arXiv subjects

Eduardo R. Mucciolo

Publications and source records attributed to Eduardo R. Mucciolo.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Algorithms to Determine Spin-Resolved Exchange-Correlation Potential for Strongly Correlated Materials

Accurate exchange-correlation (XC) potentials are essential for density functional theory, yet reliable approximations remain challenging for strongly correlated systems. In this work, we present a quantum algorithmic framework to determine spin-resolved XC potentials using a variational quantum eigensolver. Using the Hubbard model as a prototypical strongly correlated lattice system, we prepare ground states in fixed spin sectors through a Hamiltonian variational ansatz initialized from the non-interacting $(U=0)$ Slater-determinant ground state. From the resulting many-body ground states, we extract the XC energy and compute the corresponding spin-resolved XC potentials via finite differences. The accuracy of the approach is benchmarked against exact diagonalization for one- and two-dimensional Hubbard systems of various lattice sizes. We demonstrate that the variational ansatz reproduces the ground-state energies and densities with high fidelity, enabling accurate construction of both magnetic and non-magnetic XC potentials. We analyzed the dependence of the XC potentials on the interaction strength, charge, spin densities, and magnetization. We also present an empirical complexity scaling relation for the computational cost of the method at a fixed fidelity. These results illustrate how quantum computing can be used to construct spin-resolved XC functionals for correlated lattice models, providing a potential pathway for improving density functional approximations in strongly correlated materials.

cond-mat.str-el↗

arXiv2026

Green's Function Methods for Computing Supercurrents in Josephson Junctions

Interest in Josephson junctions (JJs) has increased rapidly in recent years not only because of their use in qubits and other quantum devices but also due to the unique physics supported by the JJs. The advent of various novel quantum materials for both the barrier region and the superconducting leads has led to the possibility of adding new functionalities to the JJs. Thus, there is a growing need for accurate modeling of the JJs and related systems to enable their predictive control and atomistic level understanding. This review presents an in-depth discussion of a Green's function-based formalism for computing supercurrents in JJs. The formulation is tailored for large-scale atomistic simulations and encompasses both dc and ac supercurrents. We hope that this review will provide a timely and comprehensive reference for researchers as well as beginning practitioners interested in Green's-function-based methods to model supercurrents in JJs.

cond-mat.supr-con↗

arXiv2026

Separation of Statistical Complexity and Trainability in Variational Quantum Circuits

Variational quantum algorithms (VQAs) are among the leading approaches for near-term quantum computing, yet their performance can degrade in barren plateau regimes characterized by vanishing gradients. A widely held intuition is that increasing circuit expressivity, often associated with random-state behavior, leads to a loss of trainability. Existing results show that sufficiently random circuits can lead to barren plateaus. Here we show that standard statistical signatures of randomness can emerge well before this regime, without degrading trainability. We demonstrate this behavior in structured variational circuits applied to the one-dimensional cluster-Ising model and a generalized toric code Hamiltonian. To characterize state complexity, we analyze Porter-Thomas statistics, entanglement-spectrum level statistics, and inverse participation ratios. Across both models, increasing circuit depth drives these diagnostics toward random-state-like or random-matrix-like behavior, while variational optimization remains effective, with no evidence of exponential gradient suppression in the regime studied. We interpret this behavior in terms of locality. Spectral correlations develop at relatively shallow depth through locally generated structure, while global state randomization and the associated concentration-of-measure effects are not yet realized. These results show that commonly used statistical diagnostics of complexity do not by themselves determine trainability. Instead, they point to a separation between different aspects of complexity in finite-depth variational circuits.

quant-ph↗

arXiv2025

Circuit complexity and functionality: a thermodynamic perspective

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem [1,2,3]. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (``wormhole'') connecting the two sides of an AdS ``eternal'' black hole [4]. Here we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally-equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides a new perspective on the obfuscation of programs of arbitrary length -- an important problem in cryptography -- as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with ``gases of gates''. This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide.

cond-mat.stat-mech↗

arXiv2025

A Matrix Product State Representation of Boolean Functions

We introduce a novel normal form representation of Boolean functions in terms of products of binary matrices, hereafter referred to as the Binary Matrix Product (BMP) representation. BMPs are analogous to the Tensor-Trains (TT) and Matrix Product States (MPS) used, respectively, in applied mathematics and in quantum many-body physics to accelerate computations that are usually inaccessible by more traditional approaches. BMPs turn out to be closely related to Binary Decision Diagrams (BDDs), a powerful compressed representation of Boolean functions invented in the late 80s by Bryant that has found a broad range of applications in many areas of computer science and engineering. We present a direct and natural translation of BMPs into Binary Decision Diagrams (BDDs), and derive an elementary set of operations used to manipulate and combine BMPs that are analogous to those introduced by Bryant for BDDs. Both BDDs and BMPs are practical tools when the complexity of these representations, as measured by the maximum bond dimension of a BMP (or the accumulated bond dimension across the BMP matrix train) and the number of nodes of a BDD, remains polynomial in the number of bits, $n$. In both cases, controlling the complexity hinges on optimizing the order of the Boolean variables. BMPs offer the advantage that their construction and manipulation rely on simple linear algebra -- a compelling feature that can facilitate the development of open-source libraries that are both more flexible and easier to use than those currently available for BDDs. An initial implementation of a BMP library is available on GitHub, with the expectation that the close conceptual connection to TT and MPS techniques will motivate further development of BMP methods by researchers in these fields, potentially enabling novel applications to classical and quantum computing.

