arXiv subjects

Sandy Irani

Publications and source records attributed to Sandy Irani.

At least 19 recordsLinked to original sources

arXiv2025

Local Dominance in Mixed-Strength Populations -- Fast Maximal Independent Set

In many natural and engineered systems, agents interact through local contests that determine which individuals become dominant within their neighborhoods. These interactions are shaped by inherent differences in strength, and they often lead to stable dominance patterns that emerge surprisingly quickly relative to the size of the population. This motivates the search for simple mathematical models that capture both heterogeneous agent strength and rapid convergence to stable local dominance. A widely studied abstraction of local dominance is the Maximal Independent Set (MIS) problem. In the Luby MIS protocol that provably converges quickly to an MIS, each agent repeatedly generates a strength value chosen uniformly and becomes locally dominant if its value is smaller than those of its neighbors. This provides a theoretical explanation for fast dominance convergence in populations of equal-strength agents and naturally raises the question of whether fast convergence also holds in the more realistic setting where agents are inherently mixed-strength. To investigate this question, we introduce the mixed-strength agents model, in which each agent draws its strength from its own distribution. We prove that the extension of the Luby MIS protocol where each agent repeatedly generates a strength value from its own distribution still exhibits fast dominance convergence, providing formal confirmation of the rapid convergence observed in many mixed-strength natural processes. We also show that heterogeneity can significantly change the dynamics of the process. In contrast to the equal-strength setting, a constant fraction of edges need not be eliminated per round. We construct a population and strength profile in which progress per round is asymptotically smaller, illustrating how inherent strength asymmetry produces qualitatively different global behavior.

cs.MA↗

arXiv2025

Singing a MIS

We introduce a broadcast model called the singing model, where agents are oblivious of the size and structure of the communication network, even their immediate neighborhood. Agents can sing multiple notes which are heard by their neighbors. The model is a generalization of the beeping model, where agents can only emit sound at a single frequency. We give a simple and natural protocol where agents compete with their neighbors and their strength is reflected in the number of notes they sing. It converges in $O(log(n))$ time with high probability, where $n$ is the number of agents in the network. The protocol works in an asynchronous model where rounds vary in length and have different start times. It works with completely dynamic networks where agents can be faulty. The protocol is the first to converge to an MIS in logarithmic time for dynamic networks in a network oblivious model.

cs.DS↗

arXiv2025

Cycle Basis Algorithms for Reducing Maximum Edge Participation

We study the problem of constructing cycle bases of graphs with low maximum edge participation, defined as the maximum number of basis cycles that share any single edge. This quantity, though less studied than total weight or length, plays a critical role in quantum fault tolerance because it directly impacts the overhead of lattice surgery procedures used to implement an almost universal quantum gate set. Building on a recursive algorithm of Freedman and Hastings, we introduce a family of load-aware heuristics that adaptively select vertices and edges to minimize edge participation throughout the cycle basis construction. Our approach improves empirical performance on random regular graphs and on graphs derived from small quantum codes. We further analyze a simplified balls-into-bins process to establish lower bounds on edge participation. While the model differs from the cycle basis algorithm on real graphs, it captures what can be proven for our heuristics without using complex graph theoretic properties related to the distribution of cycles in the graph. Our analysis suggests that the maximum load of our heuristics grows on the order of (log n)^2. Our results indicate that careful cycle basis construction can yield significant practical benefits in the design of fault-tolerant quantum systems. This question also carries theoretical interest, as it is essentially identical to the basis number of a graph, defined as the minimum possible maximum edge participation over all cycle bases.

cs.DS↗

arXiv2025

Memory Hierarchy Design for Caching Middleware in the Age of NVM

Advances in storage technology have introduced Non-Volatile Memory, NVM, as a new storage medium. NVM, along with Dynamic Random Access Memory (DRAM), Solid State Disk (SSD), and Disk present a system designer with a wide array of options in designing caching middleware. Moreover, design decisions to replicate a data item in more than one level of a caching memory hierarchy may enhance the overall system performance with a faster recovery time in the event of a memory failure. Given a fixed budget, the key configuration questions are: Which storage media should constitute the memory hierarchy? What is the storage capacity of each hierarchy? Should data be replicated or partitioned across the different levels of the hierarchy? We model these cache configuration questions as an instance of the Multiple Choice Knapsack Problem (MCKP). This model is guided by the specification of each type of memory along with an application's database characteristics and its workload. Although MCKP is NP-complete, its linear programming relaxation is efficiently solvable and can be used to closely approximate the optimal solution. We use the resulting simple algorithm to evaluate design tradeoffs in the context of a memory hierarchy for a Key-Value Store (e.g., memcached) as well as a host-side cache (e.g., Flashcache). The results show selective replication is appropriate with certain failure rates and workload characteristics. With a slim failure rate and frequent data updates, tiering of data across the different storage media that constitute the cache is superior to replication.

