arXiv subjects

Paraj Titum

Publications and source records attributed to Paraj Titum.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement Scaling and Problem Structure in Quantum Approximate and Adiabatic Optimization Algorithms

Entanglement is widely regarded as a key resource underlying the power of quantum algorithms and their potential to achieve quantum advantage. With the emergence of variational quantum algorithms, however, questions have arisen regarding how entanglement relates to problem structure and algorithmic performance in near-term quantum applications. Here, we examine this relationship through the Quantum Approximate Optimization Algorithm (QAOA), a specific class of variational algorithms, applied to the MaxCut problem. We show that suboptimal variational parameter training can significantly modify the observed entanglement profile, obscuring its scaling behavior. By employing a high-performance optimizer, we find empirical evidence that QAOA exhibits entanglement scaling consistent with that of fermionic Gaussian states (up to a scaling factor) across a broad range of MaxCut instances. We further compare these results with adiabatic quantum computation, observing annealing-schedule-dependent entanglement profiles whose scaling behavior differs markedly from that of QAOA. Together, these findings provide new insight into how entanglement manifests in and distinguishes these two algorithmic paradigms, highlighting its connection to both computational performance and problem structure.

quant-ph↗

arXiv2026

Superresolution in Quantum Noise Spectroscopy via Filter Design

Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate between spectral lines with arbitrarily small frequency separation. Here, we revisit this problem from the perspective of quantum control theory, utilizing the filter function formalism to derive general, analytic conditions on quantum control protocols for achieving superresolution. Building on these conditions, we develop an optimal control framework, the utility of which is demonstrated through numerical identification of superresolution control protocols in the presence of realistic, experimentally-relevant constraints. We further extend our results to entangled initial states and assess their potential advantage. Our approach is broadly applicable to a wide variety of quantum sensing platforms, and it provides a systematic path to discover novel protocols that surpass conventional resolution limits in these systems.

quant-ph↗

arXiv2026

Performance limits of a quantum receiver for detecting phase-modulated communication signals

Quantum sensors are an ideal candidate for detecting weak electromagnetic signals because of their exceptional sensitivity and compact form factor. In this work, we analyze the performance of a quantum-sensor-based receive chain for demodulating information encoded in phase-modulated electromagnetic waves. We introduce a generalized cumulant expansion to model a noisy quantum receiver and use it to compare the performance of various quantum demodulation protocols. Employing bit error probability (BEP) and channel capacity as quantitative performance metrics, we compare the capabilities of ensembles of quantum sensors - both unentangled and entangled - using Binary Phase-Shift Keying (BPSK) as a representative example of phase modulation. We identify conditions when the channel capacity of an ensemble of quantum sensors may surpass the limits of a classical electrically small antenna. Additionally, we discuss modifications to the quantum protocol that enables high-fidelity data recovery even in the presence of sensor noise and channel distortions. Finally, we explore practical performance limits of such a quantum receive chain, with a focus on NV-diamond as the quantum sensor platform.

quant-ph↗

arXiv2025

Robust series linearization of nonlinear advection-diffusion equations

We consider nonlinear partial differential equations (PDEs) for advection-diffusion processes which are augmented by an auxiliary parameter $\delta$ such that $\delta=0$ corresponds to linear advection-diffusion. We derive potentially non-perturbative series expansions in $\delta$ that provide a process to obtain the solution of the nonlinear PDE through solving a hierarchical system of linear, forced PDEs with the forcing terms dependent on solutions at lower orders in the hierarchy. We rigorously detail our approach for a particular deformation that interpolates between linear advection-diffusion and the canonical Burgers' equation modeling nonlinear advection. In this case, we prove that the series has infinite radius of convergence for arbitrary integrable initial data, analyze the cases of a Dirac-delta initial condition (IC) (i.e., the fundamental solution) in an infinite domain and arbitrary IC in a periodic domain, and demonstrate the approach to turbulent behavior in a scenario with periodic forcing. We then treat models of nonlinear diffusion involving the $p$-Laplacian operator, including generalizations of the Poisson equation in $1$ and $2$ dimensions, and the heat equation in $1+1$ dimensions. We detail series expansions for two different deformations of these equations about their linear (ordinary Laplacian) counterparts, providing numerical evidence for the convergence of the series outside of a perturbative regime and demonstrating that the rate and radius of convergence are affected by choice of deformation. Our results provide a rigorous foundation for using series expansion techniques to study nonlinear advection-diffusion PDEs, opening new pathways for analysis and potential applications for quantum-assisted computational fluid dynamics.

math.AP↗

arXiv2025

Characterizing Superconducting Qubits using Averaged Circuit Eigenvalue Sampling

Efficient characterization of noise during quantum gate operations is an essential step to building and scaling up a quantum computer. One such protocol is averaged circuit eigenvalue sampling (ACES) which efficiently characterizes a noisy gate set by reconstructing a Pauli noise model for a each gate. Here we utilize the ACES protocol to characterize two coupled superconducting qubits. For accurate reconstruction, we tailor the noise via Pauli twirling and account for measurement errors. We verify the accuracy of the protocol by comparing the predicted gate fidelities to that extracted from conventional benchmarking approaches, such as interleaved randomized benchmarking. Furthermore, we demonstrate the efficacy of ACES in accurately identifying specific noise sources by reconstructing injected phase errors in the two-qubit gates.

