Universal Error Bound for Constrained Quantum Dynamics

Gong, Zongping; Yoshioka, Nobuyuki; Shibata, Naoyuki; Hamazaki, Ryusuke

doi:10.1103/physrevlett.124.210606

Cited by 20 publications

(19 citation statements)

References 41 publications

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“…This scenario enables us to demonstrate the existence of an emergent gauge theory that is perturbatively connected to H 0 . In particular, the frameworks of constrained quantum dynamics 52,53 and the Abanin-De Roeck-Ho-Huveneers (ARHH) method 51 prove to yield useful insight.…”

Section: A Full Protectionmentioning

confidence: 99%

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Reliability of lattice gauge theories in the thermodynamic limit

Damme¹,

Lang²,

Hauke³

et al. 2021

Preprint

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Although gauge invariance is a postulate in fundamental theories of nature such as quantum electrodynamics, in quantum-simulation implementations of gauge theories it is compromised by experimental imperfections. In a recent work [Halimeh and Hauke, Phys. Rev. Lett. 125, 030503 (2020)], it has been shown in finite-size spin-1/2 quantum link lattice gauge theories that upon introducing an energy-penalty term of sufficiently large strength V , unitary gauge-breaking errors at strength λ are suppressed ∝ λ 2 /V 2 up to all accessible evolution times. Here, we show numerically that this result extends to quantum link models in the thermodynamic limit and with larger spin-S. As we show analytically, the dynamics at short times is described by an adjusted gauge theory up to a timescale that is at earliest τ adj ∝ V /V 3 0 , with V0 an energy factor. Moreover, our analytics predicts that a renormalized gauge theory dominates at intermediate times up to a timescale τren ∝ exp(V /V0)/V0. In both emergent gauge theories, V is volume-independent and scales at worst ∼ S 2 . Furthermore, we numerically demonstrate that robust gauge invariance is also retained through a single-body gauge-protection term, which is experimentally straightforward to implement in ultracold-atom setups and NISQ devices.

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Section: A Full Protectionmentioning

confidence: 99%

“…Supporting numerical results are found in Appendix A. The analytics of our paper are found in Appendix B for the Abanin-De Roeck-Ho-Huveneers (ARHH) method, 51 Appendix C for constrained quantum dynamics, 52,53 and Appendix D for the quantum Zeno effect. [54][55][56][57]…”

mentioning

confidence: 99%

Reliability of lattice gauge theories in the thermodynamic limit

Damme¹,

Lang²,

Hauke³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…A version of adiabatic theorem involving a time-independent Hamiltonian also plays an important role in the control of quantum systems via the quantum Zeno dynamics [25][26][27], and precisely in its manifestation through the strong-coupling limit [3,19,[28][29][30][31][32][33][34]. The framework developed here can be used to reproduce these results independently.…”

Section: Overview Of Applications and Previous Related Resultsmentioning

confidence: 90%

“…Still, if the dimension of an eigenspace is greater than 1, the system can evolve unitarily within the eigenspace. This is a manifestation of the quantum Zeno dynamics [3,19,[25][26][27][28][29][30][31][32][33][34], and the evolution within the eigenspaces is generated by a "Zeno Hamiltonian" [25,26].…”

Section: Strong-coupling Limitmentioning

confidence: 99%

One bound to rule them all: from Adiabatic to Zeno

Burgarth,

Facchi,

Gramegna

et al. 2021

Preprint

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We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions. We apply our result to provide explicit error bounds for the rotating-wave approximation and generalize it beyond the qubit case. We discuss the error of the rotating-wave approximation over long time and in the presence of time-dependent amplitude modulation. We also show how our universal bound can be used to derive and to generalize other known theorems such as the strong-coupling limit, the adiabatic theorem, and product formulas, which are relevant to quantum-control strategies including the Zeno control and the dynamical decoupling. Finally, we prove generalized versions of the Trotter product formula, extending its validity beyond the standard scaling assumption.

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“…While the Lieb-Robinson bound provides a bound for general operators that may not be restricted to Eq. ( 39) and leads to various dynamical constraints [85][86][87][88][89][90][91][92], it only gives a state-independent bound. Our speed limit is state-dependent through, e.g., E trans and thus can give a tighter bound than the Lieb-Robinson bound for an operator in the form of (39).…”

Section: B Speed Limit For Expectation Values Of Observablesmentioning

confidence: 99%

Speed Limits for Macroscopic Transitions

Hamazaki

2021

Preprint

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Universal Error Bound for Constrained Quantum Dynamics

Cited by 20 publications

References 41 publications

Reliability of lattice gauge theories in the thermodynamic limit

Reliability of lattice gauge theories in the thermodynamic limit

One bound to rule them all: from Adiabatic to Zeno

Speed Limits for Macroscopic Transitions

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