arXiv subjects

Peter Love

Publications and source records attributed to Peter Love.

At least 19 recordsLinked to original sources

arXiv2025

The foundational value of quantum computing for classical fluids

Quantum algorithms for classical physics problems expose new patterns of quantum information flow as compared to the many-body Schr\"{o}dinger equation. As a result, besides their potential practical applications, they also offer a valuable theoretical and computational framework to elucidate the foundations of quantum mechanics, particularly the validity of the many-body Schr\"{o}dinger equation in the limit of large number of particles, on the order of the Avogadro number. This idea is illustrated by means of a concrete example, the Block-Encoded Carleman embedding of the Lattice Boltzmann formulation of fluid dynamics (CLB).

quant-ph↗

arXiv2025

Roadblocks and Opportunities in Quantum Algorithms -- Insights from the National Quantum Initiative Joint Algorithms Workshop, May 20--22, 2024

The National Quantum Initiative Joint Algorithms Workshop brought together researchers across academia, national laboratories, and industry to assess the current landscape of quantum algorithms and discuss roadblocks to progress. The workshop featured discussions on emerging algorithmic techniques, resource constraints in near-term hardware, and opportunities for co-design across software and systems. Presented here are seven topics from the workshop, each highlighting a critical challenge or promising opportunity discussed during the event. Together, they offer a snapshot of the field's evolving priorities and a shared vision for what is needed to advance quantum computational capabilities.

quant-ph↗

arXiv2025

Data Movement Model for the Vera C. Rubin Observatory

The sky images captured nightly by the camera on the Vera C. Rubin Observatory's telescope will be processed across facilities on three continents. Data acquisition will occur at the observatory's location on Cerro Pach\'{o}n in the Andes mountains of Chile. A first copy of the raw image data set is stored at the summit and immediately transmitted via dedicated network links to the archive center within the US Data Facility at SLAC National Accelerator Laboratory in California, USA and from there to two European facilities for processing and archiving purposes. Data products resulting from periodic processing campaigns of the entire set of images collected since the beginning of the survey are made available to the scientific community in the form of data releases. In this paper we present an overall view of how we leverage the tools selected for managing the movement of data among the Rubin processing and serving facilities, including Rucio and FTS. We also present the tools we developed to integrate Rucio's data model and Rubin's Data Butler, the software abstraction layer that mediates all access to storage by pipeline tasks that implement science algorithms.

astro-ph.IM↗

arXiv2025

Carleman-lattice-Boltzmann quantum circuit with matrix access oracles

We apply Carleman linearization of the Lattice Boltzmann (CLB) representation of fluid flows to quantum emulate the dynamics of a 2D Kolmogorov-like flow. We assess the accuracy of the result and find a relative error of the order of $10^{-3}$ with just two Carleman iterates, for a range of the Reynolds number up to a few hundreds. We first define a gate-based quantum circuit for the implementation of the CLB method and then exploit the sparse nature of the CLB matrix to build a quantum circuit based on block-encoding techniques which makes use of matrix oracles. It is shown that the gate complexity of the algorithm is thereby dramatically reduced, from exponential to quadratic. However, due to the need of employing up to seven ancilla qubits, the probability of success of the corresponding circuit for a single time step is too low to enable multi-step time evolution. Several possible directions to circumvent this problem are briefly outlined.

quant-ph↗

arXiv2023

Overview of the distributed image processing infrastructure to produce the Legacy Survey of Space and Time

The Vera C. Rubin Observatory is preparing to execute the most ambitious astronomical survey ever attempted, the Legacy Survey of Space and Time (LSST). Currently the final phase of construction is under way in the Chilean Andes, with the Observatory's ten-year science mission scheduled to begin in 2025. Rubin's 8.4-meter telescope will nightly scan the southern hemisphere collecting imagery in the wavelength range 320-1050 nm covering the entire observable sky every 4 nights using a 3.2 gigapixel camera, the largest imaging device ever built for astronomy. Automated detection and classification of celestial objects will be performed by sophisticated algorithms on high-resolution images to progressively produce an astronomical catalog eventually composed of 20 billion galaxies and 17 billion stars and their associated physical properties. In this article we present an overview of the system currently being constructed to perform data distribution as well as the annual campaigns which reprocess the entire image dataset collected since the beginning of the survey. These processing campaigns will utilize computing and storage resources provided by three Rubin data facilities (one in the US and two in Europe). Each year a Data Release will be produced and disseminated to science collaborations for use in studies comprising four main science pillars: probing dark matter and dark energy, taking inventory of solar system objects, exploring the transient optical sky and mapping the Milky Way. Also presented is the method by which we leverage some of the common tools and best practices used for management of large-scale distributed data processing projects in the high energy physics and astronomy communities. We also demonstrate how these tools and practices are utilized within the Rubin project in order to overcome the specific challenges faced by the Observatory.