quant-ph↗

arXiv2025

Quantum Optimization with Classical Chaos

The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high demands on classical variational parameter optimization. Ultimately, this has necessitated investigations into alternative methods for effective QAOA parameterizations. Here, we study a parameterization scheme based on classical chaotic recursive mapping, which enables significant reductions in the scaling of the variational parameter space. Through numerical investigations of hard Maximum Satisfiability problems, we demonstrate that the chaotic mapping can effectively match the performance of standard QAOA when subject to a limited number of classical optimization iterations and short-depth circuits. Insight into this behavior is elucidated through the lens of classical dynamical systems and used to inform hybridized schemes that leverage both standard and chaotic parameterizations. It is shown that these hybridized approaches can boost QAOA performance beyond that of the standard approach alone, especially for deep circuits. Through this study, we provide a new perspective that introduces a generalized framework for specifying performant, dynamical-map-based QAOA parameterizations.

quant-ph↗

arXiv2024

Dynamically Generated Decoherence-Free Subspaces and Subsystems on Superconducting Qubits

Decoherence-free subspaces and subsystems (DFS) preserve quantum information by encoding it into symmetry-protected states unaffected by decoherence. An inherent DFS of a given experimental system may not exist; however, through the use of dynamical decoupling (DD), one can induce symmetries that support DFSs. Here, we provide the first experimental demonstration of DD-generated DFS logical qubits. Utilizing IBM Quantum superconducting processors, we investigate two and three-qubit DFS codes comprising up to six and seven noninteracting logical qubits, respectively. Through a combination of DD and error detection, we show that DFS logical qubits can achieve up to a 23% improvement in state preservation fidelity over physical qubits subject to DD alone. This constitutes a beyond-breakeven fidelity improvement for DFS-encoded qubits. Our results showcase the potential utility of DFS codes as a pathway toward enhanced computational accuracy via logical encoding on quantum processors.

quant-ph↗

arXiv2023

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron scattering experiments: (a) a generalization of the SWAP test for computing wavefunction overlaps and, (b) a generalization of the notion of matrix product operators (MPOs) to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method, and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_8$ ring. Our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

quant-ph↗

arXiv2023

Non-equilibrium critical scaling and universality in a quantum simulator

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e.~a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

quant-ph↗

arXiv2022

Provably Optimal Control for Multiplicative Amplitude Control Noise

We provide a technique to obtain provably optimal control sequences for quantum systems under the influence of time-correlated multiplicative control noise. Utilizing the circuit-level noise model introduced in [Phys. Rev. Research 3, 033229(2021)], we show that we can map the problem of finding such a sequence to a convex optimization problem with guaranteed optimality that follows from the convexity. We also show that this technique is compatible with more general off-axis time-correlated dephasing noise. In spite of losing provable optimality, numerically optimized control sequences under this scenario can still achieve nearly optimal performance when the control noise is strong relative to the dephasing contribution. This approach will enable the development of optimal quantum logic gates in systems where noise due to amplitude drifts in the control is strong relative to dephasing such as in ion-trap based quantum computers or in the limit of fast control.

quant-ph↗

arXiv2022

A tensor network discriminator architecture for classification of quantum data on quantum computers

We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on classifying a translationally invariant quantum state based on $L$ qubits of quantum data extracted from it. We detail a process in which data from single-shot experimental measurements are used to optimize an isometric tensor network, the tensors are compiled into unitary quantum operations using greedy compilation heuristics, parameter optimization on the resulting quantum circuit model removes the post-selection requirements of the isometric tensor model, and the resulting quantum model is inferenced on either product state or entangled quantum data. We demonstrate our training and inference architecture on a synthetic dataset of six-site single-shot measurements from the bulk of a one-dimensional transverse field Ising model (TFIM) deep in its antiferromagnetic and paramagnetic phases. We experimentally evaluate models on Quantinuum's H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond dimension 4 MPSs across the known quantum phase transition of the TFIM. Using linear regression on the experimental data near the transition point, we find predictions for the critical transverse field of $h=0.962$ and $0.994$ for tensor network discriminators of bond dimension $χ=2$ and $χ=4$, respectively. These predictions compare favorably with the known transition location of $h=1$ despite training on data far from the transition point. Our techniques identify families of short-depth variational quantum circuits in a data-driven and hardware-aware fashion and robust classical techniques to precondition the model parameters, and can be adapted beyond machine learning to myriad applications of tensor networks on quantum computers, such as quantum simulation and error correction.

quant-ph↗

arXiv2022

Hidden Quantum Criticality and Entanglement in Quench Dynamics

Entanglement exhibits universal behavior near the ground-state critical point where correlations are long-ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build-up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale-invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emerging universality to the vanishing effective temperature of the soft mode in spite of the quench. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators.