cs.DS↗

arXiv2024

Fast pseudorandom quantum state generators via inflationary quantum gates

We propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits, where n is the number of qudits. We argue that $\log n$ depth 2-qubit-gate-based generic random quantum circuits that are claimed to provide a lower bound on the speed of information scrambling, cannot produce computationally pseudorandom quantum states. This conclusion is connected with the presence of polynomial (in $n$) tails in the stay probability of short Pauli strings that survive evolution through such shallow circuits. We show, however, that stay-probability-tails can be eliminated and pseudorandom quantum states can be accomplished with shallow $\log n$ depth circuits built from a special universal family of `inflationary' quantum (IQ) gates. We prove that IQ-gates cannot be implemented with 2-qubit gates, but can be realized either as a subset of 2-qudit-gates in $U(d^2)$ with $d\ge 3$ and $d$ prime, or as special 3-qubit gates.

quant-ph↗

arXiv2023

Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes

Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is corrupted or intact, a step known as syndrome detection is performed. For stabilizer codes, this step consists of measuring a set of stabilizer operators. In this paper, inspired by the QEC approach, and specifically stabilizer codes, we propose a prototype quantum circuit model for classification of classical data. The core quantum circuit can be considered as a \emph{quantum perceptron} where the classification is based on syndrome detection. In this proposal, a quantum perceptron is realized by one stabilizer as part of a stabilizer code, while a quantum neural network (QNN) layer is realized by a stabilizer code which consists of many stabilizers. The concatenation of stabilizer codes results in complex QNNs. The QNN is trained by performing measurements and optimization of a set of parameterized stabilizers. We demonstrate the concept numerically. In this paper we also consider the first challenge to most applications of quantum computers, including data classification, which is to load data into the memory of the quantum computer. This loading amounts to representing the data as a quantum state, i.e., quantum state preparation. An exact amplitude encoding algorithm requires a circuit of exponential depth. We introduce an alternative recursive algorithm which approximates amplitude encoding with only a polynomial number of elementary gates. We name it recursive approximate-scheme algorithm (RASA).

quant-ph↗

arXiv2023

Atomistic modeling of a superconductor-transition-metal dichalcogenide-superconductor Josephson junction

Using an atomistic tight-binding model, we study the characteristics of a Josephson junction formed by monolayers of MoS$_2$ sandwiched between Pb superconducting electrodes. We derive and apply Green's function-based formulation to compute the Josephson current in this system, as well as the local density of states in the junction. Our analysis of diagonal and off-diagonal components of the local density of states reveals the presence of triplet superconducting correlations in the MoS$_2$ monolayers and spin-polarized subgap (Andreev bound) states. Our formulation can be extended to other systems where atomistic details and large scales are needed to obtain accurate modeling of Josephson junction physics.

cond-mat.supr-con↗

arXiv2022

Encrypted Operator Computing: a novel scheme for computation on encrypted data

We introduce a new approach to computation on encrypted data -- Encrypted Operator Computing (EOC) -- as an alternative to Fully Homomorphic Encryption (FHE). Given a plaintext vector $|{x}\rangle$, $x\in \{0,1\}^n$, and a function $F(x)$ represented as an operator $\hat F$, $\hat F\;|{x}\rangle = |{F(x)}\rangle$, the EOC scheme is based on obfuscating the conjugated operator (circuit) $\hat{F}^E = \hat E\;\hat F\;\hat{E}^{-1}$ that implements computation on encrypted data, $\hat E |{x}\rangle$. The construction of EOC hinges on the existence of a two-stage NC$^1$ reversible-circuit-based IND-CCA2 cipher $\hat{E} = \hat{N} \hat{L}$, where $\hat{L}$ and $\hat{N}$ represent, respectively, linear and non-linear NC$^1$ tree-structured circuits of 3-bit reversible gates. We make and motivate security assumptions about such a NC$^1$ cipher. Furthermore, we establish the polynomial complexity of the obfuscated circuit, the evaluator $O(\hat{F}^E)$, by proving that: (a) conjugation of each gate of $F$ with $\hat{L}$ yields a polynomial number of gates; and (b) the subsequent conjugation with $\hat{N}$ yields a polynomial number of ``chips,'' $n$-input/$n$-output reversible functions, with outputs expressed as polynomial-sized ordered Binary Decision Diagrams (OBDDs). The security of individual chips is connected to the notion of Best Possible Obfuscators which relies on poly-size OBDDs and the fact that OBDDs are normal forms that expose the functionality but hide the gate implementation of the chip. We conjecture that the addition of random pairs of NOTs between layers of $\hat{N}$ during the construction of $F^E$, a device analogous to the AddRoundKey rounds of AES, ensures the security of the the evaluator. We also present a generalization to asymmetric encryption.

