos. Consider a quantum system S governed by a Hamiltonian H .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Jarzynski-like equality for the out-of-time-ordered correlator

Halpern

2017

Phys. Rev. A

121

View full text Add to dashboard Cite

The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation relations such as Jarzynski's equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a Jarzynski-like equality for the OTOC. The equality's left-hand side equals the OTOC. The right-hand side suggests a protocol for measuring the OTOC indirectly. The protocol is platform-nonspecific and can be performed with weak measurement or with interference. Time evolution need not be reversed in any interference trial. The equality enables fluctuation relations to provide insights into holography, condensed matter, and quantum information and vice versa. DOI: 10.1103/PhysRevA.95.012120The out-of-time-ordered correlator (OTOC) F (t) diagnoses the scrambling of quantum information [1][2][3][4][5][6]: Entanglement can grow rapidly in a many-body quantum system, dispersing information throughout many degrees of freedom. F (t) quantifies the hopelessness of attempting to recover the information via local operations.Originally applied to superconductors [7], F (t) has undergone a revival recently. F (t) characterizes quantum chaos, holography, black holes, and condensed matter. The conjecture that black holes scramble quantum information at the greatest possible rate has been framed in terms of F (t) [6,8]. The slowest scramblers include disordered systems [9][10][11][12][13]. In the context of quantum channels, F (t) is related to the tripartite information [14]. Experiments have been proposed [15][16][17] and performed [18,19] to measure F (t) with cold atoms and ions, with cavity quantum electrodynamics, and with nuclear-magnetic-resonance quantum simulators.F (t) quantifies sensitivity to initial conditions, a signature of chaos. Consider a quantum system S governed by a Hamiltonian H . Suppose that S is initialized to a pure state |ψ and perturbed with a local unitary operator V . S then evolves forward in time under the unitary U = e −iH t for a duration t, is perturbed with a local unitary operator W, and evolves backward under U † . The state |ψ := U † WUV |ψ = W(t)V |ψ results. Suppose, instead, that S is perturbed with V not at the sequence's beginning, but at the end: |ψ evolves forward under U , is perturbed with W, evolves backward under U † , and is perturbed with V . The state |ψ := V U † WU |ψ = V W(t)|ψ results. The overlap between the two possible final states equals the correlator: push an ion-trap potential along some direction in space [26]. Let F := F (H f ) − F (H i ) denote the difference between the equilibrium free energies at the inverse temperature β: 1 F (H ) = − 1 β ln Z β, , wherein the partition function is Z β, := Tr(e −βH ) and = i or f . The free-energy difference has applications in chemistry, biology, and pharmacology [27]. One could measure F , in principle, by measuring th...

show abstract

Out‐of‐time‐order correlations in many‐body localized and thermal phases

et al. 2016

View full text Add to dashboard Cite

We use the out-of-time-order (OTO) correlators to study the slow dynamics in the many-body localized (MBL) phase. We investigate OTO correlators in the effective ("l-bit") model of the MBL phase, and show that their amplitudes after disorder averaging approach their long-time limits as power-laws of time. This power-law dynamics is due to dephasing caused by interactions between the localized operators that fall off exponentially with distance. The long-time limits of the OTO correlators are determined by the overlaps of the local operators with the conserved l-bits. We demonstrate numerically our results in the effective model and three other more "realistic" spin chain models. Furthermore, we extend our calculations to the thermal phase and find that for a time-independent Hamiltonian, the OTO correlators also appear to vanish as a power law at long time, perhaps due to coupling to conserved densities. In contrast, we find that in the thermal phase of a Floquet spin model with no conserved densities the OTO correlator decays exponentially at long times.

show abstract

Measurement of many-body chaos using a quantum clock

Cited by 173 publications

References 68 publications

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

Jarzynski-like equality for the out-of-time-ordered correlator

Out‐of‐time‐order correlations in many‐body localized and thermal phases

Contact Info

Product

Resources

About