Interactive shallow Clifford circuits: Quantum advantage against NC¹ and beyond

Grier, Daniel; Schaeffer, Luke

doi:10.1145/3357713.3384332

Cited by 17 publications

(64 citation statements)

References 24 publications

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“…In some cases, this will lead to an unconditional separation between noisy shallow quantum circuits and shallow classical circuits, and in some cases this will lead to a conditional separation. We note that these separations will not be identical to those obtained in Ref [GS20] due to the fact that we use quasipolynomial-size circuits to decode the syndrome qubits of the surface code.…”

Section: Introductionmentioning

confidence: 67%

“…In the first round, the quantum device is given the bases in which to measure some of the qubits and returns their measurement outcomes; and in the second round, the quantum device is given bases in which to measure the remaining qubits and returns their measurement outcomes. Grier and Schaeffer [GS20] show that any classical device which can solve such problems must be relatively powerful. More specifically, if the initial Clifford state is a constant-width grid state, then the classical device can be used to solve problems in NC 1 , and if the starting state is a poly-width grid state, then the classical device can be used to solve problems in ⊕L.…”

Section: Introductionmentioning

confidence: 99%

“…Fortunately, it was shown in Ref [GS20] that Step 2 holds 7 for the NC 1 -hardness result. We immediately obtain the following separation: Theorem 2.…”

Section: Introductionmentioning

confidence: 99%

“…That is, one could require that any classical simulation of the protocol be correct with high probability on all inputs. In this case, simply combining the results of [Bra+20] with an amplified version of [GS20] suffice to show these types of simulations can be leveraged to solve hard problems. However, we believe (much like [Bra+20]) that these results are more convincing when a weaker requirement is made on the classical simulation-namely, that the classical device need only succeed with high probability over some reasonable distribution of inputs.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, Step 2 is left as an open question in Ref [GS20] for the ⊕L-hardness result. The second major contribution of this paper (and main technical result) is to show that we can, in fact, obtain average-case hardness for this setting: Theorem 3.…”

Section: Introductionmentioning

confidence: 99%

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Interactive quantum advantage with noisy, shallow Clifford circuits

Grier,

Ju,

Schaeffer

2021

Preprint

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Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC 0 ) can solve with near certainty (probability 1 − o(1)), but that any bounded fan-in constant-depth classical circuit (NC 0 ) fails with some constant probability. We show that this robustness to noise can be achieved in the other low-depth quantum/classical circuit separations in this area. In particular, we show a general strategy for adding noise tolerance to the interactive protocols of Grier and Schaeffer. As a consequence, we obtain an unconditional separation between noisy QNC 0 circuits and AC 0 [p] circuits for all primes p ≥ 2, and a conditional separation between noisy QNC 0 circuits and log-space classical machines under a plausible complexity-theoretic conjecture.A key component of this reduction is showing average-case hardness for the classical simulation tasks-that is, showing that a classical simulation of the quantum interactive task is still powerful even if it is allowed to err with constant probability over a uniformly random input. We show that is true even for quantum tasks which are ⊕L-hard to simulate. To do this, we borrow techniques from randomized encodings used in cryptography.

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Section: Introductionmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

“…Fortunately, it was shown in Ref [GS20] that Step 2 holds 7 for the NC 1 -hardness result. We immediately obtain the following separation: Theorem 2.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interactive quantum advantage with noisy, shallow Clifford circuits

Grier,

Ju,

Schaeffer

2021

Preprint

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An Exact and Practical Classical Strategy for 2D Graph State Sampling

et al. 2023

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Constant-depth quantum circuits that prepare and measure graph states on 2D grids are proved to possess a computational quantum advantage over their classical counterparts due to quantum nonlocality and are also well suited for demonstrations on current superconducting quantum processor architectures. To simulate the partial or full sampling of 2D graph states, a practical two-stage classical strategy that can exactly generate any number of samples (bit strings) from such circuits is proposed. The strategy is inspired by exploiting specific properties of a hidden linear function problem solved by the target quantum circuit, which in particular combines traditional classical parallel algorithms and an explicit gate-based constant-depth classical circuit together. A theoretical analysis reveals that on average each sample can be obtained in nearly constant time for sampling specific circuit instances of large size. Moreover, the feasibility of the theoretical model is demonstrated by implementing typical instances up to 25 qubits on a moderate field programmable gate array platform. Therefore, the strategy can be used as a practical tool for verifying experimental results obtained from shallow quantum circuits of this type.

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Quantum Advantage from One-Way Functions

Morimae,

Yamakawa

2024

Lecture Notes in Computer Science

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Interactive shallow Clifford circuits: Quantum advantage against NC¹ and beyond

Cited by 17 publications

References 24 publications

Interactive quantum advantage with noisy, shallow Clifford circuits

Interactive quantum advantage with noisy, shallow Clifford circuits

An Exact and Practical Classical Strategy for 2D Graph State Sampling

Quantum Advantage from One-Way Functions

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