cs.CR↗

arXiv2022

Logical Majorana zero modes in a nanowire network

We present a scheme to use physical Majorana quasi-zero modes at each junction of a two-dimensional nanowire network to build a logical Majorana zero mode, the location of which is controllable through gate voltages. The wire-network is a way to realize a proposal by Yang et al. arXiv:1808.04825 to imprint a Kekulé vortex pattern on a honeycomb lattice via gate voltages. We show that a specific type of junction -- other than a naive Y- or T-junction -- is needed to realize, without breaking time-reversal symmetry, an artificial ``graphene'' system with Majorana fermions instead of complex ones at each site. The junction we propose (i) traps exactly one physical Majorana (quasi-)zero mode at each site of either a brick wall or honeycomb lattice and (ii) allows this mode to hybridize with all three neighboring sites. Using a lattice of these junctions and starting from an electronic, tight-binding model for the wires, we imprint the voltage patterns corresponding to the Kekulé vortex and observe the emergence of the logical Majorana zero mode at the vortex core. We also provide the range of parameters where this excitation could be realized experimentally.

cond-mat.mes-hall↗

arXiv2022

An Alternative Approach to Quantum Imaginary Time Evolution

There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy post-processing computational steps on a classical computer, such as solving linear equations. Here we provide an alternative approach to implement ITE. A key feature in our approach is the use of an orthogonal basis set: the propagated state is efficiently expressed in terms of orthogonal basis states at every step of the evolution. We argue that the number of basis states needed at those steps to achieve an accurate solution can be kept of the order of $n$, the number of qubits, by controlling the precision (number of significant digits) and the imaginary-time increment. The number of quantum gates per imaginary-time step is estimated to be polynomial in $n$. Additionally, while in many QAs the locality of the Hamiltonian is a key assumption, in our algorithm this restriction is not required. This characteristic of our algorithm renders it useful for studying highly nonlocal systems, such as the occupation-representation nuclear shell model. We illustrate our algorithm through numerical implementation on an IBM quantum simulator.

quant-ph↗

arXiv2022

Quantum statistical mechanics of encryption: reaching the speed limit of classical block ciphers

We cast encryption via classical block ciphers in terms of operator spreading in a dual space of Pauli strings, a formulation which allows us to characterize classical ciphers by using tools well known in the analysis of quantum many-body systems. We connect plaintext and ciphertext attacks to out-of-time order correlators (OTOCs) and quantify the quality of ciphers using measures of delocalization in string space such as participation ratios and corresponding entropies obtained from the wave function amplitudes in string space. The saturation of the string-space information entropy is accompanied by the vanishing of OTOCs. Together these signal irreversibility and chaos, which we take to be the defining properties of good classical ciphers. More precisely, we define a good cipher by requiring that the OTOCs vanish to exponential precision and that the string entropies saturate to the values associated with a random permutation, which are computed explicitly in the paper. We argue that these conditions can be satisfied by $n$-bit block ciphers implemented via random reversible circuits with ${\cal O}(n \log n)$ gates arranged on a tree structure, with layers of $n/3$ 3-bit gates, for which a "key" specifies uniquely the sequence of gates that comprise the circuit. We show that in order to reach this "speed limit" one must employ a three-stage circuit consisting of a stage implemented by layers of nonlinear gates that proliferate the number of strings, flanked by two other stages, each deploying layers of a special set of linear "inflationary" gates that accelerate the growth of small individual strings. A shallow, ${\cal O}(\log n)$-depth cipher of the type described here can be used in constructing a polynomial-overhead scheme for computation on encrypted data proposed in another publication as an alternative to Homomorphic Encryption.

cs.CR↗

arXiv2021

Machine Learning Regression for Operator Dynamics

Determining the dynamics of the expectation values for operators acting on a quantum many-body (QMB) system is a challenging task. Matrix product states (MPS) have traditionally been the "go-to" models for these systems because calculating expectation values in this representation can be done with relative simplicity and high accuracy. However, such calculations can become computationally costly when extended to long times. Here, we present a solution for efficiently extending the computation of expectation values to long time intervals. We utilize a multi-layer perceptron (MLP) model as a tool for regression on MPS expectation values calculated within the regime of short time intervals. With this model, the computational cost of generating long-time dynamics is significantly reduced, while maintaining a high accuracy. These results are demonstrated with operators relevant to quantum spin models in one spatial dimension.

