Related papers: Improved quantum data analysis
Reconstructing the state of a complex quantum system represents a pivotal task for all quantum information applications, both for characterization purposes and for verification of quantum protocols. Recent technological developments have…
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…
Following the first paper on quantum algorithms for SDP-solving by Brand\~ao and Svore in 2016, rapid developments has been made on quantum optimization algorithms. Recently Brand\~ao et al. improved the quantum SDP-solver in the so-called…
Quantum state and process tomography are typically analyzed under the assumption that devices emit independent and identically distributed (i.i.d.) states or channels. In realistic experiments, however, noise, drift, feedback, or…
With the rapid development of quantum computers, quantum algorithms have been studied extensively. However, quantum algorithms tackling statistical problems are still lacking. In this paper, we propose a novel non-oracular quantum adaptive…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
To accelerate the algorithms for the dihedral hidden subgroup problem, we present a new algorithm based on algorithm SV(shortest vector). A subroutine is given to get a transition quantum state by constructing a phase filter function, then…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…
In differential privacy (DP), we want to query a database about n users, in a way that "leaks at most eps about any individual user," even conditioned on any outcome of the query. Meanwhile, in gentle measurement, we want to measure n…
In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Given $n$ copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, quantum state certification is the task of determining whether $\rho=\rho_0$ or $\|\rho-\rho_0\|_1>\varepsilon$, where $\rho_0$ is a known reference state. We…
We study the power of quantum memory for learning properties of quantum systems and dynamics, which is of great importance in physics and chemistry. Many state-of-the-art learning algorithms require access to an additional external quantum…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…