Quantifying Quantum Speedups: Improved Classical Simulation From Tighter Magic Monotones

Seddon, James Richard Thorley; Regula, Bartosz; Pashayan, Hakop; Ouyang, Yingkai; Campbell, Earl T.

doi:10.1103/prxquantum.2.010345

Cited by 83 publications

(58 citation statements)

References 75 publications

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“…One way to evaluate the classical simulatability of quantum circuits is to quantify the simulation cost of a specific quasiprobability-based simulator [12][13][14][15][16][17]. The central idea of quasiprobability simulators is to decompose a complex operator (operation) A over a discrete set of classically tractable operators (operations) {B i }, i.e., A = i q i B i .…”

Section: Introductionmentioning

confidence: 99%

Quantifying Fermionic Nonlinearity of Quantum Circuits

Hakkaku¹,

Yuichiro²,

Mitarai³

et al. 2021

Preprint

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Variational quantum algorithms (VQA) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQA algorithms can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte-Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four-body fermionic interaction under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles (UCCSD) quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages.

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Section: Introductionmentioning

confidence: 99%

Quantifying Fermionic Nonlinearity of Quantum Circuits

Hakkaku¹,

Yuichiro²,

Mitarai³

et al. 2021

Preprint

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“…V [22]. Taking M to be the dyadic negativity [36], we show that Rðτ ⊗t jτ ⊗t δ Þ grows exponentially with the T count t for any δ ∈ ð0; 1,…”

mentioning

confidence: 96%

“…( 8) [37]. Already at δ ¼ 10 −2 and moderate overheads (∼10 2 ) one can error mitigate in regimes (t ∼ 230) in which classical simulation is currently unfeasible even with stateof-the-art algorithms [36,38,39].…”

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confidence: 99%

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Error Mitigation and Quantum-Assisted Simulation in the Error Corrected Regime

Lostaglio

Ciani

2021

Phys. Rev. Lett.

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“…We stress that the robustness RðρÞ can always be computed as a convex optimization problem. In many cases, such as the resource theories of coherence [57], multilevel coherence [58], and magic [59][60][61][62], it becomes an efficiently computable semidefinite program, while in many theories including entanglement [41,63,64] and multilevel entanglement [65] it can be computed analytically for all pure states. Furthermore, in the class of affine resource theories [66,67], which includes theories such as coherence and imaginarity [68,69], the lower bound of Theorem 2 is tight, in the sense that there always exists a task such that N C ðρjΦ θ ; MÞ ¼ RðρÞ 2 .…”

mentioning

confidence: 99%