Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

Takeuchi, Yuki; Takahashi, Yasuhiro

doi:10.1103/physreva.94.062336

“…They have shown that, under plausible complexity-theoretic assumptions, this task is classically hard for various quantum circuits that seem easier to implement than universal ones. However, these classical hardness results have been obtained in severely restricted settings, such as a noise-free setting with additive approximation [5,17,3,20] and a noise setting with multiplicative approximation [9]: the former requires us to sample the output probability distribution of a quantum circuit with additive error and the latter to sample the output probability distribution of a quantum circuit under a noise model with multiplicative error. Thus, there is great interest in considering the above task in a more reasonable setting.…”

Section: Background and Main Resultsmentioning

confidence: 99%

Classically simulating quantum circuits with local depolarizing noise

Takahashi¹,

Takeuchi²,

Tani³

2021

Theoretical Computer Science

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We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions.

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“…They have shown that, under plausible complexity-theoretic assumptions, this task is classically hard for various quantum circuits that seem easier to implement than universal ones. However, these classical hardness results have been obtained in severely restricted settings, such as a noise-free setting with additive approximation [5,18,3,21] and a noise setting with multiplicative approximation [9]: the former requires us to sample the output probability distribution of a quantum circuit with additive error and the latter to sample the output probability distribution of a quantum circuit under a noise model with multiplicative error. Thus, there is great interest in considering the above task in a more reasonable setting.…”

Section: Background and Main Resultsmentioning

confidence: 99%

Classically Simulating Quantum Circuits with Local Depolarizing Noise

Takahashi,

Takeuchi,

Tani

2020

Preprint

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We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions.

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“…To complete the proof, we show Eq. (13). First, we consider the case where Tr[g i ρ] ≥ 1 − 2ǫ is satisfied for all i.…”

Section: Because Of the Union Bound And The Hoeffding Inequalitymentioning

confidence: 99%

Verification of Many-Qubit States

Takeuchi

¹

,

Morimae

²

2018

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Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli operators. First, we introduce a protocol for verifying ground states of Hamiltonians. We next explain how to verify quantum states generated by a certain class of quantum circuits. We finally propose an adaptive test of stabilizers that enables the verification of all polynomial-time-generated hypergraph states, which include output states of the Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP) circuits. Importantly, we do not make any assumption that the identically and independently distributed copies of the same states are given: Our protocols work even if some highly complicated entanglement is created among copies in any artificial way. As applications, we consider the verification of the quantum computational supremacy demonstration with IQP models, and verifiable blind quantum computing.

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Ancilla-driven instantaneous quantum polynomial time circuit for quantum supremacy

Cited by 8 publications

References 40 publications

Classically simulating quantum circuits with local depolarizing noise

Classically simulating quantum circuits with local depolarizing noise

Classically Simulating Quantum Circuits with Local Depolarizing Noise

Verification of Many-Qubit States

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