cs.DB↗

arXiv2025

Quantum Combine and Conquer and Its Applications to Sublinear Quantum Convex Hull and Maxima Set Construction

We introduce a quantum algorithm design paradigm called combine and conquer, which is a quantum version of the "marriage-before-conquest" technique of Kirkpatrick and Seidel. In a quantum combine-and-conquer algorithm, one performs the essential computation of the combine step of a quantum divide-and-conquer algorithm prior to the conquer step while avoiding recursion. This model is better suited for the quantum setting, due to its non-recursive nature. We show the utility of this approach by providing quantum algorithms for 2D maxima set and convex hull problems for sorted point sets running in $\tilde{O}(\sqrt{nh})$ time, w.h.p., where $h$ is the size of the output.

cs.CG↗

arXiv2024

CAMP: A Cost Adaptive Multi-Queue Eviction Policy for Key-Value Stores

Cost Adaptive Multi-queue eviction Policy (CAMP) is an algorithm for a general purpose key-value store (KVS) that manages key-value pairs computed by applications with different access patterns, key-value sizes, and varying costs for each key-value pair. CAMP is an approximation of the Greedy Dual Size (GDS) algorithm that can be implemented as efficiently as LRU. In particular, CAMP's eviction policies are as effective as those of GDS but require only a small fraction of the updates to an internal data structure in order to make those decisions. Similar to an implementation of LRU using queues, it adapts to changing workload patterns based on the history of requests for different key-value pairs. It is superior to LRU because it considers both the size and cost of key-value pairs to maximize the utility of the available memory across competing applications. We compare CAMP with both LRU and an alternative that requires human intervention to partition memory into pools and assign grouping of key-value pairs to different pools. The results demonstrate CAMP is as fast as LRU while outperforming both LRU and the pooled alternative. We also present results from an implementation of CAMP using Twitter's version of memcached.

cs.DB↗

arXiv2024

Quantum Metropolis Sampling via Weak Measurement

Gibbs sampling is a crucial computational technique used in physics, statistics, and many other scientific fields. For classical Hamiltonians, the most commonly used Gibbs sampler is the Metropolis algorithm, known for having the Gibbs state as its unique fixed point. For quantum Hamiltonians, designing provably correct Gibbs samplers has been more challenging. [TOV+11] introduced a novel method that uses quantum phase estimation (QPE) and the Marriot-Watrous rewinding technique to mimic the classical Metropolis algorithm for quantum Hamiltonians. The analysis of their algorithm relies upon the use of a boosted and shift-invariant version of QPE which may not exist [CKBG23]. Recent efforts to design quantum Gibbs samplers take a very different approach and are based on simulating Davies generators [CKBG23,CKG23,RWW23,DLL24]. Currently, these are the only provably correct Gibbs samplers for quantum Hamiltonians. We revisit the inspiration for the Metropolis-style algorithm of [TOV+11] and incorporate weak measurement to design a conceptually simple and provably correct quantum Gibbs sampler, with the Gibbs state as its approximate unique fixed point. Our method uses a Boosted QPE which takes the median of multiple runs of QPE, but we do not require the shift-invariant property. In addition, we do not use the Marriott-Watrous rewinding technique which simplifies the algorithm significantly.

