arXiv subjects

Aaron Szasz

Publications and source records attributed to Aaron Szasz.

18 recordsLinked to original sources

arXiv2026

AC/DC: Automated Compilation for Dynamic Circuits

Dynamic quantum circuits incorporate mid-circuit measurements (MCMs) and feed-forward operations are crucial for manipulating quantum information. They have been broadly used in quantum error correction and quantum teleportation. Recently, they are utilized to prepare certain states and long-range entangling gates as well as reduce resource overhead in quantum algorithms. In this paper, we present AC/DC, a novel Automated Compilation framework for generating Dynamic quantum Circuits that prepare any unitary operators or states, leveraging numerical optimization-based circuit synthesis methods. The first contribution is introducing optimization objective functions incorporating MCMs and feed-forward operations. The second contribution is embedding these into a popular open-source quantum circuit synthesis framework. We demonstrate generating dynamic circuits for long range entangling gates, circuit optimization, lattice simulations, and state preparation, with validation through simulation and quantum hardware. Furthermore, we perform a noise analysis to assess the impact of MCM and gate errors, identifying scenarios where dynamic circuits provide significant benefits. The dynamic circuits generated by our framework show substantial improvements in reducing circuit depth and, in some cases, the number of gates. To our knowledge, this is the first practical procedure to generate dynamic quantum circuits, paving the way for enhanced circuit generation and optimization methods for near-term quantum computers.

quant-ph↗

arXiv2026

Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment

In the recent quantum echoes experiment, Google Quantum AI showed that out-of-time-order correlators (OTOCs) for random-circuit time evolution can be measured using a quantum processor more than 10,000x faster than they can be computed to similar accuracy via classical computation. This claim was substantiated by comparison with a variety of state-of-the-art classical simulation methods. One classical simulation method that was not explicitly tested was tensor networks with belief propagation (TNBP). TNBP should be poorly suited to simulating Google's echoes experiment: the states involved are highly entangled, a challenge for tensor network states; and the Willow chip has dense 2D connectivity, a challenge for belief propagation. Here we confirm, via a combination of theoretical scaling arguments and explicit numerical simulation, the intuition that TNBP is unable to simulate the quantum echoes experiment. We show that the OTOC circuits generate enough entanglement that they are largely incompressible, implying that other approaches in which OTOCs are computed by evolving a tensor network state in the Schrödinger picture will also fail. Our results further reinforce the claim that the quantum echoes experiment cannot be reproduced by classical computation.

quant-ph↗

arXiv2026

Observation of disorder-induced superfluidity

The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interactions on a superconducting processor with qutrit readout and control. Compressibility measurements distinguish an incompressible Mott insulator from surrounding compressible phases and reveal signatures of glassiness, reflected in non-ergodic behavior. Spatially-resolved two-point correlator measurements identify regions of the phase diagram with a non-vanishing condensate fraction. We also visualize the spectrum by measuring the dynamical structure factor. A linearly-dispersing phonon mode materializes in the superfluid, appearing even when disorder is introduced to the clean Mott insulator. Our results provide strong experimental evidence for disorder-induced superfluidity.

quant-ph↗

arXiv2026

Practical block encodings of matrix polynomials that can also be trivially controlled

Quantum circuits naturally implement unitary operations on input quantum states. However, non-unitary operations can also be implemented through block encodings, where additional ancilla qubits are introduced and later measured. While block encoding has a number of well-established theoretical applications, its practical implementation has been prohibitively expensive for current quantum hardware. In this paper, we present practical and explicit block encoding circuits implementing matrix polynomial transformations of a target matrix. With standard approaches, block-encoding a degree-$d$ matrix polynomial requires a circuit depth scaling as $d$ times the depth for block-encoding the original matrix alone. By leveraging the recently introduced Fast One-Qubit Controlled Select LCU (FOQCS-LCU) framework, we show that the additional circuit-depth overhead required for encoding matrix polynomials can be reduced to scale linearly in $d$ with no dependence on system size or the cost of block encoding the original matrix. Moreover, we demonstrate that the FOQCS-LCU circuits and their associated matrix polynomial transformations can be controlled with negligible overhead, enabling efficient applications such as Hadamard tests. Finally, we provide explicit circuits for representative spin models, together with detailed non-asymptotic gate counts and circuit depths.

quant-ph↗

arXiv2025

Quantum-Classical Separation in Bounded-Resource Tasks Arising from Measurement Contextuality