cond-mat.quant-gas↗

arXiv2021

Quantifying the Impact of Precision Errors on Quantum Approximate Optimization Algorithms

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical algorithm that seeks to achieve approximate solutions to optimization problems by iteratively alternating between intervals of controlled quantum evolution. Here, we examine the effect of analog precision errors on QAOA performance both from the perspective of algorithmic training and canonical state- and observable-dependent QAOA-relevant metrics. Leveraging cumulant expansions, we recast the faulty QAOA as a control problem in which precision errors are expressed as multiplicative control noise and derive bounds on the performance of QAOA. We show using both analytical techniques and numerical simulations that errors in the analog implementation of QAOA circuits hinder its performance as an optimization algorithm. In particular, we find that any fixed precision implementation of QAOA will be subject to an exponential degradation in performance dependent upon the number of optimal QAOA layers and magnitude of the precision error. Despite this significant reduction, we show that it is possible to mitigate precision errors in QAOA via digitization of the variational parameters, therefore at the cost of increasing circuit depth. We illustrate our results via numerical simulations and analytic and empirical error bounds as a comparison. While focused on precision errors, our approach naturally lends itself to more general noise scenarios and the calculation of error bounds on QAOA performance and broader classes of variational quantum algorithms.

quant-ph↗

arXiv2021

SchWARMA: A model-based approach for time-correlated noise in quantum circuits

Temporal noise correlations are ubiquitous in quantum systems, yet often neglected in the analysis of quantum circuits due to the complexity required to accurately characterize and model them. Autoregressive moving average (ARMA) models are a well-known technique from time series analysis that model time correlations in data. By identifying the space of completely positive trace reserving (CPTP) quantum operations with a particular matrix manifold, we generalize ARMA models to the space of CPTP maps to parameterize and simulate temporally correlated noise in quantum circuits. This approach, denoted Schrödinger Wave ARMA (SchWARMA), provides a natural path for generalization of classic techniques from signal processing, control theory, and system identification for which ARMA models and linear systems are essential. This enables the broad theory of classical signal processing to be applied to quantum system simulation, characterization, and noise mitigation.

quant-ph↗

arXiv2021

Impact of correlations and heavy-tails on quantum error correction

We show that space- and time-correlated single-qubit rotation errors can lead to high-weight errors in a quantum circuit when the rotation angles are drawn from heavy-tailed distributions. This leads to a breakdown of quantum error correction, yielding reduced or in some cases no protection of the encoded logical qubits. While heavy-tailed phenomena are prevalent in the natural world, there is very little research as to whether noise with these statistics exist in current quantum processing devices. Furthermore, it is an open problem to develop tomographic or noise spectroscopy protocols that could test for the existence of noise with such statistics. These results suggest the need for quantum characterization methods that can reliably detect or reject the presence of such errors together with continued first-principles studies of the origins of space- and time-correlated noise in quantum processors. If such noise does exist, physical or control-based mitigation protocols must be developed to mitigate this noise as it would severely hinder the performance of fault-tolerant quantum computers.

quant-ph↗

arXiv2021

Photonic Topological Anderson Insulators

The hallmark property of two-dimensional topological materials is the incredible robustness of the quantized Hall conductivity to disorder. That robustness arises from the fact that in the topological band gap, transport can occur only along the edges modes, which are immune to scattering. However, for sufficiently strong disorder, the band gap closes and the system becomes topologically trivial as all states become localized, such that all transport vanishes -- in accordance with Anderson localization. It therefore came as a surprise when it was suggested that, for a two-dimensional quantum spin-Hall topological system, the opposite could occur. In so-called topological Anderson insulators, the emergence of protected edge states and quantized transport is caused by the introduction of disorder. However, to date, the observation of the topological Anderson insulator phase has been elusive. In this article, we report the first experimental demonstration of a topological Anderson insulator. We do that in a photonic implementation: an array of helical, evanescently-coupled waveguides in a detuned honeycomb geometry. Under proper conditions, adding on-site disorder, in the form of random variations in the refractive index contrast defining the waveguides, drives the system from a trivial phase into a topological state.

cond-mat.mes-hall↗

arXiv2020

Optimal control for quantum detectors

Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise-ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. We further generalize, using numerical techniques, these results to the background noise being a correlated Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences such as CPMG are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.

quant-ph↗

arXiv2019

Circuit Complexity across a Topological Phase Transition

We use Nielsen's geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition. We find that the circuit complexities of both the ground states and non-equilibrium steady states of the Kitaev model exhibit non-analytical behaviors at the critical points, and thus can be used to detect both {\it equilibrium} and {\it dynamical} topological phase transitions. Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases. This provides a concrete example of classifying different gapped phases using Nielsen's circuit complexity. We further generalize our results to a Kitaev chain with long-range pairing, and discuss generalizations to higher dimensions. Our result opens up a new avenue for using circuit complexity as a novel tool to understand quantum many-body systems.

quant-ph↗