arXiv subjects

Hari Krovi

Publications and source records attributed to Hari Krovi.

At least 19 recordsLinked to original sources

arXiv2026

Quantum simulation of non-Markovian dynamical systems

Existing quantum algorithms for simulating dynamical systems -- from Hamiltonian simulation to linear and nonlinear differential equations solvers -- simulate Markovian dynamics, in which the system's future evolution depends solely on its current state. We turn our attention to developing quantum algorithms for non-Markovian dynamical systems where the system's future evolution depends on its past history and thus has memory. Specifically, we develop efficient algorithms for linear Volterra integro-differential equations (VIDEs) with a convolution memory kernel that output a quantum state encoding the state description over a time interval or at a particular time. Given efficient circuits for the problem inputs, our algorithms achieve an exponential speedup in system size over existing classical algorithms. We develop an algorithm for general kernels assuming that $\textsf{M} < 1$, where $\textsf{M}$ characterizes the strength of the memory term relative to the dissipation of the Markovian part of the dynamics. We complement this with lower bounds for general-kernel VIDEs when $\textsf{M} \geq 1$, showing that the problem becomes intractable for a family of systems. However, by specializing to structured kernels which admit concise decompositions over exponentials, we develop efficient quantum algorithms even when $\textsf M \geq 1$ by converting the VIDE into a larger set of ODEs, a procedure which we call Markovianization. As an application of the overall framework, we discuss the Mori-Zwanzig formalism used in open quantum systems and fluid dynamics. Overall, our results expand the range of dynamical systems that quantum computers can simulate efficiently.

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arXiv2026

Separating quantum circuits from classical LLMs

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by $\textsf{QNC}^0$ circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model ($\textsf{DLM}$) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern $\textsf{DLM}$s rely on. 2. Functional separation. We exhibit a function computable in $\land \circ \textsf{QNC}^0[\log\log n]$ (i.e., a family of O$(\log\log n)$-depth $\textsf{QNC}^0$ circuits, where $n$ is the input length, followed by a single classical $\mathsf{AND}$ gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width $n^{\Omega(1)}$. Together, our work initiates the study of quantum advantage in the era of large language models.

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arXiv2026

Simulating dynamics of RLC circuits with a quantum differential-algebraic equations solver

We introduce a quantum algorithm for simulating the dynamics of electrical circuits consisting of resistors, inductors and capacitors (aka RLC circuits) along with power sources. Given oracle access to the connectivity of the circuit and values of the electrical elements, our algorithm prepares a quantum state that encodes voltages and current values either at a specified time or the history of their evolution over a time-interval. For an RLC circuit with $N$ components, our algorithm runs in time $\textsf{polylog}(N)$ under mild assumptions on the connectivity of the circuit and values of its components. This provides an exponential speed-up over classical algorithms that take $\textsf{poly}(N)$ time in the worst-case. Our algorithm can be used to estimate energy across a set of components or dissipated power in $\textsf{polylog}(N)$ time, a problem that we prove is BQP-hard and therefore unlikely to be efficiently solved by classical algorithms. The main challenge in simulating the dynamics of RLC circuits is that they are governed by differential-algebraic equations (DAEs), a coupled system of differential equations with hidden algebraic constraints. Consequentially, existing quantum algorithms for ordinary differential equations cannot be directly utilized. We therefore develop a quantum DAE solver for simulating the time-evolution of linear DAEs. For RLC circuits, we employ modified nodal analysis to create a system of DAEs compatible with our quantum algorithm. We establish BQP-hardness by demonstrating that any network of classical harmonic oscillators, for which an energy-estimation problem is known to be BQP-hard, is a special case of an LC circuit. Our work gives theoretical evidence of quantum advantage in simulating RLC circuits and we expect that our quantum DAE solver will find broader use in the simulation of dynamical systems.

