arXiv subjects

Gaurav Saxena

Publications and source records attributed to Gaurav Saxena.

17 recordsLinked to original sources

arXiv2026

Stabilizer Statistical Mechanics: A Framework for Efficient Quantification and Classification of Magic States

The partition function is statistical mechanics' answer to an exponentially large spectrum, distilling it into a single analytic object whose temperature dependence resolves the full structure of the underlying ensemble. We show that magic, the resource separating universal quantum computation from classically simulable stabilizer dynamics, admits precisely such a description. Mapping the Pauli spectrum of a quantum state onto the energy levels of a fictitious many-body system, the Pauli gas, we construct its canonical partition function, the stabilizer partition function, and from its associated free energy a magic monotone that we call the stabilizer work. Both these objects are analytic functions of an inverse-temperature-like parameter and are efficiently estimable via Bell sampling. The framework is analytically tractable. We derive exact ensemble-averaged partition functions for Haar-random, $\nu$-compressible, and pseudomagic states, together with concentration guarantees. We show that for every value of its parameter, the stabilizer work is a faithful, Subadditive magic monotone, while remaining efficiently accessible on quantum hardware and admitting an operational interpretation. Unlike measures that probe a single moment of the Pauli distribution, the stabilizer work is intrinsically moment-generating. As the temperature is tuned from high to low, it interpolates continuously between the stabilizer 2-R\'enyi entropy and the stabilizer nullity, revealing two previously disconnected monotones as limiting cases of a single object. We demonstrate the framework on low-rank stabilizer simulation, resource interconversion, molecular ground states, and quantum many-body systems. A thermodynamics of magic is therefore not merely an analogy but a working toolkit, opening a statistical-mechanical route to magic properties of quantum systems that no single measure can access.

quant-ph↗

arXiv2026

Efficient Quantum Circuits for Coherent Conversion Between General First- and Second-Quantized Many-Body Representations

Quantum simulation at fixed particle number admits two equivalent descriptions, a first-quantized (particle) representation and a second-quantized (occupation-number) representation. Their quantum resource costs differ sharply across computational tasks, so the ability to convert coherently between them is valuable. We construct an explicit unitary $Q$, with inverse $Q^\dagger$, that maps a first-quantized state to its fixed-$N$ occupation-number form while diagnosing the input's particle-exchange symmetry. The conversion is therefore symmetry-agnostic at the input yet fully resolved at the output, and it applies uniformly to bosonic, fermionic, and parastatistical sectors. At its foundation lies a structural identification that we place at the center of this work: the quantum Schur transform supplied by Schur-Weyl duality is the non-abelian Fourier transform of the commuting pair $(S_N,U(d))$, and the occupation-number representation is its weight basis, retaining only the labels shared by both factors, the irrep $\lambda$ and the $\mathfrak{u}(d)$ weight. This reduction is lossless for bosons and fermions, while a canonical Gelfand-Tsetlin promise renders it one-to-one for the remaining sectors. Algorithmically, $Q$ composes the strong Schur transform with reversible arithmetic that computes occupations as successive row-sum differences of the Gelfand-Tsetlin pattern, yielding gate complexity $\mathrm{poly}(N,d,\log(1/\epsilon))$. The converted state is prepared efficiently in quantum memory. Any classical algorithm that outputs it explicitly, however, pays a cost set by the sector dimension, which is polynomial of degree $N$ in $d$ at fixed $N$ and exponential in $N$ when $d=\Theta(N)$. Finally, an efficient classical sampler for the induced occupation-number distribution would yield one for arbitrary quantum circuits, contrary to standard complexity assumptions.

