arXiv subjects

Jonathan E. Moussa

Publications and source records attributed to Jonathan E. Moussa.

At least 19 recordsLinked to original sources

arXiv2026

Recursive Magic State Distillation on the Surface Code

I reduce the cost to prepare magic states with lattice surgery operations on the surface code by using a recursive implementation of 15-to-1 magic state distillation. On a rotated surface code with distance $d$, $|T\rangle$ preparation requires a $d$-by-$3 d$ grid of data qubits for up to $15 d$ error correction cycles, and $|CCZ\rangle$ preparation requires a $3 d$-by-$2 d$ grid for up to $10.5 d$ cycles. However, a significantly lower physical error threshold than that of the underlying surface code is required to match the error probability of the output magic state with the logical error rate of the output surface code at large code distances.

quant-ph↗

arXiv2025

The Enduring Relevance of Semiempirical Quantum Mechanics

The development of semiempirical models to simplify quantum mechanical descriptions of atomistic systems is a practice that started soon after the discovery of quantum mechanics and continues to the present day. There are now many methods for atomistic simulation with many software implementations and many users, on a scale large enough to be considered as a software market. Semiempirical models occupied a large share of this market in its early days, but the research activity in atomistic simulation has steadily polarized over the last three decades towards general-purpose but expensive ab initio quantum mechanics methods and fast but special-purpose molecular mechanics methods. I offer perspective on recent trends in atomistic simulation from the middle ground of semiempirical modeling, to learn from its past success and consider its possible paths to future growth. In particular, there is a lot of ongoing research activity in combining semiempirical quantum mechanics with machine learning models and some unrealized possibilities of tighter integration between ab initio and semiempirical quantum mechanics with more flexible theoretical frameworks and more modular software components.

physics.chem-ph↗

arXiv2025

Quantum Metropolis-Hastings algorithm

I generalize the well-known classical Metropolis-Hastings algorithm into a quantum algorithm that can equilibrate, measure, and mix a quantum thermal state on a quantum computer. It performs non-symmetric transitions on labels of state preparation and measurement operations and rejects transitions using imprecise energies extracted by Gaussian-filtered quantum phase estimation.

quant-ph↗

arXiv2023

Model selection in atomistic simulation

There are many atomistic simulation methods with very different costs, accuracies, transferabilities, and numbers of empirical parameters. I show how statistical model selection can compare these methods fairly, even when they are very different. These comparisons are also useful for developing new methods that balance cost and accuracy. As an example, I build a semiempirical model for hydrogen clusters.

physics.chem-ph↗

arXiv2022

Low-Depth Quantum Metropolis Algorithm

We construct a simple quantum version of the classical Metropolis algorithm to prepare and observe quantum thermal states. It induces both a quantum Markov chain that mixes the quantum thermal state and a classical Markov chain that mixes its observable measurements and enables a low-depth quantum circuit implementation. A Gaussian-filtered variant of quantum phase estimation enables thermalization times proportional to the reciprocal of temperature and the logarithm of biasing error. This matches the thermalization time of imaginary-time evolution, against which our algorithm performs favorably.

quant-ph↗

arXiv2020

Minimax separation of the Cauchy kernel

We prove and apply an optimal low-rank approximation of the Cauchy kernel over separated real domains. A skeleton decomposition is the minimum over real-valued functions of the maximum relative pointwise error. We present an algorithm to optimize its parameters, demonstrate suboptimal but effective heuristic approximations, and identify numerically stable forms.

math.NA↗

arXiv2020

Engineered thermalization and cooling of quantum many-body systems

We develop a scheme for engineering genuine thermal states in analog quantum simulation platforms by coupling local degrees of freedom to driven, dissipative ancilla pseudospins. We demonstrate the scheme in a many-body quantum spin lattice simulation setting. A Born-Markov master equation describing the dynamics of the many-body system is developed, and we show that if the ancilla energies are periodically modulated, with a carefully chosen hierarchy of timescales, one can effectively thermalize the many-body system. Through analysis of the time-dependent dynamical generator, we determine the conditions under which the true thermal state is an approximate dynamical fixed point for general system Hamiltonians. Finally, we evaluate the thermalization protocol through numerical simulation and discuss prospects for implementation on current quantum simulation hardware.

quant-ph↗

arXiv2020

Robust decompositions of quantum states

Classical-quantum computational complexity separations are an important motivation for the long-term development of digital quantum computers, but classical-quantum complexity equivalences are just as important in our present era of noisy intermediate-scale quantum devices for framing near-term progress towards quantum supremacy. We establish one such equivalence using a noisy quantum circuit model that can be simulated efficiently on classical computers. With respect to its noise model, quantum states have a robust decomposition into a sequence of operations that each extend the state by one qubit without spreading errors between qubits. This enables universal quantum sampling of states with an efficient representation in this robust form and observables with low quantum weight that can be sampled from general measurements on a few qubits and computational basis measurements on the remaining qubits. These robust decompositions are not unique, and we construct two distinct variants, both of which are compatible with machine-learning methodology. They both enable efficiently computable lower bounds on von Neumann entropy and thus can be used as finite-temperature variational quantum Monte Carlo methods.