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arXiv2026

Improved quantum circuits for division

Arithmetic operations are an important component of many quantum algorithms. Optimizing quantum circuits for these operations therefore leads to more efficient implementations of the corresponding algorithms. In this paper, we develop new fault-tolerant quantum circuits for various integer division algorithms (both reversible and non-reversible). These circuits, when implemented in the Clifford+T gate set, achieve improvements in the asymptotic T-count and CNOT-count from $O(n^2)$ to $O(nm)$, and in the asymptotic T-depth from $O(n^2)$ to $O(n \log m)$, where $n$ and $m$ are the bit lengths of the dividend and divisor, respectively. The qubit counts are significantly lower than those in previous works. We achieve this through careful modifications of the division algorithms and by expressing them in terms of a primitive we call COMP-N-SUB that compares two integers and conditionally subtracts them. We show that this primitive can be implemented at a cost, in terms of both Clifford and non-Clifford gates, comparable to that of one addition. By contrast, performing comparison and conditional subtraction separately would cost roughly as much as a controlled addition plus a regular addition.

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arXiv2026

Quantum lower bounds for simulating fluid dynamics

Developing quantum algorithms to simulate fluid dynamics has become an active area of research, as accelerating fluid simulations could have significant impact in both industry and fundamental science. While many approaches have been proposed for simulating fluid dynamics on quantum computers, it is largely unclear whether these algorithms will provide speedup over existing classical approaches. In this paper we give evidence that quantum computers cannot significantly outperform classical simulations of fluid dynamics in general. We study two models of fluids: the Korteweg-de Vries (KdV) equation, which models shallow water waves, and the incompressible Euler equations, which model ideal, inviscid fluids. We show that any quantum algorithm simulating the KdV equation or the Euler equations for time $T$ requires $\Omega(T^2)$ and $e^{\Omega(T)}$ copies of the initial state in the worst case, respectively. These lower bounds hold for the task of preparing the final state, and similar bounds hold for history state preparation. We prove the lower bound for the KdV equation by investigating divergence of solitons. For the Euler equations, we show that instabilities enable fast state discrimination.

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arXiv2024

Demonstrating real-time and low-latency quantum error correction with superconducting qubits

Quantum error correction (QEC) will be essential to achieve the accuracy needed for quantum computers to realise their full potential. The field has seen promising progress with demonstrations of early QEC and real-time decoded experiments. As quantum computers advance towards demonstrating a universal fault-tolerant logical gate set, implementing scalable and low-latency real-time decoding will be crucial to prevent the backlog problem, avoiding an exponential slowdown and maintaining a fast logical clock rate. Here, we demonstrate low-latency feedback with a scalable FPGA decoder integrated into the control system of a superconducting quantum processor. We perform an 8-qubit stability experiment with up to $25$ decoding rounds and a mean decoding time per round below $1$ $μs$, showing that we avoid the backlog problem even on superconducting hardware with the strictest speed requirements. We observe logical error suppression as the number of decoding rounds is increased. We also implement and time a fast-feedback experiment demonstrating a decoding response time of $9.6$ $μs$ for a total of $9$ measurement rounds. The decoder throughput and latency developed in this work, combined with continued device improvements, unlock the next generation of experiments that go beyond purely keeping logical qubits alive and into demonstrating building blocks of fault-tolerant computation, such as lattice surgery and magic state teleportation.

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arXiv2024

Quantum algorithms to simulate quadratic classical Hamiltonians and optimal control

Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities of interest such as the kinetic energy in a given classical mechanical system in the presence of friction or damping as well as forcing or source terms, which makes the algorithm of practical interest. We show that for such systems, the quantum algorithm scales polynomially with the logarithm of the dimension of the system. We cast this problem in terms of Hamilton's equations of motion (equivalent to the first variation of the Lagrangian) and solve them using quantum algorithms for differential equations. We then consider the hardness of estimating the kinetic energy of a damped coupled oscillator system. We show that estimating the kinetic energy at a given time of this system to within additive precision is BQP hard when the strength of the damping term is bounded by an inverse polynomial in the number of qubits. We then consider the problem of designing optimal control of classical systems, which can be cast as the second variation of the Lagrangian. In this direction, we first consider the Riccati equation, which is a nonlinear differential equation ubiquitous in control theory. We give an efficient quantum algorithm to solve the Riccati differential equation well into the nonlinear regime. To our knowledge, this is the first example of any nonlinear differential equation that can be solved when the strength of the nonlinearity is asymptotically greater than the amount of dissipation. We then show how to use this algorithm to solve the linear quadratic regulator problem, which is an example of the Hamilton-Jacobi-Bellman equation.

