arXiv subjects

Farrokh Labib

Publications and source records attributed to Farrokh Labib.

13 recordsLinked to original sources

arXiv2026

Quantum amplitude estimation beyond power-of-two schedules

Non-adaptive quantum amplitude estimation (QAE) fixes its Grover depths in advance, so every circuit can run in parallel, but it has so far needed more queries than the best adaptive methods. We show that most of this gap comes from two conventional choices: subspace-based post-processing and power-of-two depth ladders. We replace the first by the exact maximum-likelihood estimate, one matrix multiplication per batch of estimates, and the second by a geometric ladder with ratio $r \approx 1.45$. The result is a fully parallel, deterministic-schedule estimator with total query complexity $2.8$-$3.1/\varepsilon$ at 95% confidence for target errors from $3.5\times 10^{-3}$ to $10^{-6}$. This matches the average-case complexity of chebAE, the best benchmarked adaptive method, within statistical uncertainty (with the lower point estimate at every scale tested), beats its maximum-observed complexity by $1.6\times$, and needs a maximum sequential depth of only $0.21/\varepsilon$ against chebAE's $2.9/\varepsilon$. Relative to csAE, the best non-adaptive benchmark, the constants improve by 30-35% at 95% and $1.5$-$1.7\times$ at 99% confidence. The optimal ratio has a simple origin. Doubling is the fastest depth growth at which the data can still tell neighboring candidate values apart, so power-of-two ladders sit at the edge of confusion and must buy reliability with extra shots; a slightly denser ladder checks every scale redundantly. An error-probability analysis reproduces the measured failure rates and locates the optimum. The likelihood formulation extends directly to noise-aware estimation, and uniformly scaling the capped ladder covers the depth-limited regime, realizing the optimal trade-off $M N_{\mathrm{tot}} \approx (0.4$-$0.6)/\varepsilon^2$ within $\sim 1.1\times$ of the schedule's Cram\'er-Rao limit.

quant-ph↗

arXiv2026

Stabilizer rank bounds for magic-state orbits

Distinct Clifford orbits of magic states can exhibit different stabilizer ranks at small tensor powers. We establish this for qutrits, where the single-qutrit Clifford group has four inequivalent orbits of magic states: Strange, Norrell, Hadamard-eigenstate, and the qutrit T-state, but a nontrivial upper bound on the asymptotic exponent had been pinned down for only the qutrit T-state. For the other three orbits we give explicit stabilizer decompositions, yielding upper bounds on the per-copy asymptotic stabilizer-rank exponent: $\gamma_S \le \log_3(2)/2 \approx 0.316$ for the Strange state, and $\gamma_{H_3}, \gamma_N \le \log_3(4)/3 \approx 0.421$ for the Hadamard-eigenstate and Norrell orbits, all strictly below the prior $\gamma_{T_3} \le 1/2$ baseline. We also prove the first nontrivial $\Omega(m / \log m)$ asymptotic lower bounds for the Hadamard-eigenstate and Norrell orbits, and exhibit two-qutrit Clifford circuits that convert two copies of these states into an injectable phase state with constant success probability, enabling constant-overhead injection of one non-Clifford diagonal gate per orbit. In the case of qubits, we give a closed-form decomposition of the qubit T-type orbit at four copies matching the existing $\gamma_T \le \log_2(3)/4 \approx 0.396$ exponent via a direct algebraic identity rather than an entangled cat-state construction. An open-source library stabrank accompanies the paper, with Lean 4 proof formalizations of all the decompositions.

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arXiv2026

Compressed Sensing for Efficient Fidelity Estimation of GHZ States

Accurately characterizing multipartite entangled states is a critical challenge in quantum information processing. In this work, we focus on applying compressed sensing techniques to efficiently estimate the fidelity of Greenberger-Horne-Zeilinger (GHZ) states. By exploiting the inherent sparsity of these states, our compressed sensing protocol drastically reduces the measurement overhead traditionally required for state verification while maintaining high accuracy. To evaluate the practical performance of this approach, we test the protocol on GHZ states using both quantum simulators and Quantinuum's trapped-ion hardware. Furthermore, we implement error detection techniques during our hardware evaluations, demonstrating the robustness and viability of compressed sensing for fidelity estimation in noisy experimental environments.

quant-ph↗

arXiv2026

Clifft: Fast Exact Simulation of Near-Clifford Quantum Circuits

Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential $T$-count scaling in stabilizer-rank approaches, and per-shot tracking overhead in sparse generalized stabilizer simulators. In this work, we introduce Clifft, an open-source simulator that shifts the dominant exponential cost from the total qubit count to a dynamic active subspace by factoring the quantum state into an offline Clifford frame, an online Pauli frame, and a dynamically sized active state vector. This architecture resolves deterministic Clifford coordinate transformations ahead of time, generalizing Stim's compile-once, sample-many execution model to circuits with non-Clifford operations. Consequently, exponential simulation costs are determined by the peak active virtual dimension, which expands during non-Clifford operations and contracts during measurements. Clifft remains within a constant factor of standard tools in the pure-Clifford and non-Clifford limits, while delivering up to orders-of-magnitude throughput gains over GPU-accelerated near-Clifford simulators on low-magic fault-tolerant benchmarks. Executing on commodity CPUs and exposing a Stim-like API, Clifft enables, to our knowledge, the first exact end-to-end simulation of magic state cultivation including the escape stage, over hundreds of billions of shots. These simulations show that escape-stage failures suppress the discrepancy between the true $T$-gate circuit and its $S$-proxy at low decoder-gap thresholds, while at high thresholds the full-protocol behavior approaches the larger discrepancy observed in the cultivation stages alone.

