arXiv subjects

Yuval R. Sanders

Publications and source records attributed to Yuval R. Sanders.

18 recordsLinked to original sources

arXiv2025

Unitary Quantum Cellular Automata for Density Classification

We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$, deterministic CA with periodic boundary conditions that solves the DCT perfectly, we explore whether a unitary quantum model can succeed. We employ the Partitioned Unitary Quantum Cellular Automaton (PUQCA), a number-conserving model, and, via evolutionary search, find solutions to the DCT where the success condition is stipulated in terms of measurement probabilities rather than convergence to fixed-point configurations. Finally, we identify a classically simulable regime of the PUQCA in which we find rules that solve the DCT at fixed system sizes and analyze their performance.

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arXiv2025

A Resource Allocating Compiler for Lattice Surgery

The emerging field of quantum resource estimation is aimed at providing estimates of the hardware requirements (`quantum resources') needed to execute a useful, fault-tolerant quantum computation. Given that quantum computers are intended to compete with supercomputers, useful quantum computations are likely to involve the use of millions of qubits and error correction clock cycles. The compilation and benchmarking of these circuits depends on placement and routing algorithms, which are infeasible to construct at scale by hand. We offer a compiler that transforms a quantum circuit into a sequence of lattice surgery operations. The compiler manages memory in terms of surface code patches and costs the space-time volume and cycle counts of the input circuits. These compiled lattice surgery objects are then recursively repurposed as gates for larger scale compilations. Our code is available on GitHub under a permissive software license and we welcome community contributions.

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arXiv2024

Assessing Quantum and Classical Approaches to Combinatorial Optimization: Testing Quadratic Speed-ups for Heuristic Algorithms

Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot support a credible claim of quantum advantage. Here, we highlight the challenges involved in benchmarking quantum and classical heuristics for combinatorial optimization (CO), with a focus on the Sherrington-Kirkpatrick problem. Whereas hope remains that a quadratic quantum advantage is possible,our numerical analysis casts doubt on the idea that current methods exhibit any quantum advantage at all. This doubt arises because even a simple classical approach can match with quantum methods we investigated. We conclude that more careful numerical investigations are needed to evaluate the potential for quantum advantage in CO, and we give some possible future directions for such investigations.

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arXiv2024

Prospects for Quantum Computation in Propellant Design: Assessing the Stability of Cyclic Ozone in Nanoscale Confinement

Cyclic ozone additives have the potential to markedly increase the specific impulse of rocket fuel. This would translate to greater efficiency and reduced costs for space lift by granting more payload per rocket. While practical efforts to capture this isomer have been unsuccessful, it is possible that cyclic ozone would be stabilized in confined geometries. The required synthetic methods are nonetheless difficult to design and require theory-driven inputs that lie beyond the scope of classical methods. Quantum computation has the potential to enable these calculations, though the underlying hardware requirements remain unclear for many practical applications. We present an end-to-end analysis of how quantum methods could support efforts to isolate cyclic ozone via fullerene encapsulation. Our discussion extends beyond asymptotic complexity, reporting both logical- and physical-level resource estimates for ground-state energy determination via quantum phase estimation (QPE), computed using multiple independent resource estimation stacks - Azure Quantum Resource Estimator (AzureQRE), PennyLane's resource estimation framework, and MIT Lincoln Lab's pyLIQTR toolkit - to cross-check resource estimates and bracket realistic overheads. Taken collectively, these data delineate a plausible scale for realistic, computationally-aided molecular design efforts using fault-tolerant quantum computation.

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arXiv2024

Quantum computing for corrosion-resistant materials and anti-corrosive coatings design

Corrosion is a pervasive issue that impacts the structural integrity and performance of materials across various industries, imposing a significant economic impact globally. In fields like aerospace and defense, developing corrosion-resistant materials is critical, but progress is often hindered by the complexities of material-environment interactions. While computational methods have advanced in designing corrosion inhibitors and corrosion-resistant materials, they fall short in understanding the fundamental corrosion mechanisms due to the highly correlated nature of the systems involved. This paper explores the potential of leveraging quantum computing to accelerate the design of corrosion inhibitors and corrosion-resistant materials, with a particular focus on magnesium and niobium alloys. We investigate the quantum computing resources required for high-fidelity electronic ground-state energy estimation (GSEE), which will be used in our hybrid classical-quantum workflow. Representative computational models for magnesium and niobium alloys show that 2292 to 38598 logical qubits and $(1.04$ to $1962) \times 10^{13}$ T-gates are required for simulating the ground-state energy of these systems under the first quantization encoding using plane waves basis.