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arXiv2023

Accurate and Honest Approximation of Correlated Qubit Noise

Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the number of qubits. We propose an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, we first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual noise channel into components based on interqubit correlation degree. We generate a $k$-th order approximate noise channel by truncating the cluster expansion and incorporating noise components with correlations up to the $k$-th degree. We require that the approximate noise channels must be accurate and also ``honest", i.e., the actual errors are not underestimated in our physical models. As an example application, we apply our method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,2]] codeword, which is one of the four Bell states. We find that, for realistic noise strength typical for fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic characterization of multi-qubit noise correlations, it enables the potential for accurate, honest and scalable approximations to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient yet still retain essential noise features of the entire device.

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arXiv2023

A quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this work, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional, electrostatic limit. Rather than solving this equation in its native spatial and velocity phase-space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. The Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. This representation results in a system of linear ordinary differential equations which can be solved with well-developed quantum algorithms: Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

physics.plasm-ph↗

arXiv2022

Superresolution at the quantum limit beyond two point sources

Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point sources (with a known centroid) was shown to achieve the quantum Cramer-Rao bound. This work made implicit use of reflection symmetry of the sources. Here we present a framework that uses more general symmetry in a constellation to construct a quantum measurement that achieves the quantum Cramer-Rao bound in estimation of parameters. We show how this technique can be used to estimate parameters simultaneously in symmetric point-source constellations with more than two point sources. In order to use symmetry explicitly, we make use discrete point spread functions in momentum space that maintain this symmetry. This framework allows us to use techniques from quantum computing such as Fourier transforms and linear optical circuits to implement the optimal measurement. To our knowledge, this is first work that shows for more than two point sources achievable quantum limits of estimation and modal transformations.

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arXiv2022

Average-case hardness of estimating probabilities of random quantum circuits with a linear scaling in the error exponent

We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as follows. For Haar random circuits with $m$ gates, we improve on prior results by showing $\mathsf{coC_=P}$ hardness of average-case additive approximations to an imprecision of $2^{-O(m)}$. Efficient classical simulation of such problems would imply the collapse of the polynomial hierarchy. For constant depth circuits i.e., when $m=O(n)$, this linear scaling in the exponent is within a constant of the scaling required to show hardness of sampling. Prior to our work, such a result was shown only for Boson Sampling in Bouland et al (2021). We also use recent results in polynomial interpolation to show $\mathsf{coC_=P}$ hardness under $\mathsf{BPP}$ reductions rather than $\mathsf{BPP}^{\mathsf{NP}}$ reductions. This improves the results of prior work for Haar random circuits both in terms of the error scaling and the power of reductions. Next, we consider random $p=1$ QAOA and IQP circuits and show that in the average-case, it is $\mathsf{coC_=P}$ hard to approximate the output probability to within an additive error of $2^{-O(n)}$. For $p=1$ QAOA circuits, this work constitutes the first average-case hardness result for the problem of approximating output probabilities for random QAOA circuits, which include Sherrington-Kirkpatrick and Erdös-Renyi graphs. For IQP circuits, a consequence of our results is that approximating the Ising partition function with imaginary couplings to an additive error of $2^{-O(n)}$ is hard even in the average-case, which extends prior work on worst-case hardness of multiplicative approximation to Ising partition functions.