quant-ph↗

arXiv2023

Commuting Local Hamiltonian Problem on 2D beyond qubits

We study the complexity of local Hamiltonians in which the terms pairwise commute. Commuting local Hamiltonians (CLHs) provide a way to study the role of non-commutativity in the complexity of quantum systems and touch on many fundamental aspects of quantum computing and many-body systems, such as the quantum PCP conjecture and the area law. Despite intense research activity since Bravyi and Vyalyi introduced the CLH problem two decades ago [BV03], its complexity remains largely unresolved; it is only known to lie in NP for a few special cases. Much of the recent research has focused on the physically motivated 2D case, where particles are located on vertices of a 2D grid and each term acts non-trivially only on the particles on a single square (or plaquette) in the lattice. In particular, Schuch [Sch11] showed that the CLH problem on 2D with qubits is in NP. Aharonov, Kenneth and Vigdorovich~[AKV18] then gave a constructive version of this result, showing an explicit algorithm to construct a ground state. Resolving the complexity of the 2D CLH problem with higher dimensional particles has been elusive. We prove two results for the CLH problem in 2D: (1) We give a non-constructive proof that the CLH problem in 2D with qutrits is in NP. As far as we know, this is the first result for the commuting local Hamiltonian problem on 2D beyond qubits. Our key lemma works for general qudits and might give new insights for tackling the general case. (2) We consider the factorized case, also studied in [BV03], where each term is a tensor product of single-particle Hermitian operators. We show that a factorized CLH in 2D, even on particles of arbitrary finite dimension, is equivalent to a direct sum of qubit stabilizer Hamiltonians. This implies that the factorized 2D CLH problem is in NP. This class of CLHs contains the Toric code as an example.

quant-ph↗

arXiv2023

Quantum Tutte Embeddings

Using the framework of Tutte embeddings, we begin an exploration of \emph{quantum graph drawing}, which uses quantum computers to visualize graphs. The main contributions of this paper include formulating a model for quantum graph drawing, describing how to create a graph-drawing quantum circuit from a given graph, and showing how a Tutte embedding can be calculated as a quantum state in this circuit that can then be sampled to extract the embedding. To evaluate the complexity of our quantum Tutte embedding circuits, we compare them to theoretical bounds established in the classical computing setting derived from a well-known classical algorithm for solving the types of linear systems that arise from Tutte embeddings. We also present empirical results obtained from experimental quantum simulations.

cs.DS↗

arXiv2022

Translationally Invariant Constraint Optimization Problems

We study the complexity of classical constraint satisfaction problems on a 2D grid. Specifically, we consider the complexity of function versions of such problems, with the additional restriction that the constraints are translationally invariant, namely, the variables are located at the vertices of a 2D grid and the constraint between every pair of adjacent variables is the same in each dimension. The only input to the problem is thus the size of the grid. This problem is equivalent to one of the most interesting problems in classical physics, namely, computing the lowest energy of a classical system of particles on the grid. We provide a tight characterization of the complexity of this problem, and show that it is complete for the class $FP^{NEXP}$. Gottesman and Irani (FOCS 2009) also studied classical translationally-invariant constraint satisfaction problems; they show that the problem of deciding whether the cost of the optimal solution is below a given threshold is NEXP-complete. Our result is thus a strengthening of their result from the decision version to the function version of the problem. Our result can also be viewed as a generalization to the translationally invariant setting, of Krentel's famous result from 1988, showing that the function version of SAT is complete for the class $FP^{NP}$. An essential ingredient in the proof is a study of the complexity of a gapped variant of the problem. We show that it is NEXP-hard to approximate the cost of the optimal assignment to within an additive error of $\Omega(N^{1/4})$, for an $N \times N$ grid. To the best of our knowledge, no gapped result is known for CSPs on the grid, even in the non-translationally invariant case. As a byproduct of our results, we also show that a decision version of the optimization problem which asks whether the cost of the optimal assignment is odd or even is also complete for $P^{NEXP}$.

cs.CC↗

arXiv2022

Modified Iterative Quantum Amplitude Estimation is Asymptotically Optimal

In this work, we provide the first QFT-free algorithm for Quantum Amplitude Estimation (QAE) that is asymptotically optimal while maintaining the leading numerical performance. QAE algorithms appear as a subroutine in many applications for quantum computers. The optimal query complexity achievable by a quantum algorithm for QAE is $O\left(\frac{1}{\epsilon}\log \frac{1}{\alpha}\right)$ queries, providing a speedup of a factor of $1/\epsilon$ over any other classical algorithm for the same problem. The original algorithm for QAE utilizes the quantum Fourier transform (QFT) which is expected to be a challenge for near-term quantum hardware. To solve this problem, there has been interest in designing a QAE algorithm that avoids using QFT. Recently, the iterative QAE algorithm (IQAE) was introduced by Grinko et al. with a near-optimal $O\left(\frac{1}{\epsilon}\log \left(\frac{1}{\alpha} \log \frac{1}{\epsilon}\right)\right)$ query complexity and small constant factors. In this work, we combine ideas from the preceding line of work to introduce a QFT-free QAE algorithm that achieves a query complexity upper bound of $\frac{62}{\epsilon}\ln\frac{6}{\alpha}$ which matches the optimal $O\left(\frac{1}{\epsilon}\log \frac{1}{\alpha}\right)$ query complexity. We supplement our analysis with numerical experiments comparing our performance with IQAE where we find that our modifications retain the high performance, and in some cases even improve the numerical results.