quant-ph↗

arXiv2026

Designing quantum technologies with a quantum computer

Interacting spin systems in solids underpin a wide range of quantum technologies, from quantum sensors and single-photon sources to spin-defect-based quantum registers and processors. We develop a quantum-computer-aided framework for simulating such devices using a general many-body electron-spin-resonance Hamiltonian that incorporates zero-field splitting, the Zeeman effect, hyperfine interactions, dipole-dipole spin-spin interactions, and electron-phonon decoherence. Within this framework, we combine Gray-encoded qudit-to-qubit mappings, qubit-wise commuting aggregation, and a multi-reference selected quantum Krylov fast-forwarding hybrid algorithm, aiming to access extended-time dynamics within the constraints of NISQ and early fault-tolerant hardware. Numerical simulations demonstrate the computation of operationally useful quantities including autocorrelation functions up to $\sim100$ ns, together with microwave absorption spectra and the $\ell_1$-norm of coherence, achieving 18-30$\%$ reductions in gate counts and circuit depth for Trotterized time-evolution circuits compared to unoptimized implementations. Using the nitrogen vacancy center in diamond as a testbed, we benchmark the framework against classical simulations and identify the reference-state selection in sQKFF as the primary factor governing accuracy at fixed hardware cost. This methodology provides a flexible blueprint for using quantum computers to design, compare, and optimize solid-state spin-qubit technologies under experimentally realistic conditions.

quant-ph↗

arXiv2025

Error-Mitigation Enabled Multicomponent Quantum Simulations Beyond the Born-Oppenheimer Approximation

We introduce a multicomponent unitary coupled cluster framework for quantum simulations of molecular systems that incorporate both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation. Using the nuclear-electronic orbital formalism, we construct mcUCC ans\"atze for positronium hydride and molecular hydrogen with a quantum proton, and analyze hardware requirements for different excitation truncations. To further reduce resource costs effectively, we employ the local unitary cluster Jastrow ansatz and implement it experimentally on IBM Q's Heron superconducting hardware. With the Physics-Inspired Extrapolation error mitigation protocol, the computed ground-state energies remain within chemical accuracy, consistent with the stated uncertainty level. These results provide the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware and outline a path toward scalable algorithms unifying electronic and nuclear degrees of freedom.

quant-ph↗

arXiv2025

Quenching, Fast and Slow: Breaking Kibble-Zurek Universal Scaling by Jumping along Geodesics

A major drawback of adiabatic quantum computing (AQC) is fulfilling the energy gap constraint, which requires the total evolution time to scale inversely with the square of the minimum energy gap. Failure to satisfy this condition violates the adiabatic approximation, potentially undermining computational accuracy. Recently, several approaches have been proposed to circumvent this constraint. One promising approach is to use the family of adiabatic shortcut procedures to fast-forward AQC. One caveat, however, is that it requires an additional Hamiltonian that is very challenging to implement experimentally. Here, we investigate an alternate pathway that avoids any extra Hamiltonian in the evolution to fast-forward the adiabatic dynamics by traversing geodesics of a quantum system. We find that jumping along geodesics offers a striking mechanism to highly suppress the density of excitations in many-body systems. Particularly, for the spin-$1/2$ XY model, we analytically prove and numerically demonstrate a rate-independent defect plateau, which contrasts with well-established results for the Kibble-Zurek and anti-Kibble-Zurek mechanisms.

quant-ph↗

arXiv2025

Universal initial state preparation for first quantized quantum simulations

Preparing symmetry-adapted initial states is a principal bottleneck in first-quantized quantum simulation. We present a universal approach that efficiently maps any polynomial-size superposition of occupation-number configurations to the first-quantized representation on a digital quantum computer. The method exploits the Jordan--Schwinger Lie algebra homomorphism, which identifies number-conserving second-quantized operators with their first-quantized action and induces an equivariant bijection between Fock occupations and $\mathfrak{su}(d)$ weight states within the Schur--Weyl decomposition. Operationally, we deterministically prepare an superposition of target Schur labels and apply the inverse quantum Schur transform. For $L$ configurations of $N$ particles over $d$ modes prepared to accuracy $\epsilon$, the most efficient variant of the algorithm runs with non-Clifford gate complexity $\mathrm{poly}(L, N, \log d, \log \epsilon^{-1})$. The protocol applies universally to fermions, bosons, and Green's paraparticles in arbitrary single-particle bases. Resource estimates establish practicality within leading first-quantized pipelines, with statistics-aware specializations promising further reductions.

