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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method

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 Hadamard test circuit structure and only requires simple classical postprocessing. QMEGS is the first algorithm to simultaneously satisfy the following two properties: (1) It can achieve the Heisenberg-limited scaling without relying on any spectral gap assumption. (2) With a positive energy gap and additional assumptions on the initial state, QMEGS can estimate all dominant eigenvalues to ϵ accuracy utilizing a significantly reduced circuit depth compared to the standard quantum phase estimation algorithm. In the most favorable scenario, the maximal runtime can be reduced to as low as log(1/ϵ). This implies that QMEGS serves as an efficient and versatile approach, achieving the best-known results for both gapped and gapless systems. Numerical results validate the efficiency of our proposed algorithm in various regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Reductive quantum phase estimation

Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here, we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a smaller number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a tradeoff between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application. Published by the American Physical Society 2024

Papadopoulos, Nicholas J. C. (ORCID:00000002635700↗
DOE OSTI2025

LuGo: An enhanced quantum phase estimation implementation

Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard implementation of QPE faces challenges related to time complexity and circuit depth, which limit its practicality for large-scale computations. We introduce LuGo, a novel framework designed to enhance the performance of QPE by reducing circuit duplication, as well as using parallelization techniques to achieve faster generation of the QPE circuit and gate reduction. We validate the effectiveness of our framework by generating quantum linear solver circuits, which require both QPE and inverse QPE, to solve linear systems of equations. LuGo achieves significant improvements in both computational efficiency and hardware requirements without compromising on accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to generate a circuit that solves a 2 6 × 2 6 system matrix by a factor of 50.68 and over 31× reduction of quantum gates and circuit depth, with no fidelity loss on an ideal quantum simulator. Furthermore, we demonstrated the versatility and scalability of LuGo enabled HHL algorithm by simulating a canonical Hele-Shaw fluid problem using a quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.

Quantum algorithm↗
DOE OSTI2020

Python Robust Phase Estimation (PyRPE)

Robust Phase Estimation (RPE) is a quantum algorithm to determine the relative phases of eigenstates of a unitary operator. This code implements the classical portion of the RPE algorithm, useful both in simulation (e.g., Sandia's pyGSTi or IBM's Qiskit simulators) and on actual quantum hardware (e.g., IBM's Qiskit Quantum Experience). It additionally implements improvements in these dependent software packages, for both required core function of the RPE and improved usability. SAND2020-12547 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

Russo, Antonio↗
DOE OSTI2025

Hardware-Efficient Quantum Phase Estimation via Local Control

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

Schiffer, Benjamin F. [Max Planck Institute of Qua↗
DOE OSTI2021

Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation

Here, we adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a single auxiliary qubit. As a proof of concept, we calculate the energies of the ground state and low-lying electronic excitations of a hydrogen molecule in a minimal basis on a cloud quantum computer. The denominative robustness of our approach is then quantified in terms of a high tolerance to coherent errors in the state preparation and measurement. Conceptually, we note that all quantum phase estimation algorithms ultimately evaluate eigenvalue differences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Growth phase estimation for abundant bacterial populations sampled longitudinally from human stool metagenomes

Longitudinal sampling of the stool has yielded important insights into the ecological dynamics of the human gut microbiome. However, human stool samples are available approximately once per day, while commensal population doubling times are likely on the order of minutes-to-hours. Despite this mismatch in timescales, much of the prior work on human gut microbiome time series modeling has assumed that day-to-day fluctuations in taxon abundances are related to population growth or death rates, which is likely not the case. Here, we propose an alternative model of the human gut as a stationary system, where population dynamics occur internally and the bacterial population sizes measured in a bolus of stool represent a steady-state endpoint of these dynamics. We formalize this idea as stochastic logistic growth. We show how this model provides a path toward estimating the growth phases of gut bacterial populations in situ. We validate our model predictions using an in vitro Escherichia coli growth experiment. Finally, we show how this method can be applied to densely-sampled human stool metagenomic time series data. We discuss how these growth phase estimates may be used to better inform metabolic modeling in flow-through ecosystems, like animal guts or industrial bioreactors.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Consistency testing for robust phase estimation

In this work, we present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for applications such as estimating the effective process parameters of noisy hardware, but its robustness is dependent on the noise satisfying certain threshold assumptions. We provide consistency checks that can indicate when those thresholds have been violated, which can be difficult or impossible to test directly. We test these consistency checks for several common noise models, and identify two possible checks with high accuracy in locating the point in a robust phase estimation run at which further estimates should not be trusted. One of these checks may be chosen based on resource availability, or they can be used together in order to provide additional verification.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Quantum phase estimation for a class of generalized eigenvalue problems

Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems Hv = λv , such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to generalized eigenvalue problems Av = λBv , which arise in many areas of science and engineering. Here, we answer this question affirmatively. A restricted class of generalized eigenvalue problems could be solved as efficiently as standard eigenvalue problems. A paradigmatic example is provided by Sturm-Liouville problems. Another example comes from linear ideal magnetohydrodynamics, where phase estimation could be used to determine the stability of magnetically confined plasmas in fusion reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Optimal Coherent Quantum Phase Estimation [Slides]

Many applications of quantum phase estimation (QPE) require it to be implemented coherently and with high confidence. We outline an algorithm that achieves both goals using optimal resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Toward quantum computing for high-energy excited states in molecular systems: quantum phase estimations of core-level states

This paper explores the utility of the quantum phase estimation (QPE) in calculating high-energy excited states characterized by promotions of electrons occupying inner energy shells. These states have been intensively studied over the last few decades especially in supporting the experimental effort at light sources. Results obtained with the QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is also discussed.

Bauman, Nicholas P.↗
DOE OSTI2022

Effects of cosine tapering window on quantum phase estimation

Here, we provide a modification to the quantum phase estimation algorithm (QPEA) [Abrams and Lloyd, Phys. Rev. Lett. 83, 5162 (1999); Cleve et al., Proc. R. Soc. A 454, 339 (1998); Nielsen and Chuang, Quantum computation and quantum information, 2002.] inspired by classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Phase estimation algorithm for the multibeam optical metrology

Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can be translated into the classical linear optical framework. The developed setup made of beam splitters, mirrors and phase shifters demonstrates how the classical coherence, similarly to the quantum coherence, poses a resource for obtaining information about the measurable physical quantities. Our study opens route to the reliable implementation of the small-scale unitary algorithms on path-encoded qudits, thus establishing an easily accessible platform for unitary computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes

While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical simulations of these quantum algorithms. In particular, the quantum phase estimation (QPE) algorithm is among several approaches that have attracted much attention in recent years for its genuine quantum character. However, it is memory-intensive to simulate and intractable for moderate system sizes. Herein, this paper discusses the performance and applicability of QPESIM, a new simulation of the QPE algorithm designed to take advantage of modest computational resources. In particular, we demonstrate the versatility of QPESIM in simulating various electronic states by examining the ground and core-level states of H 2 O. For these states, we also discuss the effect of the active-space size on the quality of the calculated energies. For the high-energy core-level states, we demonstrate that new QPE simulations for active spaces defined by 15 active orbitals significantly reduce the errors in core-level excitation energies compared to earlier QPE simulations using smaller active spaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Interferometric binary phase estimations

We propose an interferometric scheme where each photon returns one bit of the binary expansion of an unknown phase. It sets up a method for estimating the phase value at arbitrary uncertainty. This strategy is global, since it requires no prior information, and it achieves the Heisenberg bound independently of the output statistics. We provide simulations and a characterization of this architecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Marine Boundary Layer Cloud Boundaries and Phase Estimation Using Airborne Radar and In Situ Measurements During the SOCRATES Campaign over Southern Ocean

The Southern Ocean Clouds, Radiation, Aerosol Transport Experimental Study (SOCRATES) was an aircraft-based campaign (15 January–26 February 2018) that deployed in situ probes and remote sensors to investigate low-level clouds over the Southern Ocean (SO). A novel methodology was developed to identify cloud boundaries and classify cloud phases in single-layer, low-level marine boundary layer (MBL) clouds below 3 km using the HIAPER Cloud Radar (HCR) and in situ measurements. The cloud base and top heights derived from HCR reflectivity, Doppler velocity, and spectrum width measurements agreed well with corresponding lidar-based and in situ estimates of cloud boundaries, with mean differences below 100 m. A liquid water content–reflectivity (LWC-Z) relationship, LWC = 0.70Z0.29, was derived to retrieve the LWC and liquid water path (LWP) from HCR profiles. The cloud phase was classified using HCR measurements, temperature, and LWP, yielding 40.6% liquid, 18.3% mixed-phase, and 5.1% ice samples, along with drizzle (29.1%), rain (3.2%), and snow (3.7%) for drizzling cloud cases. The classification algorithm demonstrates good consistency with established methods. This study provides a framework for the boundary and phase detection of MBL clouds, offering insights into SO cloud microphysics and supporting future efforts in satellite retrievals and climate model evaluation.

MBL clouds over Southern Ocean↗