quant-ph↗

arXiv2021

Quantum search-to-decision reductions and the state synthesis problem

It is a useful fact in classical computer science that many search problems are reducible to decision problems; this has led to decision problems being regarded as the $\textit{de facto}$ computational task to study in complexity theory. In this work, we explore search-to-decision reductions for quantum search problems, wherein a quantum algorithm makes queries to a classical decision oracle to output a desired quantum state. In particular, we focus on search-to-decision reductions for $\mathsf{QMA}$, and show that there exists a quantum polynomial-time algorithm that can generate a witness for a $\mathsf{QMA}$ problem up to inverse polynomial precision by making one query to a $\mathsf{PP}$ decision oracle. We complement this result by showing that $\mathsf{QMA}$-search does $\textit{not}$ reduce to $\mathsf{QMA}$-decision in polynomial-time, relative to a quantum oracle. We also explore the more general $\textit{state synthesis problem}$, in which the goal is to efficiently synthesize a target state by making queries to a classical oracle encoding the state. We prove that there exists a classical oracle with which any quantum state can be synthesized to inverse polynomial precision using only one oracle query and to inverse exponential precision using two oracle queries. This answers an open question of Aaronson from 2016, who presented a state synthesis algorithm that makes $O(n)$ queries to a classical oracle to prepare an $n$-qubit state, and asked if the query complexity could be made sublinear.

quant-ph↗

arXiv2021

Hamiltonian Complexity in the Thermodynamic Limit

Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating the ground energy of a fixed, translationally invariant Hamiltonian in the thermodynamic limit, to within a given precision; the number of bits $n$ for the precision is the sole input to the problem. The complexity of this problem captures how difficult it is for the physicist to measure or compute another digit in the approximation of a physical quantity in the thermodynamic limit. We show that this problem is contained in $\mbox{FEXP}^{\mbox{QMA-EXP}}$ and is hard for $\mbox{FEXP}^{\mbox{NEXP}}$. This means that the problem is doubly exponentially hard in the size of the input. As an ingredient in our construction, we study the problem of computing the ground energy of translationally invariant finite 1D chains. A single Hamiltonian term, which is a fixed parameter of the problem, is applied to every pair of particles in a finite chain. The length of the chain is the sole input to the problem and the task is to compute an approximation of the ground energy. No thresholds are provided as in the standard formulation of the local Hamiltonian problem. We show that this problem is contained in $\mbox{FP}^{\mbox{QMA-EXP}}$ and is hard for $\mbox{FP}^{\mbox{NEXP}}$. Our techniques employ a circular clock in which the ground energy is calibrated by the length of the cycle. This requires more precise expressions for the ground states of the resulting matrices than was required for previous QMA-completeness constructions and even exact analytical bounds for the infinite case which we derive using techniques from spectral graph theory. To our knowledge, this is the first use of the circuit-to-Hamiltonian construction which shows hardness for a function class.

quant-ph↗

arXiv2021

Electronic Structure in a Fixed Basis is QMA-complete

Finding the ground state energy of electrons subject to an external electric field is a fundamental problem in computational chemistry. We prove that this electronic-structure problem, when restricted to a fixed single-particle basis and fixed number of electrons, is QMA-complete. Schuch and Verstraete have shown hardness for the electronic-structure problem with an additional site-specific external magnetic field, but without the restriction to a fixed basis. In their reduction, a local Hamiltonian on qubits is encoded in the site-specific magnetic field. In our reduction, the local Hamiltonian is encoded in the choice of spatial orbitals used to discretize the electronic-structure Hamiltonian. As a step in their proof, Schuch and Verstraete show a reduction from the antiferromagnetic Heisenberg Hamiltonian to the Fermi-Hubbard Hamiltonian. We combine this reduction with the fact that the antiferromagnetic Heisenberg Hamiltonian is QMA-hard to observe that the Fermi-Hubbard Hamiltonian on generic graphs is QMA-hard, even when all the hopping coefficients have the same sign. We then reduce from Fermi-Hubbard by showing that an instance of Fermi-Hubbard can be closely approximated by an instance of the Electronic-Structure Hamiltonian in a fixed basis. Finally, we show that estimating the energy of the lowest-energy Slater-determinant state (i.e., the Hartree-Fock state) is NP-complete for the Electronic-Structure Hamiltonian in a fixed basis.

