# An approximate description of quantum states

@article{Paini2019AnAD, title={An approximate description of quantum states}, author={Marco Paini and Amir Kalev}, journal={arXiv: Quantum Physics}, year={2019} }

We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of $N$. We show, in fact, that the error in the estimation of the observables' expectation values decreases as the inverse of the square root of the number of the system's identical preparations and increases, at most, linearly in a suitably defined, $N$-independent, seminorm of the observables. Building the…

## 23 Citations

### Quantifying the Sensitivity to Errors in Analog Quantum Simulation

- Physics
- 2020

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results…

### Predicting Gibbs State Expectation Values with Pure Thermal Shadows

- Computer Science
- 2022

A quantum algorithm is proposed that can predict M linear functions of an arbitrary Gibbs state with only O ( log M ) experimental measurements and can be successfully employed as a subroutine for training an 8-qubit fully connected quantum Boltzmann machine.

### Information-theoretic bounds on quantum advantage in machine learning

- Computer SciencePhysical review letters
- 2021

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.

### Efficient estimation of Pauli observables by derandomization

- MathematicsPhysical review letters
- 2021

An efficient derandomization procedure is proposed that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one.

### Exponential Separations Between Learning With and Without Quantum Memory

- Physics2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

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.

### The randomized measurement toolbox

- Physics
- 2022

Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex…

### Virtual linear map algorithm for classical boost in near-term quantum computing

- Computer Science
- 2022

This paper introduces the Virtual Linear Map Algorithm (VILMA), a new method that enables not only to estimate multiple operator averages using classical post-processing of informationally complete measurement outcomes, but also to do so for the image of the measured reference state under low-depth circuits of arbitrary, not necessarily physical, k -local maps.

### On Classical and Hybrid Shadows of Quantum States

- Physics
- 2022

Classical shadows are a computationally eﬃcient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by…

### Symmetry-resolved dynamical purification in synthetic quantum matter

- PhysicsSciPost Physics
- 2022

When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of…

### Quantum-Computation and Applications

- Physics
- 2020

This research notebook on quantum computation and applications for quantum engineers, researchers, and scientists discusses and summarized the core principles and practical application areas of quantum computation, and describes a substantial difference between quantum and classical computation paradigm.