arXiv subjects

Stefanos Kourtis

Publications and source records attributed to Stefanos Kourtis.

At least 19 recordsLinked to original sources

arXiv2026

The table maker's quantum search

We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target precision of $n$ digits for all possible precision-$n$ floating-point inputs in a given interval. For elementary functions $f$ related to the exponential function, quantum search takes time $\tilde O(2^{n/2} \log (1/δ))$ to return, with probability $1-δ$, the hardness to round $f$ over all $n$-bit floating-point inputs in a given binade. For periodic elementary functions in large binades, standalone quantum search yields an asymptotic speedup over the best known classical algorithms and heuristics. We then estimate the resources required for a fault-tolerant implementation of the proposed algorithm for the $\sin$ and $\cos$ functions in double precision. We find that, although the algorithm can in principle compete with the fastest known practical method for computing the hardness to round over all binades in the format, it requires qubit coherence times that are unrealistically long for present technology.

quant-ph↗

arXiv2026

Concentration-Free Quantum Kernel Learning in the Rydberg Blockade

Quantum kernel methods (QKMs) offer an appealing framework for machine learning on near-term quantum computers. However, QKMs generically suffer from exponential concentration, requiring an exponential number of measurements to resolve kernel values, with the exception of trivial (i.e., classically simulable) kernels. Here we propose a QKM that is free of exponential concentration, yet remains hard to simulate classically. Our QKM utilizes the weak ergodicity-breaking many-body dynamics in the Rydberg blockade of coherently driven neutral atom arrays. We demonstrate the fundamental properties of our QKM by analytically solving an approximate toy model of its underpinning quantum dynamics, as well as by extensive numerical simulations on randomly generated datasets. We further show that the proposed kernel exhibits effective learning on real data. The proposed QKM can be implemented in current neutral atom quantum computers. Along the way, we uncover novel physical insights into the thermalization of weak ergodicity-breaking systems through the non-stabilizerness of the underlying Rydberg-blockaded dynamics, which directly governs the classical simulability of the proposed kernel.

cond-mat.str-el↗

arXiv2026

Counting with the quantum alternating operator ansatz

We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random sampling and approximate counting and employs QAOA as a solution sampler. We first prove that VQCount improves upon previous work by reducing exponentially the number of samples needed to obtain an approximation within an arbitrary small multiplicative factor of the exact count. Using tensor network simulations, we then study the typical performance of VQCount with shallow circuits on synthetic instances of two #P-hard problems, positive #NAE3SAT and positive #1-in-3SAT. We employ the original quantum approximate optimization algorithm version of QAOA, as well as the Grover-mixer variant which guarantees a uniform solution probability distribution. We observe a tradeoff between QAOA success probability and sampling uniformity, which we exploit to achieve an empirical efficiency gain over both naive rejection sampling and Grover-based quantum counting. Our results highlight the potential and limitations of variational algorithms for approximate counting.

quant-ph↗

arXiv2026

Unconventional early-time relaxation in the Rydberg chain

We show that unconventional relaxation dynamics of special initial states in one-dimensional arrays of Rydberg atoms produce non-generic decay of the initial-state survival probability (SP) at very early times. Using the PXP hamiltonian as a minimal model of the Rydberg blockade, we prove that the early-time SP for states exhibiting quantum many-body scarring (QMBS) decays at a characteristic rate, whose finite-size scaling is determined solely by scars. We numerically investigate the effects of both revival-enhancing and ergodicity-restoring deformations of the PXP hamiltonian and find results consistent with the limiting cases of integrable and ergodic dynamics, respectively. We moreover argue that such unconventional early relaxation of scarred initial states is characteristic of a whole class of QMBS models. Since the SP can be easily measured experimentally, our findings enable us to probe the presence of scars at time scales much shorter than that of thermalization.

cond-mat.stat-mech↗

arXiv2025

Quantum Counting in the Rydberg Blockade

We propose a quantum algorithm for approximately counting the number of solutions to planar 2-satisfiability (2SAT) formulas natively on neutral atom quantum computers. Our algorithm maps Boolean variables to atomic registers arranged in space according to a given formula, so that 2SAT constraints are enforced via the Rydberg blockade between neighboring atoms. A quench under Rydberg dynamics of an initial computational basis state produces a superposition of all solutions after a sufficiently long evolution. For almost uniform superpositions, a polynomial number of measurements is enough to estimate the solution count up to any constant multiplicative factor via sampling based counting. We demonstrate numerically that this protocol leads to almost uniform solution sampling in 1D and 2D grids and that it produces accurate counts for 2SAT instances on punctured grids, suggesting its general applicability as a heuristic for #P-complete problems.