quant-ph↗

arXiv2016

The Subset Assignment Problem for Data Placement in Caches

We introduce the subset assignment problem in which items of varying sizes are placed in a set of bins with limited capacity. Items can be replicated and placed in any subset of the bins. Each (item, subset) pair has an associated cost. Not assigning an item to any of the bins is not free in general and can potentially be the most expensive option. The goal is to minimize the total cost of assigning items to subsets without exceeding the bin capacities. This problem is motivated by the design of caching systems composed of banks of memory with varying cost/performance specifications. The ability to replicate a data item in more than one memory bank can benefit the overall performance of the system with a faster recovery time in the event of a memory failure. For this setting, the number $n$ of data objects (items) is very large and the number $d$ of memory banks (bins) is a small constant (on the order of $3$ or $4$). Therefore, the goal is to determine an optimal assignment in time that minimizes dependence on $n$. The integral version of this problem is NP-hard since it is a generalization of the knapsack problem. We focus on an efficient solution to the LP relaxation as the number of fractionally assigned items will be at most $d$. If the data objects are small with respect to the size of the memory banks, the effect of excluding the fractionally assigned data items from the cache will be small. We give an algorithm that solves the LP relaxation and runs in time $O({3^d \choose d+1} \text{poly}(d) n \log(n) \log(nC) \log(Z))$, where $Z$ is the maximum item size and $C$ the maximum storage cost.

cs.DS↗

arXiv2012

A Comparison of Performance Measures for Online Algorithms

This paper provides a systematic study of several proposed measures for online algorithms in the context of a specific problem, namely, the two server problem on three colinear points. Even though the problem is simple, it encapsulates a core challenge in online algorithms which is to balance greediness and adaptability. We examine Competitive Analysis, the Max/Max Ratio, the Random Order Ratio, Bijective Analysis and Relative Worst Order Analysis, and determine how these measures compare the Greedy Algorithm, Double Coverage, and Lazy Double Coverage, commonly studied algorithms in the context of server problems. We find that by the Max/Max Ratio and Bijective Analysis, Greedy is the best of the three algorithms. Under the other measures, Double Coverage and Lazy Double Coverage are better, though Relative Worst Order Analysis indicates that Greedy is sometimes better. Only Bijective Analysis and Relative Worst Order Analysis indicate that Lazy Double Coverage is better than Double Coverage. Our results also provide the first proof of optimality of an algorithm under Relative Worst Order Analysis.

cs.DS↗

arXiv2010

Ground State Entanglement in One Dimensional Translationally Invariant Quantum Systems

We examine whether it is possible for one-dimensional translationally-invariant Hamiltonians to have ground states with a high degree of entanglement. We present a family of translationally invariant Hamiltonians {H_n} for the infinite chain. The spectral gap of H_n is Omega(1/poly(n)). Moreover, for any state in the ground space of H_n and any m, there are regions of size m with entanglement entropy Omega(min{m,n}). A similar construction yields translationally-invariant Hamiltonians for finite chains that have unique ground states exhibiting high entanglement. The area law proven by Hastings gives a constant upper bound on the entanglement entropy for 1D ground states that is independent of the size of the region but exponentially dependent on 1/Delta, where Delta is the spectral gap. This paper provides a lower bound, showing a family of Hamiltonians for which the entanglement entropy scales polynomially with 1/Delta. Previously, the best known such bound was logarithmic in 1/Delta.

quant-ph↗

arXiv2010

The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems

We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we show hardness of a classical tiling problem on an N x N 2-dimensional grid and a quantum problem involving finding the ground state energy of a 1-dimensional quantum system of N particles. In both cases, the only input is N, provided in binary. We show that the classical problem is NEXP-complete and the quantum problem is QMA_EXP-complete. Thus, an algorithm for these problems which runs in time polynomial in N (exponential in the input size) would imply that EXP = NEXP or BQEXP = QMA_EXP, respectively. Although tiling in general is already known to be NEXP-complete, to our knowledge, all previous reductions require that either the set of tiles and their constraints or some varying boundary conditions be given as part of the input. In the problem considered here, these are fixed, constant-sized parameters of the problem. Instead, the problem instance is encoded solely in the size of the system.

quant-ph↗