quant-ph↗

arXiv2025

Quantum Resilience: Canadian Innovations in Quantum Error Correction and Quantum Error Mitigation

In celebration of the 2025 International Year of Quantum Science and Technology, this article highlights the pioneering achievements and ongoing innovations in quantum error correction and quantum error mitigation by Canadian institutions, academia and industry alike. Emphasizing Canada's central role in advancing these two related areas, we summarize landmark theoretical breakthroughs, cutting-edge experiments, and emerging techniques aimed at reducing and/or eliminating errors incurred when using a quantum computer. This community-focused overview underscores Canada's leadership in addressing the critical challenge of noise in quantum information science.

quant-ph↗

arXiv2025

Physics-Inspired Extrapolation for efficient error mitigation and hardware certification

Quantum error mitigation (QEM) is essential for the noisy intermediate-scale quantum era, and will remain relevant for early fault-tolerant quantum computers, where logical error rates are still significant. However, most QEM methods incur an exponential sampling overhead to achieve unbiased estimates, limiting their practical applicability. Recently, error mitigation by restricted evolution (EMRE) was shown to estimate expectation values with constant sampling overhead, albeit with a small bias that grows with circuit size and noise level. Building upon the EMRE framework, here, we propose physics-inspired extrapolation (PIE), a linear circuit runtime protocol that achieves enhanced accuracy without incurring substantial overhead. Unlike traditional heuristic zero-noise extrapolation methods, PIE provides a theoretical foundation for the operational interpretation of its fitting parameters and demonstrates convergence to unbiased estimates as noise decreases. Distinctively, the slope of the extrapolation fit corresponds to the max-relative entropy between the ideal and noisy circuits, enabling quantitative hardware certification alongside error mitigation, with no additional computational overhead. We also demonstrate the efficacy of this method on IBMQ hardware and apply it to simulate 84-qubit quantum dynamics efficiently. Our results show that PIE yields accurate, low-variance error mitigated estimates, establishing it as a practical and scalable strategy for both error mitigation and hardware certification for near-term and early fault-tolerant quantum computers.

quant-ph↗

arXiv2024

Constant Runtime Error Mitigation via Restricted Evolution

Error mitigation techniques, while instrumental in extending the capabilities of near-term quantum computers, often suffer from exponential resource scaling with noise levels. To address this limitation, we introduce a novel approach, namely, constant runtime error mitigation by restricted evolution (EMRE). Through numerical simulations, we demonstrate that EMRE surpasses the performance of Probabilistic Error Cancellation (PEC) while maintaining constant sampling overhead. The constant sampling overhead comes at the cost of a small non-zero bias. We provide a methodology to compute the optimal bias by connecting it to a resource-theoretic measure. We also evaluate bounds on the bias under different noise models and give exact results for the case of depolarizing and dephasing noise. Using these exact results, we derive an even more efficient strategy to implement EMRE. Additionally, we introduce Hybrid EMREs (HEMREs), a continuous family of error mitigation protocols that encompass PEC and EMRE as special cases. HEMREs offer a tunable bias parameter, enabling a trade-off between sample complexity and error reduction. The numerical evidence suggests the scalability and practicality of our proposal. Hence, our error mitigation protocols provide flexibility in balancing error mitigation with computational overhead, catering to practical application requirements of near-term and early-fault tolerant quantum devices.