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arXiv2022

Selection and improvement of product formulae for best performance of quantum simulation

Quantum algorithms for simulation of Hamiltonian evolution are often based on product formulae. The fractal methods give a systematic way to find arbitrarily high-order product formulae, but result in a large number of exponentials. On the other hand, product formulae with fewer exponentials can be found by numerical solution of simultaneous nonlinear equations. It is also possible to reduce the cost of long-time simulations by processing, where a kernel is repeated and a processor need only be applied at the beginning and end of the simulation. In this work, we found thousands of new product formulae, and numerically tested these formulae, together with many formulae from prior literature. We provide methods to fairly compare product formulae of different lengths and different orders. For the case of 8th order, we have found new product formulae with exceptional performance, about two orders of magnitude better accuracy than prior work, both in the processed and non-processed cases. The processed product formula provides the best performance due to being shorter than the non-processed product formula. It outperforms all other tested product formulae over a range of many orders of magnitude in system parameters $T$ (time) and $\epsilon$ (allowable error). That includes reasonable combinations of parameters to be used in quantum algorithms, where the size of the simulation is large enough to be classically intractable, but not so large it takes an impractically long time on a quantum computer.

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arXiv2022

Entanglement in quantum field theory via wavelet representations

Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free scalar bosonic and Ising model fermionic QFTs using wavelets. Making use of the orthogonality and self similarity of the wavelet basis functions, we demonstrate some well known relations such as scale dependent subsystem entanglement entropy and renormalization of correlations in the ground state. We also find some new applications of the wavelet transform as a compressed representation of ground states of QFTs which can be used to illustrate quantum phase transitions via fidelity overlap and holographic entanglement of purification.

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arXiv2022

Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory

We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcomes the ground-state-generation bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms -- Fourier-based and wavelet-based -- to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized-QFT modes. The Fourier-based algorithm is limited to translationally invariant QFTs. Numerical simulations show that the wavelet-based algorithm successfully yields the ground state for a QFT with broken translational invariance. Furthermore, the cost of preparing particle excitations in the wavelet approach is independent of the energy scale. Our algorithms require a routine for generating one-dimensional Gaussian (1DG) states. We replace the standard method for 1DG-state generation, which requires the quantum computer to perform lots of costly arithmetic, with a novel method based on inequality testing that significantly reduces the need for arithmetic. Our method for 1DG-state generation is generic and could be extended to preparing states whose amplitudes can be computed on the fly by a quantum computer.

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arXiv2021

Optimal scaling quantum linear systems solver via discrete adiabatic theorem

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number $κ$ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of $\log(κ)$. Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in $κ$, matching a known lower bound on the complexity. Our $\mathcal{O}(κ\log(1/ε))$ complexity is also optimal in terms of the combined scaling in $κ$ and the precision $ε$. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.

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arXiv2021

Channel Discord and Distortion

Discord, originally notable as a signature of bipartite quantum correlation,in fact can be nonzero classically, i.e., arising from noisy measurements by one of the two parties. Here we redefine classical discord to quantify channel distortion,in contrast to the previous restriction of classical discord to a state,and we then show a monotonic relationship between classical (channel) discord and channel distortion. We show that classical discord is equivalent to (doubly stochastic) channel distortion by numerically discovering a monotonic relation between discord and total-variation distance for a bipartite protocol with one party having a noiseless channel and the other party having a noisy channel. Our numerical method includes randomly generating doubly stochastic matrices for noisy channels and averaging over a uniform measure of input messages. Connecting discord with distortion establishes discord as a signature of classical, not quantum, channel distortion.