quant-ph↗

arXiv2025

Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates

Monitored many-body systems can exhibit a phase transition between entangling and disentangling dynamical phases by tuning the strength of measurements made on the system as it evolves. This phenomenon is called the measurement-induced phase transition (MIPT). Understanding the properties of the MIPT is a prominent challenge for both theory and experiment at the intersection of many-body physics and quantum information. Realizing the MIPT experimentally is particularly challenging due to the postselection problem, which demands a number of experimental realizations that grows exponentially with the number of measurements made during the dynamics. Proposed approaches that circumvent the postselection problem typically rely on a classical decoding process that infers the final state based on the measurement record. But the complexity of this classical process generally also grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome these difficulties. We construct a tree-shaped quantum circuit whose nodes are Haar-random unitary operators followed by weak measurements of tunable strength. For these circuits, we show that the MIPT can be detected without postselection using only a simple classical decoding process whose complexity grows linearly with the number of qubits. Our protocol exploits the recursive structure of tree circuits, which also enables a complete theoretical description of the MIPT, including an exact solution for its critical point and scaling behavior. We experimentally realize the MIPT on Quantinuum's H1-1 trapped-ion quantum computer and show that the experimental results are precisely described by theory. Our results close the gap between analytical theory and postselection-free experimental observation of the MIPT.

quant-ph↗

arXiv2024

Resonant inelastic X-ray scattering in the topological semimetal FeSi

The energy spectrum of topological semimetals contains protected degeneracies in reciprocal space that correspond to Weyl, Dirac, or multifold fermionic states. To exploit the unconventional properties of these states, one has to access the electronic structure of the three-dimensional bulk. In this work, we present the first joint theory-experiment study of the electronic structure of a candidate topological semimetal with resonant inelastic X-ray scattering (RIXS). We resolve the bulk electronic states of FeSi using momentum-dependent RIXS at the Fe $L_3$ edge. We observe a broad excitation continuum devoid of sharp features, consistent with particle-hole scattering in an underlying electronic band structure. Using density functional theory (DFT), we calculate the electronic structure of FeSi and derive a band theory formulation of RIXS in the fast collision approximation to model the scattering process with zero adjustable parameters. While band theory predicts an excitation continuum with broad spectral features similar to the observed ones, discrepancies between theory and experiment suggest the presence of low-energy processes that DFT alone does not account for. This first study of RIXS in a topological semimetal shows that RIXS is a useful tool for revealing unanticipated behavior of bulk electronic states in this class of materials.

cond-mat.str-el↗

arXiv2024

Tensor networks for $p$-spin models

We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system exactly and is thus lossless, yet leads to qualitative changes in runtime scaling in different regimes of the model. First, we find that bond compression emulates the so-called leaf-removal algorithm, solving the problem efficiently in the "easy" phase. Past a dynamical phase transition, we observe superpolynomial runtimes, reflecting the appearance of a core component. We then develop a graphical method to study the scaling of contraction for a minimal ensemble of core-only instances. We find subexponential scaling, improving on the exponential scaling that occurs without compression. Our results suggest that our tensor network algorithm subsumes the classical leaf removal algorithm and simplifies redundancies in the $p$-spin model through lossless compression, all without explicit knowledge of the problem's structure.

cond-mat.stat-mech↗

arXiv2024

Fermionic Machine Learning

We introduce fermionic machine learning (FermiML), a machine learning framework based on fermionic quantum computation. FermiML models are expressed in terms of parameterized matchgate circuits, a restricted class of quantum circuits that map exactly to systems of free Majorana fermions. The FermiML framework allows for building fermionic counterparts of any quantum machine learning (QML) model based on parameterized quantum circuits, including models that produce highly entangled quantum states. Importantly, matchgate circuits are efficiently simulable classically, thus rendering FermiML a flexible framework for utility benchmarks of QML methods on large real-world datasets. We initiate the exploration of FermiML by benchmarking it against unrestricted PQCs in the context of classification with random quantum kernels. Through experiments on standard datasets (Digits and Wisconsin Breast Cancer), we demonstrate that FermiML kernels are on-par with unrestricted PQC kernels in classification tasks using support-vector machines. Furthermore, we find that FermiML kernels outperform their unrestricted candidates on multi-class classification, including on datasets with several tens of relevant features. We thus show how FermiML enables us to explore regimes previously inaccessible to QML methods.

quant-ph↗

arXiv2024

Low-depth Clifford circuits approximately solve MaxCut

We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, \emph{ADAPT-Clifford}, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an $N$-vertex graph by building a depth $O(N)$ Clifford circuit. The algorithm has runtime complexity $O(N^2)$ and $O(N^3)$ for sparse and dense graphs, respectively, and space complexity $O(N^2)$, with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to $\sim94\%$ of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW.