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arXiv2022

Improved quantum algorithms for linear and nonlinear differential equations

We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In Berry et al., (2017), a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices. The algorithm here is also exponentially faster than the bounds derived in Berry et al., (2017) for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in Liu et al., (2021)). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by Xue et al., (2021), but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse, invertible matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas Liu et al., (2021) and Xue et al., (2021) additionally require normality.

quant-ph↗

arXiv2021

Subexponential rate versus distance with time-multiplexed quantum repeaters

Quantum communications capacity using direct transmission over length-$L$ optical fiber scales as $R \sim e^{-αL}$, where $α$ is the fiber's loss coefficient. The rate achieved using a linear chain of quantum repeaters equipped with quantum memories, probabilistic Bell state measurements (BSMs) and switches used for spatial multiplexing, but no quantum error correction, was shown to surpass the direct-transmission capacity. However, this rate still decays exponentially with the end-to-end distance, viz., $R \sim e^{-s{αL}}$, with $s < 1$. We show that the introduction of temporal multiplexing - i.e., the ability to perform BSMs among qubits at a repeater node that were successfully entangled with qubits at distinct neighboring nodes at {\em different} time steps - leads to a sub-exponential rate-vs.-distance scaling, i.e., $R \sim e^{-t\sqrt{αL}}$, which is not attainable with just spatial or spectral multiplexing. We evaluate analytical upper and lower bounds to this rate, and obtain the exact rate by numerically optimizing the time-multiplexing block length and the number of repeater nodes. We further demonstrate that incorporating losses in the optical switches used to implement time multiplexing degrades the rate-vs.-distance performance, eventually falling back to exponential scaling for very lossy switches. We also examine models for quantum memory decoherence and describe optimal regimes of operation to preserve the desired boost from temporal multiplexing. Quantum memory decoherence is seen to be more detrimental to the repeater's performance over switching losses.

quant-ph↗

arXiv2020

Continuous-variable quantum repeater based on quantum scissors and mode multiplexing

Quantum repeaters are indispensable for high-rate, long-distance quantum communications. The vision of a future quantum internet strongly hinges on realizing quantum repeaters in practice. Numerous repeaters have been proposed for discrete-variable (DV) single-photon-based quantum communications. Continuous variable (CV) encodings over the quadrature degrees of freedom of the electromagnetic field mode offer an attractive alternative. For example, CV transmission systems are easier to integrate with existing optical telecom systems compared to their DV counterparts. Yet, repeaters for CV have remained elusive. We present a novel quantum repeater scheme for CV entanglement distribution over a lossy bosonic channel that beats the direct transmission exponential rate-loss tradeoff. The scheme involves repeater nodes consisting of a) two-mode squeezed vacuum (TMSV) CV entanglement sources, b) the quantum scissors operation to perform nondeterministic noiseless linear amplification of lossy TMSV states, c) a layer of switched, mode multiplexing inspired by second-generation DV repeaters, which is the key ingredient apart from probabilistic entanglement purification that makes DV repeaters work, and d) a non-Gaussian entanglement swap operation. We report our exact results on the rate-loss envelope achieved by the scheme.

quant-ph↗

arXiv2019

Numerical finite-key analysis of quantum key distribution

Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments however predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two novel semi-definite programs (SDPs). The first uses the relation between smooth min-entropy and quantum relative entropy, and the second uses the relation between the smooth min-entropy and quantum fidelity. We then solve these SDPs using convex optimization solvers and obtain some of the first numerical calculations of finite key rates for several different protocols, such as BB84, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.

quant-ph↗

arXiv2019

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCCassisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.

quant-ph↗

arXiv2019

An efficient high dimensional quantum Schur transform

The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an $n$ fold tensor product $V^{\otimes n}$ of a vector space $V$ of dimension $d$. Bacon, Chuang and Harrow \cite{BCH07} gave a quantum algorithm for this transform that is polynomial in $n$, $d$ and $\logε^{-1}$, where $ε$ is the precision. In a footnote in Harrow's thesis \cite{H05}, a brief description of how to make the algorithm of \cite{BCH07} polynomial in $\log d$ is given using the unitary group representation theory (however, this has not been explained in detail anywhere. In this article, we present a quantum algorithm for the Schur transform that is polynomial in $n$, $\log d$ and $\logε^{-1}$ using a different approach. Specifically, we build this transform using the representation theory of the symmetric group and in this sense our technique can be considered a "dual" algorithm to \cite{BCH07}. A novel feature of our algorithm is that we construct the quantum Fourier transform over the so called \emph{permutation modules}, which could have other applications.

quant-ph↗

arXiv2018

BQP-completeness of Scattering in Scalar Quantum Field Theory

Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

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