Decoupling with Random Quantum Circuits

Brown, Winton G.; Fawzi, Omar

doi:10.1007/s00220-015-2470-1

Cited by 105 publications

(137 citation statements)

References 47 publications

Supporting

Mentioning

132

Contrasting

Order By: Relevance

“…Given a many-body Hamiltonian with local interactions, relaxation describes the initial decay of local perturbations as measured by simple autocorrelation functions. Scrambling describes the slower spreading of quantum information across all the degrees of freedom of the system, rendering such information invisible to local probes [14][15][16]. Scrambling is distinct from relaxation, with the time needed to scramble information over a set of degrees of freedom typically scaling in some way with the number of said degrees of freedom.…”

mentioning

confidence: 99%

Slow scrambling in disordered quantum systems

2017

View full text Add to dashboard Cite

In this work we study the effect of static disorder on the growth of commutators-a probe of information scrambling in quantum many-body systems-in a variety of contexts. We find generically that disorder slows the onset of scrambling and, in the case of a many-body localized (MBL) state, partially halts it. In the MBL state, we show using a fixed point Hamiltonian that operators exhibit slow logarithmic growth under time evolution and compare the result with the expected growth of commutators in (de)localized noninteracting disordered models. Finally, using a scaling argument, we state a conjecture on the growth of commutators in a weakly interacting diffusive metal. DOI: 10.1103/PhysRevB.95.060201 Introduction. Understanding the nature of thermalization in closed quantum systems is one of the great challenges of modern many-body physics [1][2][3][4], especially in light of many recent experiments probing thermalization in isolated quantum many-body systems [5][6][7][8][9][10][11][12]. Of particular interest are the time scales for various aspects of thermalization, from early-time relaxation to scrambling at intermediate times to the late-time buildup of complexity [13]. Given a many-body Hamiltonian with local interactions, relaxation describes the initial decay of local perturbations as measured by simple autocorrelation functions. Scrambling describes the slower spreading of quantum information across all the degrees of freedom of the system, rendering such information invisible to local probes [14][15][16]. Scrambling is distinct from relaxation, with the time needed to scramble information over a set of degrees of freedom typically scaling in some way with the number of said degrees of freedom.It is interesting to study the effects of static disorder on the process of thermalization because disorder is common in experimental systems and because it can lead to qualitatively new physics. In the limit of noninteracting particles, weak disorder in low dimensions or sufficiently strong disorder in three or more dimensions causes localization [17,18], which completely arrests thermalization. However, noninteracting particles, being integrable, already fail to thermalize, even when they remain delocalized. Thus it is particularly interesting to study scrambling in interacting disordered systems. It is known that the noninteracting delocalized limit can remain metallic in the presence of interactions, and recent work has shown that the localized limit is also stable to interactions [19][20][21][22][23], resulting in many-body localization [24,25].To probe scrambling in these systems, we study the growth of commutators of local operators. The study of such commutators is closely related to the physics of classical chaos [26] and diagnoses a quantum version of the butterfly effect, whereby a small local perturbation eventually spreads over the entire system [27]. To set up the precise computations, consider two local unitary operators, V and W , along with time

show abstract

mentioning

confidence: 99%

Slow scrambling in disordered quantum systems

2017

View full text Add to dashboard Cite

show abstract

“…It turns out that decoupling results also apply to approximate k-designs [20,23,24]. For non-rigid circuits like the particle gas, decoupling was proven directly [26].Application of our results. Consider a system of N weakly interacting spins, subject to the Hamiltonian H =Ĥ0 +V , whereĤ0 = J i |↑ ↑|i andV is a random nearest-neighbour perturbation that conserves the total spin (with |V | |Ĥ0|); this system is also studied in the preprint version of [5].…”

mentioning

confidence: 54%

“…It turns out that decoupling results also apply to approximate k-designs [20,23,24]. For non-rigid circuits like the particle gas, decoupling was proven directly [26].…”

Section: B Time Scalesmentioning

confidence: 99%

“…As the set of all unitaries in Ω is full of operators that are unrelated to our physical setting (like non-local evolutions, ruled out by our knowledge), it is desirable to obtain similar probabilistic statements about smaller sets that still contain UΩ (like those generated by local interactions). This is possible, because the decoupling approach [20][21][22][23] used to obtain our results is very general, and can be applied to more physical sets of unitaries, consisting of local two-body interactions [24][25][26], or time-independent Hamiltonians [7,8,24]. For a more detailed discussion, see Section III A.…”

Section: B Entropy: Measuring Correlationsmentioning

confidence: 99%

“…The question then is how long it takes for the reference to lose all information about the state of a given subsystem. One option is to apply existing decoupling techniques to this problem, for instance in the case of local circuits, where evolution time can be measured in terms of circuit size [23][24][25][26]). Another direction is to adapt existing techniques used in non-equilibrium thermodynamics to our setting.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Relative thermalization

et al. 2016

View full text Add to dashboard Cite

When studying thermalization of quantum systems, it is typical to ask whether a system interacting with an environment will evolve towards a local thermal state. Here, we show that a more general and relevant question is "when does a system thermalize relative to a particular reference?" By relative thermalization we mean that, as well as being in a local thermal state, the system is uncorrelated with the reference. We argue that this is necessary in order to apply standard statistical mechanics to the study of the interaction between a thermalized system and a reference. We then derive a condition for relative thermalization of quantum systems interacting with an arbitrary environment. This condition has two components: the first is state-independent, reflecting the structure of invariant subspaces, like energy shells, and the relative sizes of system and environment; the second depends on the initial correlations between reference, system and environment, measured in terms of conditional entropies. Intuitively, a small system interacting with a large environment is likely to thermalize relative to a reference, but only if, initially, the reference was not highly correlated with the system and environment. Our statement makes this intuition precise, and we show that in many natural settings this thermalization condition is approximately tight. Established results on thermalization, which usually ignore the reference, follow as special cases of our statements. I. THE CASE FOR RELATIVE THERMALIZATION A. Subjectivity in thermodynamicsThermodynamics was originally developed to study and improve the performance of steam engines: to turn the heat of a gas into work, as efficiently as possible. Today, it is also being applied to study heat and work flows in the micro and nano regimes. In fact, advances in the manipulation of small systems have allowed us to extract work from systems such as quantum dots and trapped ions [1,2]. Yet, thermodynamics as a science is still adapting to this new regime, and it still bears some of the traits of the gaseous systems for which it was first designed. For example, the information available about the state of a gas used to be limited and objective: we would measure the temperature, pressure and volume of a gas, but we could not keep track of each individual particle. Crucially, all conceivable observers had access to the same information about the state of the system, and could manipulate it in equivalent ways-like letting a gas expand to obtain work. And yet, since very early on, several thought experiments have challenged the idea that thermodynamics should be objective. In 1871 James Maxwell realized that a "demon" able to measure the position and velocity of the particles of a gas could extract more work from it than the typical observer implicit in standard thermodynamics [3]. Picking up on Maxwell's idea on the power of information, Leó Szilárd imagined a partitioned box with a single-particle gas on one side. Depending on their information on the location of the particle, tw...

show abstract

Entanglement Dynamics in Hybrid Quantum Circuits

Potter

Vasseur

2022

Quantum Science and Technology

View full text Add to dashboard Cite

Decoupling with Random Quantum Circuits

Cited by 105 publications

References 47 publications

Slow scrambling in disordered quantum systems

Slow scrambling in disordered quantum systems

Relative thermalization

Entanglement Dynamics in Hybrid Quantum Circuits

Contact Info

Product

Resources

About