astro-ph.IM↗

arXiv2021

Classically optimal variational quantum algorithms

Hybrid quantum-classical algorithms, such as variational quantum algorithms (VQA), are suitable for implementation on NISQ computers. In this Letter we expand an implicit step of VQAs: the classical pre-computation subroutine which can non-trivially use classical algorithms to simplify, transform, or specify problem instance-specific variational quantum circuits. In VQA there is a trade-off between quality of solution and difficulty of circuit construction and optimization. In one extreme, we find VQA for MAXCUT which are exact, but circuit design or variational optimization is NP-HARD. At the other extreme are low depth VQA, such as QAOA, with tractable circuit construction and optimization but poor approximation ratios. Combining these two we define the Spanning Tree QAOA (ST-QAOA) to solve MAXCUT, which uses an ansatz whose structure is derived from an approximate classical solution and achieves the same performance guarantee as the classical algorithm and hence can outperform QAOA at low depth. In general, we propose integrating these classical pre-computation subroutines into VQA to improve heuristic or guaranteed performance.

quant-ph↗

arXiv2020

Implementation of Measurement Reduction for the Variational Quantum Eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.

quant-ph↗

arXiv2020

Feynman-path type simulation using stabilizer projector decomposition of unitaries

We propose a classical simulation method for quantum circuits based on decomposing unitary gates into a sum of stabilizer projectors. By only decomposing the non-Clifford gates, we take advantage of the Gottesman-Knill theorem and build a bridge between stabilizer-based simulation and Feynman-path-type simulation. We give two variants of this method: stabilizer-based path-integral recursion (SPIR) and stabilizer projector contraction (SPC). We also analyze further advantages and disadvantages of our method compared to the Bravyi-Gosset algorithm and recursive Feynman path-integral algorithms. We construct a parametrized circuit ensemble and identify the parameter regime in this ensemble where our method offers superior performance. We also estimate the time cost for simulating quantum supremacy experiments with our method and motivate potential improvements of the method.

quant-ph↗

arXiv2019

Measurement reduction in variational quantum algorithms

Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The number of terms can become overwhelmingly large for problems at the scale of NISQ hardware that may soon be available. We approach this problem from the perspective of contextuality, and use unitary partitioning (developed independently by Izmaylov et al. [J. Chem. Theory Comput. 16, 190 (2020)]) to define variational quantum eigensolver procedures in which additional unitary operations are appended to the ansatz preparation to reduce the number of terms. This approach may be scaled to use all coherent resources available after ansatz preparation. We also study the use of asymmetric qubitization to implement the additional coherent operations with lower circuit depth. We investigate this technique for lattice Hamiltonians, random Pauli Hamiltonians, and electronic structure Hamiltonians. Using this technique, we find a constant factor speedup for lattice and random Pauli Hamiltonians. For electronic structure Hamiltonians, we prove that linear term reduction with respect to the number of orbitals, which has been previously observed in numerical studies, is always achievable. For systems represented on 10--30 qubits, we find that there is a reduction in the number of terms by approximately an order of magnitude. Applied to the plane-wave dual basis representation of fermionic Hamiltonians, however, unitary partitioning offers only a constant factor reduction. Finally, we show that noncontextual Hamiltonians may be reduced to effective commuting Hamiltonians using unitary partitioning.

quant-ph↗

arXiv2018

Approximate stabilizer rank and improved weak simulation of Clifford-dominated circuits for qudits

Bravyi and Gosset recently gave classical simulation algorithms for quantum circuits dominated by Clifford operations. These algorithms scale exponentially with the number of T-gate in the circuit, but polynomially in the number of qubits and Clifford operations. Here we extend their algorithm to qudits of odd prime dimensions. We generalize their approximate stabilizer rank method for weak simulation to qudits and obtain the scaling of the approximate stabilizer rank with the number of single-qudit magic states. We also relate the canonical form of qudit stabilizer states to Gauss sum evaluations. We give an O(n^3) algorithm to calculating the inner product of two n-qudit stabilizer states.

quant-ph↗

arXiv2018

Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits

One of the lowest-order corrections to Gaussian quantum mechanics in infinite-dimensional Hilbert spaces are Airy functions: a uniformization of the stationary phase method applied in the path integral perspective. We introduce a "periodized stationary phase method" to discrete Wigner functions of systems with odd prime dimension and show that the $\frac{\pi}{8}$ gate is the discrete analog of the Airy function. We then establish a relationship between the stabilizer rank of states and the number of quadratic Gauss sums necessary in the periodized stationary phase method. This allows us to develop a classical strong simulation of a single qutrit marginal on $t$ qutrit $\frac{\pi}{8}$ gates that are followed by Clifford evolution, and show that this only requires $3^{\frac{t}{2}+1}$ quadratic Gauss sums. This outperforms the best alternative qutrit algorithm (based on Wigner negativity and scaling as $\sim\hspace{-3pt} 3^{0.8 t}$ for $10^{-2}$ precision) for any number of $\frac{\pi}{8}$ gates to full precision.