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arXiv2021

A Resource Theory of Quantum Measurements

Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information. The objects of the theory are equivalence classes of positive operator-valued measures (POVMs), and the free transformations are changes to a measurement device that can only deteriorate its ability to report information about a physical system. We show that catalysis and purification, protocols that are possible in other resource theories, are impossible in our resource theory for quantum measurements. Standard measures of information gain are shown to be resource monotones, and the resource theory is applied to the task of quantum state discrimination.

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arXiv2020

Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated annealing including those using qubitization or Szegedy walks to quantize classical Markov chains and those simulating spectral gap amplified Hamiltonians encoding a Gibbs state. We also optimize fault-tolerant realizations of the adiabatic algorithm, quantum enhanced population transfer, the quantum approximate optimization algorithm, and other approaches. Many of these methods are bottlenecked by calls to the same subroutines; thus, optimized circuits for those primitives should be of interest regardless of which heuristic is most effective in practice. We compile these bottlenecks for several families of optimization problems and report for how long and for what size systems one can perform these heuristics in the surface code given a range of resource budgets. Our results discourage the notion that any quantum optimization heuristic realizing only a quadratic speedup will achieve an advantage over classical algorithms on modest superconducting qubit surface code processors without significant improvements in the implementation of the surface code. For instance, under quantum-favorable assumptions (e.g., that the quantum algorithm requires exactly quadratically fewer steps), our analysis suggests that quantum accelerated simulated annealing would require roughly a day and a million physical qubits to optimize spin glasses that could be solved by classical simulated annealing in about four CPU-minutes.

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arXiv2020

Quantum State Discrimination as Bayesian Experimental Design

We show that quantum state discrimination sits neatly in the framework of Bayesian experimental design. In this setting, the two main branches of quantum state discrimination (minimal error and maximal confidence) simply correspond to two different utility functions. This view allows straightforward extensions and mixing of different discrimination tasks by examining the utility functions, and to describe multi-objective discrimination tasks. In addition, the probability of success and the total confidence are resource monotones quantifying the usefulness of measurements. We give general conditions under which utility functions lead to resource monotones in the resource theory of quantum measurement.

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arXiv2020

Randomized benchmarking for qudit Clifford gates

We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single-and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.

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arXiv2019

Black-box quantum state preparation without arithmetic

Black-box quantum state preparation is an important subroutine in many quantum algorithms. The standard approach requires the quantum computer to do arithmetic, which is a key contributor to the complexity. Here we present a new algorithm that avoids arithmetic. We thereby reduce the number of gates by a factor of 286-374 over the best prior work for realistic precision; the improvement factor increases with the precision. As quantum state preparation is a crucial subroutine in many approaches to simulating physics on a quantum computer, our new method brings useful quantum simulation closer to reality.

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arXiv2018

Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians

Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.

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arXiv2017

Exponentially More Precise Quantum Simulation of Fermions in the Configuration Interaction Representation

We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New Journal of Physics 18, 033032 (2016)], we employ a recently developed technique for simulating Hamiltonian evolution, using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require $\widetilde{\cal O}(N)$ qubits, where $N$ is the number of single-particle spin-orbitals, the CI matrix representation requires $\widetilde{\cal O}(η)$ qubits where $η\ll N$ is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as $\widetilde{\cal O}(η^2 N^3 t)$.

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arXiv2014

Efficient estimation of resonant coupling between quantum systems

We present an efficient method for the characterization of two coupled discrete quantum systems, one of which can be controlled and measured. For two systems with transition frequencies $ω_q$, $ω_r$, and coupling strength $g$ we show how to obtain estimates of $g$ and $ω_r$ whose error decreases exponentially in the number of measurement shots rather than as a power law expected in simple approaches. Our algorithm can thereby identify $g$ and $ω_r$ simultaneously with high precision in a few hundred measurement shots. This is achieved by adapting measurement settings upon data as it is collected. We also introduce a method to eliminate erroneous estimates with small overhead. Our algorithm is robust against the presence of relaxation and typical noise. Our results are applicable to many candidate technologies for quantum computation, in particular, for the characterization of spurious two-level systems in superconducting qubits or stripline resonators.

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