The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen--Specker--Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

quant-ph↗

arXiv2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

quant-ph↗

arXiv2025

Observation of disorder-free localization using a (2+1)D lattice gauge theory on a quantum processor

Disorder-induced phenomena in quantum many-body systems pose significant challenges for analytical methods and numerical simulations at relevant time and system scales. To reduce the cost of disorder-sampling, we investigate quantum circuits initialized in states tunable to superpositions over all disorder configurations. In a translationally-invariant lattice gauge theory (LGT), these states can be interpreted as a superposition over gauge sectors. We observe localization in this LGT in the absence of disorder in one and two dimensions: perturbations fail to diffuse despite fully disorder-free evolution and initial states. However, Rényi entropy measurements reveal that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a longstanding challenge in many-body localization studies.

quant-ph↗

arXiv2025

Multi-Target Density Matrix Renormalization Group X algorithm and its application to circuit quantum electrodynamics

Obtaining accurate representations of the eigenstates of an array of coupled superconducting qubits is a crucial step in the design of circuit quantum electrodynamics (QED)-based quantum processors. However, exact diagonalization of the device Hamiltonian is challenging for system sizes beyond tens of qubits. Here, we employ a variant of the density matrix renormalization group (DMRG) algorithm, DMRG-X, to efficiently obtain localized eigenstates of a 2D transmon array without the need to first compute lower-energy states. We also introduce MTDMRG-X, a new algorithm that combines DMRG-X with multi-target DMRG to efficiently compute excited states even in regimes with strong eigenstate hybridization. We showcase the use of these methods for the analysis of long-range couplings in a multi-transmon Hamiltonian including qubits and couplers, and we discuss eigenstate localization. These developments facilitate the design and parameter optimization of large-scale superconducting quantum processors.

quant-ph↗

arXiv2025

Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor

Models of interacting many-body quantum systems that may realize new exotic phases of matter, notably quantum spin liquids, are challenging to study using even state-of-the-art classical methods such as tensor network simulations. Quantum computing provides a promising route for overcoming these difficulties to find ground states, dynamics, and more. In this paper, we argue that recently developed hybrid quantum-classical algorithms based on real-time evolution are promising methods for solving a particularly important model in the search for spin liquids, the antiferromagnetic Heisenberg model on the two-dimensional kagome lattice. We show how to construct efficient quantum circuits to implement time evolution for the model and to evaluate key observables on the quantum computer, and we argue that the method has favorable scaling with increasing system size. We then restrict to a 12-spin star plaquette from the kagome lattice and a related 8-spin system, and we give an empirical demonstration on these small systems that the hybrid algorithms can efficiently find the ground state energy and the magnetization curve. For these demonstrations, we use four levels of approximation: exact state vectors, exact state vectors with statistical noise from sampling, noisy classical emulators, and (for the 8-spin system only) real quantum hardware, specifically the Quantinuum H1-1 processor; for the noisy simulations and hardware demonstration, we also employ error mitigation strategies based on the symmetries of the Hamiltonian. Our results strongly suggest that these hybrid algorithms present a promising direction for studying quantum spin liquids and more generally for resolving important unsolved problems in condensed matter theory and beyond.

quant-ph↗

arXiv2024

Thermalization and Criticality on an Analog-Digital Quantum Simulator

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems toward this goal requires flexible initial state preparation, precise time evolution, and extensive probes for final state characterization. We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. Emulating a two-dimensional (2D) XY quantum magnet, we leverage a wide range of measurement techniques to study quantum states after ramps from an antiferromagnetic initial state. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions attributed to the interplay between quantum and classical coarsening of the correlated domains. This interpretation is corroborated by injecting variable energy density into the initial state, which enables studying the effects of the eigenstate thermalization hypothesis (ETH) in targeted parts of the eigenspectrum. Finally, we digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization. These results establish the efficacy of superconducting analog-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

quant-ph↗

arXiv2023

Phase diagrams of spin-$S$ Kitaev ladders

We investigate the ground states of spin-$S$ Kitaev ladders using exact analytical solutions (for $S = 1/2$), perturbation theory, and the density matrix renormalization group (DMRG) method. We find an even-odd effect: in the case of half-integer $S$, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer $S$, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer $S$ we find a transition between two distinct SPT orders, and for integer $S$ we find unnecessary first order phase transitions within a trivial phase

