Related papers: Sharp Error Bounds on Quantum Boolean Summation in…
For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the $1/\sqrt{t}$ scaling where $t$ is the total probing time, in which case the maximal possible quantum…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
Period finding and phase estimation are fundamental in quantum computing. Prior work has established lower bounds on their success probabilities. Such quantum algorithms measure a state $|\hat\ell\rangle$ in an $n$-qubit computational…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
With a finite amount of measurement data acquired in variational quantum algorithms, the statistical benefits of several optimized numerical estimation schemes, including the scaled parameter-shift (SPS) rule and finite-difference (FD)…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…
The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental…
The ability of the Quantum Approximate Optimization Algorithm (QAOA) to deliver a quantum advantage on combinatorial optimization problems is still unclear. Recently, a scaling advantage over a classical solver was postulated to exist for…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…
Quantum parameter estimation holds significant promise for achieving high precision through the utilization of the most informative measurements. While various lower bounds have been developed to assess the best accuracy for estimates, they…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this…
We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f:X x Y-->{0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
The minimum mean-square error (MMSE) achievable by optimal estimation of a random variable $Y\in\mathbb{R}$ given another random variable $X\in\mathbb{R}^{d}$ is of much interest in a variety of statistical settings. In the context of…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently a quantum approximate Bayesian optimization algorithm (QABOA) that includes two…