quant-ph↗

arXiv2024

Practical limitations of quantum data propagation on noisy quantum processors

The variational quantum imaginary time evolution algorithm is efficient in finding the ground state of a quantum Hamiltonian. This algorithm involves solving a system of linear equations in a classical computer and the solution is then used to propagate a quantum wavefunction. Here, we show that owing to the noisy nature of current quantum processors, such a quantum algorithm or the family of quantum algorithms will require single- and two-qubit gates with very low error probability to produce reliable results. Failure to meet such condition will result in erroneous quantum data propagation even for a relatively small quantum circuit ansatz. Specifically, we provide the upper bounds on how the relative error in variational parameters' propagation scales with the probability of noise in quantum hardware. We also present an exact expression of how the relative error in variational parameter propagation scales with the probability of partially depolarizing noise.

quant-ph↗

arXiv2024

Stage: Query Execution Time Prediction in Amazon Redshift

Query performance (e.g., execution time) prediction is a critical component of modern DBMSes. As a pioneering cloud data warehouse, Amazon Redshift relies on an accurate execution time prediction for many downstream tasks, ranging from high-level optimizations, such as automatically creating materialized views, to low-level tasks on the critical path of query execution, such as admission, scheduling, and execution resource control. Unfortunately, many existing execution time prediction techniques, including those used in Redshift, suffer from cold start issues, inaccurate estimation, and are not robust against workload/data changes. In this paper, we propose a novel hierarchical execution time predictor: the Stage predictor. The Stage predictor is designed to leverage the unique characteristics and challenges faced by Redshift. The Stage predictor consists of three model states: an execution time cache, a lightweight local model optimized for a specific DB instance with uncertainty measurement, and a complex global model that is transferable across all instances in Redshift. We design a systematic approach to use these models that best leverages optimality (cache), instance-optimization (local model), and transferable knowledge about Redshift (global model). Experimentally, we show that the Stage predictor makes more accurate and robust predictions while maintaining a practical inference latency and memory overhead. Overall, the Stage predictor can improve the average query execution latency by $20\%$ on these instances compared to the prior query performance predictor in Redshift.

cs.DB↗

arXiv2022

Quantifying dynamical magic with completely stabilizer preserving operations as free

In this paper, we extend the resource theory of magic to the channel case by considering completely stabilizer preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO preserving and completely CSPO preserving superchannels. We quantify the magic of quantum channels by extending the generalized robustness and the min relative entropy of magic from the state to the channel domain and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear programming feasibility problem and hence can be efficiently solved. Lastly, we give a classical simulation algorithm whose runtime is related to the generalized robustness of magic for channels. Our algorithm depends on some pre-defined precision, and if there is no bound on the desired precision then it achieves a constant runtime.

quant-ph↗

arXiv2020

Multiphoton Bell-type inequality: a tool to unearth nonlocality of continuous variable quantum optical systems

We consider a multiphoton Bell-type inequality to study nonlocality in four-mode continuous variable systems, which goes beyond two-photon states and can be applied to mixed as well as states with fluctuating photon number. We apply the inequality to a wide variety of states such as pure and mixed Gaussian states (including squeezed thermal states) and non-Gaussian states. We consider beam splitters as a model for leakage and show that the inequality is able to detect nonclassicality of noisy Gaussian states as well. Finally, we investigate nonlocality in pair-coherent states and entangled coherent states, which are prominent examples of nonclassical, non-Gaussian states.