cond-mat.str-el↗

arXiv2023

Numerical circuit synthesis and compilation for multi-state preparation

Near-term quantum computers have significant error rates and short coherence times, so compilation of circuits to be as short as possible is essential. Two types of compilation problems are typically considered: circuits to prepare a given state from a fixed input state, called "state preparation"; and circuits to implement a given unitary operation, for example by "unitary synthesis". In this paper we solve a more general problem: the transformation of a set of $m$ states to another set of $m$ states, which we call "multi-state preparation". State preparation and unitary synthesis are special cases; for state preparation, $m=1$, while for unitary synthesis, $m$ is the dimension of the full Hilbert space. We generate and optimize circuits for multi-state preparation numerically. In cases where a top-down approach based on matrix decompositions is also possible, our method finds circuits with substantially (up to 40%) fewer two-qubit gates. We discuss possible applications, including efficient preparation of macroscopic superposition ("cat") states and synthesis of quantum channels.

quant-ph↗

arXiv2022

Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations

We investigate a highly frustrated spin-1 model on the triangular lattice, with nearest- and next-nearest-neighbor antiferromagnetic $S\cdot S$ interactions and nearest-neighbor $(S\cdot S)^2$ interactions. Using the density matrix renormalization group (DMRG) technique, we find three magnetically ordered phases, namely 120$^\circ$ spiral order, stripe order, and tetrahedral order, as well as two spin nematic phases: ferroquadrupolar and antiferroquadrupolar. While our data could be consistent with a spin liquid phase between the 120$^\circ$ spiral and antiferroquadrupolar orders, the more likely scenario is a direct continuous transition between these two orders.

cond-mat.str-el↗

arXiv2021

Phase diagram of the anisotropic triangular lattice Hubbard model

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. When one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice Néel order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

cond-mat.str-el↗

arXiv2021

Towards Cosmological Simulations of Dark Matter on Quantum Computers

State-of-the-art cosmological simulations on classical computers are limited by time, energy, and memory usage. Quantum computers can perform some calculations exponentially faster than classical computers, using exponentially less energy and memory, and may enable extremely large simulations that accurately capture the whole dynamic range of structure in the Universe within statistically representative cosmic volumes. However, not all computational tasks exhibit a `quantum advantage'. Quantum circuits act linearly on quantum states, so nonlinearities (e.g. self-gravity in cosmological simulations) pose a significant challenge. Here we outline one potential approach to overcome this challenge and solve the (nonlinear) Schrodinger-Poisson equations for the evolution of self-gravitating dark matter, based on a hybrid quantum-classical variational algorithm framework (Lubasch 2020). We demonstrate the method with a proof-of-concept mock quantum simulation, envisioning a future where quantum computers will one day lead simulations of dark matter.

astro-ph.CO↗

arXiv2020

Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.

cond-mat.str-el↗

arXiv2019

A measure of quantum correlations that lies approximately between entanglement and discord

When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally by a wider class of measures such as the quantum discord. In this work, I introduce a simple thought experiment defining a new measure of quantum correlations, which I call the accord, and write the result as a minimax optimization over unitary matrices. I find the exact result for pure states as a simple function of the Schmidt coefficients and provide a complete proof, and I likewise provide and prove the result for several classes of mixed states, notably including all states of two qubits and the experimentally relevant case of a pure state mixed with colorless noise. I demonstrate that for two qubit states the accord provides a tight lower bound on the discord; for Bell diagonal states it is also an upper bound on entanglement.

quant-ph↗

arXiv2017

Electrical and thermal transport in the quasi-atomic limit of coupled Luttinger liquids

We introduce a new model for quasi one-dimensional materials, motivated by intriguing but not yet well-understood experiments that have shown two-dimensional polymer films to be promising materials for thermoelectric devices. We consider a two-dimensional material consisting of many one-dimensional systems, each treated as a Luttinger liquid, with weak (incoherent) coupling between them. This approximation of strong interactions within each one-dimensional chain and weak coupling between them is the "quasi-atomic limit." We find integral expressions for the (interchain) transport coefficients, including the electrical and thermal conductivities and the thermopower, and we extract their power law dependencies on temperature. Luttinger liquid physics is manifested in a violation of the Wiedemann-Franz law; the Lorenz number is larger than the Fermi liquid value by a factor between $γ^2$ and $γ^4$, where $γ\geq 1$ is a measure of the electron-electron interaction strength in the system.

cond-mat.str-el↗