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arXiv2024

Towards violations of Local Friendliness with quantum computers

Local Friendliness (LF) inequalities follow from seemingly reasonable assumptions about reality: (i) ``absoluteness of observed events'' (e.g., every observed event happens for all observers) and (ii) ``local agency'' (e.g., free choices can be made uncorrelated with other events outside their future light cone). Extended Wigner's Friend Scenario (EWFS) thought experiments show that textbook quantum mechanics violates these inequalities. Thus, experimental evidence of these violations would make these two assumptions incompatible. In [Nature Physics 16, 1199 (2020)], the authors experimentally implemented an EWFS, using a photonic qubit to play the role of each of the ``friends'' and measured violations of LF. One may question whether a photonic qubit is a physical system that counts as an ``observer'' and thereby question whether the experiment's outcome is significant. Intending to measure increasingly meaningful violations, we propose using a statistical measure called the ``branch factor'' to quantify the ``observerness'' of the system. We then encode the EWFS as a quantum circuit such that the components of the circuit that define the friend are quantum systems of increasing branch factor. We run this circuit on quantum simulators and hardware devices, observing LF violations as the system sizes scale. As errors in quantum computers reduce the significance of the violations, better quantum computers can produce better violations. Our results extend the state of the art in proof-of-concept experimental violations from branch factor 0.0 to branch factor 16.0. This is an initial result in an experimental program for measuring LF violations at increasingly meaningful branch factors using increasingly more powerful quantum processors and networks. We introduce this program as a fundamental science application for near-term and developing quantum technology.

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arXiv2024

Quantum amplitude estimation from classical signal processing

We demonstrate that the problem of amplitude estimation, a core subroutine used in many quantum algorithms, can be mapped directly to a problem in signal processing called direction of arrival (DOA) estimation. The DOA task is to determine the direction of arrival of an incoming wave with the fewest possible measurements. The connection between amplitude estimation and DOA allows us to make use of the vast amount of signal processing algorithms to post-process the measurements of the Grover iterator at predefined depths. Using an off-the-shelf DOA algorithm called ESPRIT together with a compressed-sensing based sampling approach, we create a phase-estimation free, parallel quantum amplitude estimation (QAE) algorithm with a worst-case sequential query complexity of $\sim 4.3/\varepsilon$ and a parallel query complexity of $\sim 0.26/\varepsilon$ at 95% confidence. This performance is statistically equivalent and a $16\times$ improvement over Rall and Fuller [Quantum 7, 937 (2023)], for sequential and parallel query complexity respectively, which to our knowledge is the best published result for amplitude estimation. The approach presented here provides a simple, robust, parallel method to performing QAE, with many possible avenues for improvement borrowing ideas from the wealth of literature in classical signal processing.

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arXiv2021

Quantum Motif Clustering

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of them obtain square-root like speedups over the fastest classical algorithms in various settings. In order to use approximate counting in the context of clustering, we show that for general weighted graphs the performance of spectral clustering is mostly left unchanged by the presence of constant (relative) errors on the edge weights. Finally, we extend the original analysis of motif clustering in order to better understand the role of multiple `anchor nodes' in motifs and the types of relationships that this method of clustering can and cannot capture.

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arXiv2021

Stabilizer rank and higher-order Fourier analysis

We establish a link between stabilizer states, stabilizer rank, and higher-order Fourier analysis -- a still-developing area of mathematics that grew out of Gowers's celebrated Fourier-analytic proof of Szemer\'edi's theorem \cite{gowers1998new}. We observe that $n$-qudit stabilizer states are so-called nonclassical quadratic phase functions (defined on affine subspaces of $\mathbb{F}_p^n$ where $p$ is the dimension of the qudit) which are fundamental objects in higher-order Fourier analysis. This allows us to import tools from this theory to analyze the stabilizer rank of quantum states. Quite recently, in \cite{peleg2021lower} it was shown that the $n$-qubit magic state has stabilizer rank $\Omega(n)$. Here we show that the qudit analog of the $n$-qubit magic state has stabilizer rank $\Omega(n)$, generalizing their result to qudits of any prime dimension. Our proof techniques use explicitly tools from higher-order Fourier analysis. We believe this example motivates the further exploration of applications of higher-order Fourier analysis in quantum information theory.

