Fast-forwarding of Hamiltonians and exponentially precise measurements

Atia, Yosi; Aharonov, Dorit

doi:10.1038/s41467-017-01637-7

Cited by 92 publications

(126 citation statements)

References 66 publications

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“…whose holographic dual is a two-sided black hole in Anti-de Sitter space [15] (Figure 1). Since black hole dynamics is chaotic, we don't expect shortcuts (fast forwarding in [16]) before exponentially long time. The complexity will increase linearly with time after an initial transient period of order the thermal time [7] [6].…”

Section: Known Results About Holographic Complexitymentioning

confidence: 99%

Complexity and boost symmetry

Zhao

2018

Phys. Rev. D

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We find that the time dependence of holographic complexity is controlled by the Rindler boost symmetry across the horizon. By studying the collision energy experienced by an infalling object, we see the breaking of this boost symmetry is closely related to firewalls, which in turn shows the connection between the time dependence of complexity and firewalls. We further identify the black and white hole interiors as two tapes storing different parts of the minimal circuit preparing the state. Depending on whether the quantum gates are being laid on the tape at a particular moment, each tape can be in two states: working, or locked. We interpret the existence of firewalls as the locking of tapes.2 In these four assumptions, assumption 2 essentially implies assumptions 1, 3, and 4. I thank Daniel Harlow for pointing this out.

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Section: Known Results About Holographic Complexitymentioning

confidence: 99%

Complexity and boost symmetry

Zhao

2018

Phys. Rev. D

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“…Related, but distinct, arguments for limits on computational speed related to energy are given in [26][27][28][29]. Another relationship between the energy-time uncertainty principle and computational complexity, which is not based on associating T ⊥ with the time necessary for a logical operation, was recently given in [30]. For several reasons, equating T −1 ⊥ with a maximum computational clock speed seems quite plausible.…”

Section: Introductionmentioning

confidence: 99%

Fast quantum computation at arbitrarily low energy

Jordan

2017

Phys. Rev. A

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One version of the energy-time uncertainty principle states that the minimum time T ⊥ for a quantum system to evolve from a given state to any orthogonal state is h/(4∆E) where ∆E is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that T ⊥ ≥ h/(2 E ) where E is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted T ⊥ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system's energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to E and ∆E as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

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“…Simulating the dynamics of a quantum system for time T typically requires Ω(T) gates so that a generic Hamiltonian evolution cannot be achieved in sublinear time. This result is known as the "no fast-forwarding theorem", and holds both for a typical unknown Hamiltonian 27 and for the query model setting 28 . However, there are particular Hamiltonians that can be fastforwarded, which means that the quantum circuit depth does not need to grow significantly with simulation time.…”

Section: Introductionmentioning

confidence: 93%

Variational fast forwarding for quantum simulation beyond the coherence time

et al. 2020

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Trotterization-based, iterative approaches to quantum simulation (QS) are restricted to simulation times less than the coherence time of the quantum computer (QC), which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called variational fast forwarding (VFF), for decreasing the quantum circuit depth of QSs. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function’s operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. In addition, we implement VFF on Rigetti’s QC to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF.

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Fast-forwarding of Hamiltonians and exponentially precise measurements

Cited by 92 publications

References 66 publications

Complexity and boost symmetry

Complexity and boost symmetry

Fast quantum computation at arbitrarily low energy

Variational fast forwarding for quantum simulation beyond the coherence time

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