REVIEW 4 cited by
Certifying almost all quantum states with few single-qubit measurements
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Certifying almost all quantum states with few single-qubit measurements
read the original abstract
Certifying that an n-qubit state synthesized in the lab is close to the target state is a fundamental task in quantum information science. However, existing rigorous protocols either require deep quantum circuits or exponentially many single-qubit measurements. In this work, we prove that almost all n-qubit target states, including those with exponential circuit complexity, can be certified from only O(n^2) single-qubit measurements. This result is established by a new technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state, and for learning and verifying neural networks, tensor networks, and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties that would otherwise require an exponential number of measurements. We demonstrate these applications in numerical experiments with up to 120 qubits, and observe advantage over existing methods such as cross-entropy benchmarking (XEB).
Forward citations
Cited by 4 Pith papers
-
Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
Develops an optimization-free disentangling algorithm and algebraic criterion for efficient CAMPS representations of Clifford circuits doped with αI+βP gates, enabling polynomial classical simulation for more circuits...
-
Sample- and Hardware-Efficient Fidelity Estimation by Stripping Phase-Dominated Magic
Phase stripping reduces target-state magic to enable O(poly(n)) or O(1) sample fidelity estimation for phase-dominated states using a single fan-out gate plus nonlinear Pauli post-processing.
-
Efficient certification of intractable quantum states with few Pauli measurements
The paper claims Clifford-enhanced product states can be certified with O(n^2/epsilon^2) Pauli measurements in the i.i.d. setting and polynomially many in the adversarial setting, but the central estimator is derived ...
-
RandomMeas.jl: A Julia Package for Randomized Measurements in Quantum Devices
RandomMeas.jl is a modular Julia package implementing randomized measurement protocols and classical shadow estimators for quantum computing applications.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.