Related papers: Heisenberg limited multiple eigenvalue estimation …
Evaluating the entanglement spectrum is essential for characterizing exotic quantum phases such as quantum criticality and topological order. However, for large quantum many-body systems, this task is hindered by the exponential measurement…
Within the quantum phase representation we derive Heisenberg limits, in closed form, for N00N states and two other classes of states that can perform better in terms of local performance metrics relevant for multiply-peaked distributions.…
Multiparameter estimation is a general problem that aims at measuring unknown physical quantities, obtaining high precision in the process. In this context, the adoption of quantum resources promises a substantial boost in the achievable…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…
Gradient estimation is a central challenge in training parameterized quantum circuits (PQCs) for hybrid quantum-classical optimization and learning problems. This difficulty arises from several factors, including the exponential…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…
We propose a quantum lidar protocol to jointly estimate the range and velocity of a target by illuminating it with a single beam of pulsed displaced squeezed light. In the lossless scenario, we show that the mean-squared errors of both…
A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…
We propose a scheme for parameter estimation with cluster states. We find that phase estimation with cluster states under a many-body Hamiltonian and separable measurements leads to a precision at the Heisenberg limit. As noise models we…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding…
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Estimating quantum time-series such as the Loschmidt amplitude $f(t)=\langle\psi|\mathrm{e}^{-\mathrm{i}Ht}|\psi\rangle$ is central to spectroscopy, Hamiltonian analysis, and many phase-estimation algorithms. Direct estimation via the…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time…
We present an efficient and robust protocol for quantum-enhanced sensing using a single qubit in the topological waveguide system. Our method relies on the topological-paired bound states, which are localized near the qubit and can be…
Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum…