Related papers: Heisenberg-limited quantum phase estimation of mul…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
Quantum phase estimation is the flagship algorithm for quantum simulation on fault-tolerant quantum computers. We demonstrate that an \emph{off-grid} compressed sensing protocol, combined with a state-of-the-art signal classification…
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder…
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…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigenvalue Gaussian filtered Search (QMEGS). QMEGS leverages the…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop and analyze a scheme that achieves near-optimal precision up to a constant…
In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert \psi \rangle$ of $U$ with unknown…
As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…
We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis…
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…
The calibration of high-quality two-qubit entangling gates is an essential component in engineering large-scale, fault-tolerant quantum computers. However, many standard calibration techniques are based on randomized circuits that are only…
The fidelity susceptibility serves as a universal probe for quantum phase transitions, offering an order-parameter-free metric that captures ground-state sensitivity to Hamiltonian perturbations and exhibits critical scaling. Classical…
Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…
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.…