quant-ph↗

arXiv2018

Quantum chemistry calculations on a trapped-ion quantum simulator

Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multi-qubit quantum simulators.

quant-ph↗

arXiv2018

The Non-Disjoint Ontic States of the Grassmann Ontological Model, Transformation Contextuality, and the Single Qubit Stabilizer Subtheory

We show that it is possible to construct a preparation non-contextual ontological model that does not exhibit "transformation contextuality" for single qubits in the stabilizer subtheory. In particular, we consider the "blowtorch" map and show that it does not exhibit transformation contextuality under the Grassmann Wigner-Weyl-Moyal (WWM) qubit formalism. Furthermore, the transformation in this formalism can be fully expressed at order $\hbar^0$ and so does not qualify as a candidate quantum phenomenon. In particular, we find that the Grassmann WWM formalism at order $\hbar^0$ corresponds to an ontological model governed by an additional set of constraints arising from the relations defining the Grassmann algebra. Due to this additional set of constraints, the allowed probability distributions in this model do not form a single convex set when expressed in terms of disjoint ontic states and so cannot be mapped to models whose states form a single convex set over disjoint ontic states. However, expressing the Grassmann WWM ontological model in terms of non-disjoint ontic states corresponding to the monomials of the Grassmann algebra results in a single convex set. We further show that a recent result by Lillystone et al. that proves a broad class of preparation and measurement non-contextual ontological models must exhibit transformation contextuality lacks the generality to include the ontological model considered here; Lillystone et al.'s result is appropriately limited to ontological models whose states produce a single convex set when expressed in terms of disjoint ontic states. Therefore, we prove that for the qubit stabilizer subtheory to be captured by a preparation, transformation and measurement non-contextual ontological theory, it must be expressed in terms of non-disjoint ontic states, unlike the case for the odd-dimensional single-qudit stabilizer subtheory.

quant-ph↗

arXiv2018

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.

quant-ph↗

arXiv2017

Measurement Contextuality and Planck's Constant

Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of $\hbar$---all orders higher than $\hbar^0$ can be interpreted as quantum corrections to the order $\hbar^0$ term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order $\hbar^0$ terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of $\hbar$ as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order $\hbar^0$ contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. On the other hand, odd-dimensional qudit observables generally possess non-zero order $\hbar^0$ terms, and higher, in their WWM formulation, and so exhibit contextuality depending on the state measured: odd-dimensional qudit states that exhibit measurement contextuality have an order $\hbar^1$ contribution that allows for the violation of classical bounds while states that do not exhibit measurement contextuality have insufficiently large order $\hbar^1$ contributions.

quant-ph↗

arXiv2017

Discrete Wigner Formalism for Qubits and Non-Contextuality of Clifford Gates on Qubit Stabilizer States

We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two---producing an exterior, or Grassmann, algebra---which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is non-contextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order $\hbar^0$ with a finite number of terms. The $T$-gate, which extends the Clifford gate set to one capable of universal quantum computation, require a semiclassical expansion of the propagator to order $\hbar^1$. We compare this approach to previous quasi-probability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasi-probability distributions from the odd $d$-dimensional case to $d=2$ qubits, which describe the non-contextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.

quant-ph↗

arXiv2017

Discrete Wigner Function Derivation of the Aaronson-Gottesman Tableau Algorithm

The Gottesman-Knill theorem established that stabilizer states and operations can be efficiently simulated classically. For qudits with dimension three and greater, stabilizer states and Clifford operations have been found to correspond to positive discrete Wigner functions and dynamics. We present a discrete Wigner function-based simulation algorithm for odd-$d$ qudits that has the same time and space complexity as the Aaronson-Gottesman algorithm. We show that the efficiency of both algorithms is due to the harmonic evolution in the symplectic structure of discrete phase space. The differences between the Wigner function algorithm and Aaronson-Gottesman are likely due only to the fact that the Weyl-Heisenberg group is not in $SU(d)$ for $d=2$ and that qubits have state-independent contextuality. This may provide a guide for extending the discrete Wigner function approach to qubits.

quant-ph↗

arXiv2017

Semiclassical Formulation of Gottesman-Knill and Universal Quantum Computation

We give a path integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hbar$. The largest power of $\hbar$ required to describe the evolution is a traditional measure of classicality. We show that the action of the Clifford operators on stabilizer states can be fully described by a single contribution of a path integral truncated at order $\hbar^0$ and so are "classical," just like propagation of Gaussians under harmonic Hamiltonians in the continuous case. Such operations have no dependence on phase or quantum interference. Conversely, we show that supplementing the Clifford group with gates necessary for universal quantum computation results in a propagator consisting of a finite number of semiclassical path integral contributions truncated at order $\hbar^1$ , a number that nevertheless scales exponentially with the number of qudits. The same sum in continuous systems has an infinite number of terms at order $\hbar^1$.

quant-ph↗