quant-ph↗

arXiv2019

Dynamical Resource Theory of Quantum Coherence

Decoherence is all around us. Every quantum system that interacts with the environment is doomed to decohere. The preservation of quantum coherence is one of the major challenges faced in quantum technologies, but its use as a resource is very promising and can lead to various operational advantages, for example in quantum algorithms. Hence, much work has been devoted in recent years to quantify the coherence present in a system. In the present paper, we formulate the quantum resource theory of dynamical coherence. The underlying physical principle we follow is that the free dynamical objects are those that cannot preserve or distribute coherence. This leads us to identify classical channels as the free elements in this theory. Consequently, even the quantum identity channel is not free as all physical systems undergo decoherence and hence, the preservation of coherence should be considered a resource. In our work, we introduce four different types of free superchannels (analogous to MIO, DIO, IO, and SIO) and discuss in detail two of them, namely, dephasing-covariant incoherent superchannels (DISC), maximally incoherent superchannels (MISC). The latter consists of all superchannels that do not generate non-classical channels from classical ones. We quantify dynamical coherence using channel-divergence-based monotones for MISC and DISC. We show that some of these monotones have operational interpretations as the exact, the approximate, and the liberal coherence cost of a quantum channel. Moreover, we prove that the liberal asymptotic cost of a channel is equal to a new type of regularized relative entropy. Finally, we show that the conversion distance between two channels under MISC and DISC can be computed using a semi-definite program (SDP).

quant-ph↗

arXiv2019

Solar X-ray Monitor (XSM) On-board Chandrayaan-2 Orbiter

Solar X-ray Monitor (XSM) is one of the scientific instruments on-board Chandrayaan-2 orbiter. The XSM along with instrument CLASS (Chandras Large Area Soft x-ray Spectrometer) comprise the remote X-ray fluorescence spectroscopy experiment of Chandrayaan-2 mission with an objective to determine the elemental composition of the lunar surface on a global scale. XSM instrument will measure the solar X-rays in the energy range of 1-15 keV using state-of-the-art Silicon Drift Detector (SDD). The Flight Model (FM) of the XSM payload has been designed, realized and characterized for various operating parameters. XSM provides energy resolution of 180 eV at 5.9 keV with high time cadence of one second. The X-ray spectra of the Sun observed with XSM will also contribute to the study of solar corona. The detailed description and the performance characteristics of the XSM instrument are presented in this paper.

astro-ph.IM↗

arXiv2018

Biometric Recognition System (Algorithm)

Fingerprints are the most widely deployed form of biometric identification. No two individuals share the same fingerprint because they have unique biometric identifiers. This paper presents an efficient fingerprint verification algorithm which improves matching accuracy. Fingerprint images get degraded and corrupted due to variations in skin and impression conditions. Thus, image enhancement techniques are employed prior to singular point detection and minutiae extraction. Singular point is the point of maximum curvature. It is determined by the normal of each fingerprint ridge, and then following them inward towards the centre. The local ridge features known as minutiae is extracted using cross-number method to find ridge endings and ridge bifurcations. The proposed algorithm chooses a radius and draws a circle with core point as centre, making fingerprint images rotationally invariant and uniform. The radius can be varied according to the accuracy depending on the particular application. Morphological techniques such as clean, spur and H-break is employed to remove noise, followed by removing spurious minutiae. Templates are created based on feature vector extraction and databases are made for verification and identification for the fingerprint images taken from Fingerprint Verification Competition (FVC2002). Minimum Euclidean distance is calculated between saved template and the test fingerprint image template and compared with the set threshold for matching decision. For the performance evaluation of the proposed algorithm various measures, equal error rate (EER), Dmin at EER, accuracy and threshold are evaluated and plotted. The measures demonstrate that the proposed algorithm is more effective and robust.

cs.CV↗

arXiv2013

New Dimension Value Introduction for In-Memory What-If Analysis

OLAP systems operate on historical data and provide answers to analysts queries. Recent in-memory implementations provide significant performance improvement for real time ad-hoc analysis. Philosophy and techniques of what-if analysis on data warehouse and in-memory data store based OLAP systems have been covered in great detail before but exploration of new dimension value (attribute) introduction has been limited in the context of what-if analysis. We extend the approach of Andrey Balmin et al of using select modify operator on data graph to introduce new values for dimensions and measures in a read-only in-memory data store as scenarios. Our system constructs scenarios without materializing the rows and stores the row information as queries. The rows associated with the scenarios are constructed as and when required by an ad-hoc query.

cs.DB↗