quant-ph↗

arXiv2019

Assessment of localized and randomized algorithms for electronic structure

As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only attained by localized or randomized algorithms that have large cost prefactors in the difficult regime of low-temperature metals. Using large copper clusters in a minimal-basis semiempirical model as our reference system, we study the costs of these algorithms relative to a conventional cubic-scaling algorithm using matrix diagonalization and a recent quadratic-scaling algorithm using sparse matrix factorization and rational function approximation. The linear-scaling algorithms are competitive at the high temperatures relevant for warm dense matter, but their cost prefactors are prohibitive near ambient temperatures. To further reduce costs, we consider hybridized algorithms that combine localized and randomized algorithms. While simple hybridized algorithms do not improve performance, more sophisticated algorithms using recent concepts from structured linear algebra show promising initial performance results on a simple-cubic orthogonal tight-binding model.

physics.comp-ph↗

arXiv2016

Minimax rational approximation of the Fermi-Dirac distribution

Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use $O( \log (βΔ) \log (ε^{-1}))$ poles to achieve an error tolerance $ε$ at temperature $β^{-1}$ over an energy interval $Δ$. We apply minimax approximation to reduce the number of poles by a factor of four and replace $Δ$ with $Δ_{\mathrm{occ}}$, the occupied energy interval. This is particularly beneficial when $Δ\gg Δ_{\mathrm{occ}}$, such as in electronic structure calculations that use a large basis set.

physics.comp-ph↗

arXiv2016

Quantum circuits for qubit fusion

We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, $C_1^2 \subset C_2^4 \subset C_3^2$, where $C_n^m$ is the $n$th level of the $m$-dimensional qudit Clifford hierarchy. If we can convert between logical qubits and qudits, then qudit Clifford operators are qubit non-Clifford operators. Conversion is achieved by qubit fusion and qudit fission using stabilizer circuits that consume a resource state. This resource is a fused qubit stabilizer state with a fault-tolerant state preparation using stabilizer circuits.

quant-ph↗

arXiv2016

Transversal Clifford gates on folded surface codes

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. The specific application of these codes to universal quantum computation based on qubit fusion is also discussed.

quant-ph↗

arXiv2016

Linear embedding of free energy minimization

Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to attain. Such properties include the preservation of convexity, lower bounds on free energy, and applicability to systems without subsystem structure. We satisfy all of these properties by embedding free energy minimization into a linear program over energy-resolved expectation values. Numerical results on small systems are encouraging, but a lack of size consistency necessitates further development for large systems.

physics.comp-ph↗

arXiv2015

Multivalley effective mass theory simulation of donors in silicon

Last year, Salfi et al. made the first direct measurements of a donor wave function and found extremely good theoretical agreement with atomistic tight-binding [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multi-valley effective mass theory, applied properly, does achieve close agreement with tight-binding and hence gives reliable predictions. To demonstrate this, we variationally solve the coupled six-valley Shindo-Nara equations, including silicon's full Bloch functions. Surprisingly, we find that including the full Bloch functions necessitates a tetrahedral, rather than spherical, donor central cell correction to accurately reproduce the experimental energy spectrum of a phosphorus impurity in silicon. We cross-validate this method against atomistic tight-binding calculations, showing that the two theories agree well for the calculation of donor-donor tunnel coupling. Further, we benchmark our results by performing a statistical uncertainty analysis, confirming that derived quantities such as the wave function profile and tunnel couplings are robust with respect to variational energy fluctuations. Finally, we apply this method to exhaustively enumerate the tunnel coupling for all donor-donor configurations within a large search volume, demonstrating conclusively that the tunnel coupling has no spatially stable regions. Though this instability is problematic for reliably coupling donor pairs for two-qubit operations, we identify specific target locations where donor qubits can be placed with scanning tunneling microscopy technology to achieve reliably large tunnel couplings.

cond-mat.mes-hall↗

arXiv2014

Comment on "Self-Averaging Stochastic Kohn-Sham Density-Functional Theory"

In a recent Letter, Baer et al. present a stochastic method for Kohn-Sham density functional theory calculations. Their convergence criterion is the self-averaging total energy per electron, which requires a number of statistical samples that decreases with system size and enables a sublinear-scaling computational cost. However, the electron density, atomic forces, orbital energies, and many other physical quantities do not self-average, and this procedure causes their statistical errors to grow with system size. Convergence of non-self-averaging quantities requires that the number of samples be maintained with system size and is incompatible with a sublinear-scaling cost.

cond-mat.mtrl-sci↗

arXiv2014

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

quant-ph↗

arXiv2014

Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange

The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy depends on an arbitrary choice of mean field, and it scales as $\mathcal{O}(n^5)$ operations and $\mathcal{O}(n^3)$ memory for $n$ electrons. We derive a new algorithm that reduces its scaling to $\mathcal{O}(n^3)$ operations and $\mathcal{O}(n^2)$ memory using controlled approximations and a new self-consistent field that approximates Brueckner coupled-cluster doubles (BCCD) theory with RPA+SOSEX, referred to as Brueckner RPA (BRPA) theory. The algorithm comparably reduces the scaling of second-order M$\mathrm{ø}$ller-Plesset (MP2) perturbation theory with smaller cost prefactors than RPA+SOSEX. Within a semiempirical model, we study H$_2$ dissociation to test accuracy and H$_n$ rings to verify scaling.

cond-mat.mtrl-sci↗

arXiv2013

Comment on "Adiabatic Quantum Algorithm for Search Engine Ranking"

In their Letter, Garnerone et al. claim that an adiabatic quantum algorithm can extract information about a PageRank vector with either a polynomial or exponential reduction in time resources over the classical algorithm with comparable space resources. Here we argue that the quantum algorithm offers no obvious advantage over the classical algorithm and fails to preserve the fundamental stability property of the classical PageRank algorithm.

quant-ph↗