quant-ph↗

arXiv2023

Finite-rate sparse quantum codes aplenty

We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing, finite rate, sparsity, and maximum-degree constraints simultaneously in a CSP that we can then solve numerically. Using a state-of-the-art CSP solver, we obtain convincing evidence for the existence of a satisfiability threshold. Furthermore, the extent of the satisfiable phase increases with the number of qubits. In that phase, finding sparse codes becomes an easy problem. Moreover, we observe that the sparse codes found in the satisfiable phase practically achieve the channel capacity for erasure noise. Our results show that intermediate-size finite-rate sparse quantum codes are easy to find, while also demonstrating a flexible methodology for generating good codes with custom properties. We therefore establish a complete and customizable pipeline for random quantum code discovery.

quant-ph↗

arXiv2022

Qubit Vitrification and Entanglement Criticality on a Quantum Simulator

Many elusive quantum phenomena emerge from the interaction of a quantum system with its classical environment. Quantum simulators enable us to program this interaction by using measurement operations. Measurements generally remove part of the quantum entanglement built between the qubits inside a simulator. While in simple cases entanglement may disappear at a constant rate as we measure qubits one by one, the evolution of entanglement under measurements for a given class of quantum states is generally unknown. Here, we show that consecutive measurements of the qubits in a quantum simulator can lead to criticality, separating two phases of entanglement. We prepare an entangled superposition of ground states to a classical spin model and show that progressively measuring the qubits drives the simulator into a spin glass phase of entanglement. By entangling and measuring up to 48 qubits in this fashion, we determine the vitrification point and its critical exponent, which obey spin glass theory exactly. Our findings show that measurements alone can trigger entanglement criticality and suggest that coupling to a classical environment can drive critical phenomena in more general quantum states.

quant-ph↗

arXiv2022

Entanglement phase transition with spin glass criticality

We define an ensemble of random Clifford quantum circuits whose output state undergoes an entanglement phase transition between two volume-law phases as a function of measurement rate. Our setup maps exactly the output state to the ground space of a spin glass model. We identify the entanglement phases using an order parameter that is accessible on a quantum chip. We locate the transition point and evaluate a critical exponent, revealing spin glass criticality. Our work establishes an exact statistical mechanics theory of an entanglement phase transition.

cond-mat.dis-nn↗

arXiv2022

Interplay of broken symmetry and delocalized excitations in the insulating state of 1$T$-TaS$_2$

Coexistence of localized and extended excitations is central to the macroscopic properties of correlated materials. For 5d transition metal compounds, electron correlations alone generally do not lead to a metal-insulator (Mott) transition, with insulating behavior usually resulting from their coupling with magnetic ordering and/or structural distortions. 1$T$-TaS$_2$ is a prototypical example of such correlated insulating behavior, with a high-symmetry metallic phase transforming into a distorted, charge density wave (CDW) insulating state at low temperatures. The relevance of the localized electron physics at play in 3d compounds to these 5d transition metal compounds remains an open question. We resolved this standing controversy in 1$T$-TaS$_2$ combining resonant inelastic X-ray spectroscopy and first-principles calculations. We observed five electronic excitations arising from the interband transitions of the Ta 5d orbitals and the S 3p ligand state, with none of the excitations on the order of the Mott gap. These excitations cannot be explained within the framework of standard multiplet calculations that assume a localized wavefunction, but instead, are captured by a band theory framework accounting for the low symmetry of the crystal field in the CDW state. Our findings suggest that the electronic property of 1$T$-TaS$_2$ is dominated by both plasmonic quasiparticles and inter-band transitions associated with a Drude-type response, with no resonance associated with a putative Mott transition. Our discovery provides new insights into the electron localization and the onset of insulating behavior in 5d transition metal materials.

cond-mat.mtrl-sci↗

arXiv2021

Hyper-optimized tensor network contraction

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a variety of benchmarks, including the random quantum circuit instances recently implemented on Google quantum chips. We find that the paths obtained can be very close to optimal, and often many orders or magnitude better than the most established approaches. As different underlying geometries suit different methods, we also introduce a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems and particularly for the benchmarking of new quantum chips. Concretely, we estimate a speed-up of over 10,000$\times$ compared to the original expectation for the classical simulation of the Sycamore `supremacy' circuits.

quant-ph↗

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↗

arXiv2019

Fast counting with tensor networks

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

cond-mat.stat-mech↗

arXiv2019

Evaluating the Jones polynomial with tensor networks

We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a $q$-state Potts model defined as a planar graph with weighted edges that corresponds to the knot. For any integer $q$, we cast this partition function into tensor network form and employ fast tensor network contraction protocols to obtain the exact tensor trace, and thus the value of the Jones polynomial. By sampling random knots via a grid-walk procedure and computing the full tensor trace, we demonstrate numerically that the Jones polynomial can be evaluated in time that scales subexponentially with the number of crossings in the typical case. This allows us to evaluate the Jones polynomial of knots that are too complex to be treated with other available methods. Our results establish tensor network methods as a practical tool for the study of knots.

cond-mat.stat-mech↗