Quantum advantages for Pauli channel estimation

  title={Quantum advantages for Pauli channel estimation},
  author={Senrui Chen and Sisi Zhou and Alireza Seif and Liang Jiang},
  journal={Physical Review A},
We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices. The specific task we consider is to simultaneously learn all the eigenvalues of an n-qubit Pauli channel to ±ε precision. We give an estimation protocol with an n-qubit ancilla that succeeds with high probability using only O(n/ε2) copies of the Pauli channel… 
5 Citations

Figures from this paper

Tight Bounds for Quantum State Certification with Incoherent Measurements
This work focuses on algorithms which use incoherent measurements, i.e. which only measure one copy of ρ at a time, and can be implemented without persistent quantum memory and thus represent a large class of protocols that can be run on current or near-term devices.
Exponential Separations Between Learning With and Without Quantum Memory
It is proved that to estimate absolute values of all $n-qubit Pauli observables, algorithms with k < n qubits of quantum memory require at least $\Omega(2^{(n-k)/3})$ samples, but there is an algorithm using $n$-qu bit quantum memory which only requires $\mathcal{O}(n)$ samples.
Quantum advantage in learning from experiments
This research presents a probabilistic model of the black hole that combines quantum entanglement, superposition, and superposition to describe the fabric of space-time.
Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
It is proved that a wide class of variational quantum models—which are shallow, and exhibit no barren plateus—have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known.
The learnability of Pauli noise
Senrui Chen,1, ∗ Yunchao Liu,2, † Matthew Otten,3, ‡ Alireza Seif,1, § Bill Fefferman,4, ¶ and Liang Jiang1, ‖ 1Pritzker School of Molecular Engineering, University of Chicago, IL 60637, USA


Efficient Estimation of Pauli Channels
These results enable a host of applications beyond just characterizing noise in a large-scale quantum system: they pave the way to tailoring quantum codes, optimizing decoders, and customizing fault tolerance procedures to suit a particular device.
Sample-optimal tomography of quantum states
A measurement scheme (POVM) that uses O( (dr/ δ ) ln(d/δ) ) copies to estimate ρ to error δ in infidelity and proves for the first time that such “product” measurements have asymptotically suboptimal scaling with d and r.
Recovering quantum gates from few average gate fidelities
This Letter provides a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured with respect to random Clifford unitaries for characterizing multiqubit unitary gates.
Mixed-state Pauli-channel parameter estimation
It is shown, that unlike the pure state case, the quantum correlated state protocol can yield greater estimation accuracy than any independent state protocol and that these gains persist even when the system states are separable and, in some cases, when quantum discord is absent after channel invocation.
Fundamental limits to quantum channel discrimination
This work investigates the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations, and derives ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution.
Entanglement is Necessary for Optimal Quantum Property Testing
It is shown that with independent measurements, $\Omega(d^{4/3}/\epsilon^{2})$ is necessary, even if the measurements are chosen adaptively, which resolves a question posed in [7].
Efficient learning of quantum noise
The results pave the way for noise metrology in next-generation quantum devices, calibration in the presence of crosstalk, bespoke quantum error-correcting codes 10 and customized fault-tolerance protocols 11 that can greatly reduce the overhead in a quantum computation.
Fast Estimation of Sparse Quantum Noise
A heuristic version of the algorithm that uses simplified Clifford circuits on data from an IBM 14-qubit superconducting device and an open source implementation is experimentally validated, showing that accurate and precise estimation of the probability of arbitrary-weight Pauli errors is possible even when the signal is two orders of magnitude below the measurement noise floor.
General Benchmarks for Quantum Repeaters
Using a technique based on quantum teleportation, we simplify the most general adaptive protocols for key distribution, entanglement distillation and quantum communication over a wide class of
Information-theoretic bounds on quantum advantage in machine learning
It is proven that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model, and it is proved that the exponential quantum advantage is possible.