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arXiv2020

Low depth algorithms for quantum amplitude estimation

We design and analyze two new low depth algorithms for amplitude estimation (AE) achieving an optimal tradeoff between the quantum speedup and circuit depth. For $\beta \in (0,1]$, our algorithms require $N= \tilde{O}( \frac{1}{ \epsilon^{1+\beta}})$ oracle calls and require the oracle to be called sequentially $D= O( \frac{1}{ \epsilon^{1-\beta}})$ times to perform amplitude estimation within additive error $\epsilon$. These algorithms interpolate between the classical algorithm $(\beta=1)$ and the standard quantum algorithm ($\beta=0$) and achieve a tradeoff $ND= O(1/\epsilon^{2})$. These algorithms bring quantum speedups for Monte Carlo methods closer to realization, as they can provide speedups with shallower circuits. The first algorithm (Power law AE) uses power law schedules in the framework introduced by Suzuki et al \cite{S20}. The algorithm works for $\beta \in (0,1]$ and has provable correctness guarantees when the log-likelihood function satisfies regularity conditions required for the Bernstein Von-Mises theorem. The second algorithm (QoPrime AE) uses the Chinese remainder theorem for combining lower depth estimates to achieve higher accuracy. The algorithm works for discrete $\beta =q/k$ where $k \geq 2$ is the number of distinct coprime moduli used by the algorithm and $1 \leq q \leq k-1$, and has a fully rigorous correctness proof. We analyze both algorithms in the presence of depolarizing noise and provide numerical comparisons with the state of the art amplitude estimation algorithms.

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arXiv2020

High-entropy dual functions over finite fields and locally decodable codes

We show that for infinitely many primes $p$, there exist dual functions of order $k$ over $\mathbb{F}_p^n$ that cannot be approximated in $L_\infty$-distance by polynomial phase functions of degree $k-1$. This answers in the negative a natural finite-field analog of a problem of Frantzikinakis on $L_\infty$-approximations of dual functions over $\mathbb{N}$ (a.k.a. multiple correlation sequences) by nilsequences.

math.NT↗

arXiv2019

Quasirandom quantum channels

Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of sparse vertex transitive graphs using the famous Grothendieck inequality. Here we generalize these results to the non-commutative, or `quantum', case, where a transition matrix becomes a quantum channel. In particular, we show that for irreducibly covariant quantum channels, expansion is equivalent to a natural analog of uniformity for graphs, generalizing the result of Conlon and Zhao. Moreover, we show that in these results, the non-commutative and commutative (resp.) Grothendieck inequalities yield the best-possible constants.

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arXiv2018

Bounding quantum-classical separations for classes of nonlocal games

We bound separations between the entangled and classical values for several classes of nonlocal $t$-player games. Our motivating question is whether there is a family of $t$-player XOR games for which the entangled bias is $1$ but for which the classical bias goes down to $0$, for fixed $t$. Answering this question would have important consequences in the study of multi-party communication complexity, as a positive answer would imply an unbounded separation between randomized communication complexity with and without entanglement. Our contribution to answering the question is identifying several general classes of games for which the classical bias can not go to zero when the entangled bias stays above a constant threshold. This rules out the possibility of using these games to answer our motivating question. A previously studied set of XOR games, known not to give a positive answer to the question, are those for which there is a quantum strategy that attains value 1 using a so-called Schmidt state. We generalize this class to mod-$m$ games and show that their classical value is always at least $\frac{1}{m} + \frac{m-1}{m} t^{1-t}$. Secondly, for free XOR games, in which the input distribution is of product form, we show $\beta(G) \geq \beta^*(G)^{2^t}$ where $\beta(G)$ and $\beta^*(G)$ are the classical and entangled biases of the game respectively. We also introduce so-called line games, an example of which is a slight modification of the Magic Square game, and show that they can not give a positive answer to the question either. Finally we look at two-player unique games and show that if the entangled value is $1-\epsilon$ then the classical value is at least $1-\mathcal{O}(\sqrt{\epsilon \log k})$ where $k$ is the number of outputs in the game. Our proofs use semidefinite-programming techniques, the Gowers inverse theorem and hypergraph norms.

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arXiv2017

The tautological ring of $\mathcal{M}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relations

We use relations in the tautological ring of the moduli spaces $\overline{\mathcal{M}}_{g,n}$ derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the $r$-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spaces $\mathcal{M}_{g,n}$. In particular, we give a new proof for the result of Looijenga (for $n=1$) and Buryak et al. (for $n\geq 2$) that $\dim R^{g-1}(\mathcal{M}_{g,n}) \leq n$. We also give a new proof of the result of Looijenga (for $n=1$) and Ionel (for arbitrary $n\geq 1$) that $R^{i}(\mathcal{M}_{g,n}) =0$ for $i\geq g$ and give some estimates for the dimension of $R^{i}(\mathcal{M}_{g,n})$ for $i\leq g-2$.

math.AG↗