arXiv subjects

I. Marvian

Publications and source records attributed to I. Marvian.

4 recordsLinked to original sources

arXiv2021

Error mitigation via stabilizer measurement emulation

Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols. This and other open-loop error mitigation techniques are critical for quantum information processing in the era of Noisy Intermediate-Scale Quantum technology. However, despite its utility, dynamical decoupling does not address errors which occur at unstructured times during a circuit, including certain commonly-encountered noise mechanisms such as cross-talk and imperfectly calibrated control pulses. Here, we introduce and demonstrate an alternative technique - `quantum measurement emulation' (QME) - that effectively emulates the measurement of stabilizer operators via stochastic gate application, leading to a first-order insensitivity to coherent errors. The QME protocol enables error suppression based on the stabilizer code formalism without the need for costly measurements and feedback, and it is particularly well-suited to discrete coherent errors that are challenging for DD to address.

quant-ph↗

arXiv2016

An efficient quantum algorithm for spectral estimation

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well - consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum-classical division of labor: The time-critical steps are implemented in quantum superposition, while an interjacent step, requiring only exponentially few parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.

quant-ph↗

arXiv2008

Building all Time Evolutions with Rotationally Invariant Hamiltonians

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption whose validity is not obvious. We introduce two different schemes by which any arbitrary unitary time evolution and measurement can be implemented with desired accuracy by using rotationally invariant Hamiltonians that act on the given system and two ancillary systems serving as reference frames. These frames specify the z and x directions and are independent of the desired time evolution. We also investigate the effects of quantum fluctuations that inevitably arise due to usage of a finite system as a reference frame and estimate how fast these fluctuations tend to zero when the size of the reference frame tends to infinity. Moreover we prove that for a general symmetry any symmetric quantum operations can be implemented just by using symmetric interactions and ancillas in the symmetric states.

quant-ph↗

arXiv2005

How the quality of a received EPR pair depends on the distances from an EPR source?

Let an EPR source which generates maximally entangled pairs be located so that it has distances $L_1$ and $L_2$ to two users. After taking into account various effects like loss of photons, deficiencies in the source and detectors, an entangled pair traveling through the channel may loose its perfect correlation due to errors in the channel. How the entanglement of the received pair depends on the above distances and the local properties of the channels used for this transmission? What is the best location of the source if we want to achieve the highest fidelity? What is the threshold distance beyond which the entanglement of the pair vanishes and becomes useless for using in teleportation. We discuss these problems for the Pauli channel which simulates the effect of optical fibers and possibly the atmosphere on the polarization-entangled photons.

quant-ph↗