quant-ph↗

arXiv2021

Breakdown of universality in three-dimensional Dirac semimetals with random impurities

Dirac-Weyl semimetals are unique three-dimensional (3D) phases of matter with gapless electrons and novel electrodynamic properties believed to be robust against weak perturbations. Here, we unveil the crucial influence of the disorder statistics and impurity diversity in the stability of incompressible electrons in 3D semimetals. Focusing on the critical role played by rare impurity configurations, we show that the abundance of low-energy resonances in the presence of diluted random potential wells endows rare localized zero-energy modes with statistical significance, thus lifting the nodal density of states. The strong nonperturbative effect here reported converts the 3D Dirac-Weyl semimetal into a compressible metal even at the lowest impurity densities. Our analytical results are validated by high-resolution real-space simulations in record-large 3D lattices with up to 536 000 000 orbitals.

cond-mat.mes-hall↗

arXiv2021

Simulation of Quantum Many-Body Systems on Amazon Cloud

Quantum many-body systems (QMBs) are some of the most challenging physical systems to simulate numerically. Methods involving approximations for tensor network (TN) contractions have proven to be viable alternatives to algorithms such as quantum Monte Carlo or simulated annealing. However, these methods are cumbersome, difficult to implement, and often have significant limitations in their accuracy and efficiency when considering systems in more than one dimension. In this paper, we explore the exact computation of TN contractions on two-dimensional geometries and present a heuristic improvement of TN contraction that reduces the computing time, the amount of memory, and the communication time. We run our algorithm for the Ising model using memory optimized x1.32x large instances on Amazon Web Services (AWS) Elastic Compute Cloud (EC2). Our results show that cloud computing is a viable alternative to supercomputers for this class of scientific applications.

cs.DC↗

arXiv2020

Nonuniversal Entanglement Level Statistics in Projection-driven Quantum Circuits

We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We encounter two phase transitions with increasing projection rate: The first is the volume-to-area law transition observed in quantum circuits with projective measurements; The second separates the pure Poisson level statistics phase at large projective measurement rates from a regime of residual level repulsion in the entanglement spectrum within the area-law phase, characterized by non-universal level spacing statistics that interpolates between the Wigner-Dyson and Poisson distributions. By applying a tensor network contraction algorithm introduced in Ref. [1] to the circuit spacetime, we identify this second projective-measurement-driven transition as a percolation transition of entangled bonds. The same behavior is observed in both circuits of random two-qubit unitaries and circuits of universal gate sets, including the set implemented by Google in its Sycamore circuits.

cond-mat.stat-mech↗

arXiv2020

Quantum Coherence in Ergodic and Many-Body Localized Systems

Quantum coherence quantifies the amount of superposition a quantum state can have in a given basis. Since there is a difference in the structure of eigenstates of the ergodic and many-body localized systems, we expect them also to differ in terms of their coherences in a given basis. Here, we numerically calculate different measures of quantum coherence in the excited eigenstates of an interacting disordered Hamiltonian as a function of the disorder. We show that quantum coherence can be used as an order parameter to detect the well-studied ergodic to many-body-localized phase transition. We also perform quantum quench studies to distinguish the behavior of coherence in thermalized and localized phases. We then present a protocol to calculate measurement-based localizable coherence to investigate the thermal and many-body localized phases. The protocol allows one to investigate quantum correlations experimentally in a non-destructive way, in contrast to measures that require tracing out a subsystem, which always destroys coherence and correlation.

cond-mat.str-el↗

arXiv2020

Epitaxial metals for interconnects beyond Cu

The experimentally measured resistivity of Co(0001) and Ru(0001) single crystal thin films, grown on c-plane sapphire substrates, as a function of thickness is modeled using the semiclassical model of Fuchs-Sondheimer. The model fits show that the resistivity of Ru would cross below that for Co at a thickness of approximately 20 nm. For Ru films with thicknesses above 20 nm, transmission electron microscopy evidences threading and misfit dislocations, stacking faults and deformation twins. Exposure of Co films to ambient air, and the deposition of oxide layers of SiO2, MgO, Al2O3 and Cr2O3 on Ru degrade the surface specularity of the metallic layer. However, for the Ru films, annealing in a reducing ambient restores the surface specularity. Epitaxial electrochemical deposition of Co on epitaxially-deposited Ru layers is used as an example to demonstrate the feasibility of generating epitaxial interconnects for back-end of line structures. An electron transport model based on a tight-binding approach is described, with Ru interconnects used an example. The model allows conductivity to be computed for structures comprising large ensembles of atoms (10^5-10^6), scales linearly with system size and can also incorporate defects.

cond-mat.mes-hall↗