
Interactive shallow Clifford circuits: quantum advantage against NC^1 and beyond
Recent work of Bravyi et al. and followup work by Bene Watts et al. dem...
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Estimating the entropy of shallow circuit outputs is hard
The decision problem version of estimating the Shannon entropy is the En...
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Noise and the frontier of quantum supremacy
Noise is the defining feature of the NISQ era, but it remains unclear if...
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Spoofing Linear CrossEntropy Benchmarking in Shallow Quantum Circuits
The linear crossentropy benchmark (Linear XEB) has been used as a test ...
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Efficient classical simulation of random shallow 2D quantum circuits
Random quantum circuits are commonly viewed as hard to simulate classica...
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Quantum Advantage from Conjugated Clifford Circuits
A wellknown result of Gottesman and Knill states that Clifford circuits...
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Simulating Noisy Quantum Circuits with Matrix Product Density Operators
Simulating quantum circuits with classical computers requires resources ...
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Interactive quantum advantage with noisy, shallow Clifford circuits
Recent work by Bravyi et al. constructs a relation problem that a noisy constantdepth quantum circuit (QNC^0) can solve with near certainty (probability 1  o(1)), but that any bounded fanin constantdepth classical circuit (NC^0) fails with some constant probability. We show that this robustness to noise can be achieved in the other lowdepth 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 logspace classical machines under a plausible complexitytheoretic conjecture. A key component of this reduction is showing averagecase 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 ⊕Lhard to simulate. To do this, we borrow techniques from randomized encodings used in cryptography.
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