Related papers: Tensor-based phase difference estimation on time s…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
Quantum Kernel Estimation (QKE) is a technique based on leveraging a quantum computer to estimate a kernel function that is classically difficult to calculate, which is then used by a classical computer for training a Support Vector Machine…
Quantum phase estimation is a cornerstone in quantum algorithm design, allowing for the inference of eigenvalues of exponentially-large sparse matrices.The maximum rate at which these eigenvalues may be learned, --known as the Heisenberg…
This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of…
Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a…
We present a comprehensive end-to-end quantum algorithm for tensor problems, including tensor PCA and planted kXOR, that achieves potential superquadratic quantum speedups over classical methods. We build upon prior works by…
Error mitigation is essential for the practical implementation of quantum algorithms on noisy intermediate-scale quantum (NISQ) devices. This work explores and extends Clifford Data Regression (CDR) to mitigate noise in quantum chemistry…
The advent of noisy-intermediate scale quantum computers has introduced the exciting possibility of achieving quantum speedups in machine learning tasks. These devices, however, are composed of a small number of qubits, and can faithfully…
We show how phase and amplitude estimation algorithms can be parallelized. This can reduce the gate depth of the quantum circuits to that of a single Grover operator with a small overhead. Further, we show that for quantum amplitude…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
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…
Quantum error mitigation (QEM) protocols have provably exponential bounds on the cost scaling; however, exploring which regimes QEM can recover usable results is still of sizable interest. The expected absence of complete error correction…
We study the performance of our previously proposed Projective Quantum Eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H$_2$, we find that we are able to obtain…
Leakage errors, in which a qubit is excited to a level outside the qubit subspace, represent a significant obstacle in the development of robust quantum computers. We present a computationally efficient simulation methodology for studying…
We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit and quantum measurement. With a proper initial state of the ancillary qubit and an optimized evolution time, the quantum…
We construct a general wave function with the topological order by introducing the $\mathbb{Z}_{2}$ gauge degrees of freedom, characterizing both the toric code state and double semion state. Via calculating the correlation length defined…
We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped $\textrm{Yb}^+$ ion qubit. We estimate these phases with uncertainties less than $4\cdot10^{-4}$ radians using…
In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…