arXiv subjects

Leandro Aolita

Publications and source records attributed to Leandro Aolita.

At least 37 records · Page 2Linked to original sources

arXiv2025

Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't

In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine theoretical no-go results and their implications, addressing misconceptions about the practicality of quantum error mitigation techniques and variational quantum algorithms. By emphasizing the nuances of error scaling, circuit depth, and algorithmic feasibility, we highlight viable near-term applications and synergies between error mitigation and early fault-tolerant architectures. Our discussion explores strategies for addressing current challenges, such as barren plateaus in variational circuits and the integration of quantum error mitigation and quantum error correction techniques. We aim to underscore the importance of continued innovation in hardware and algorithmic design to bridge the gap between theoretical potential and practical utility, paving the way for meaningful quantum advantage in the era of late noisy intermediate scale and early fault-tolerant quantum devices.

quant-ph↗

arXiv2024

Partition function estimation with a quantum coin toss

Estimating quantum partition functions is a critical task in a variety of fields. However, the problem is classically intractable in general due to the exponential scaling of the Hamiltonian dimension $N$ in the number of particles. This paper introduces a quantum algorithm for estimating the partition function $Z_β$ of a generic Hamiltonian $H$ up to multiplicative error based on a quantum coin toss. The coin is defined by the probability of applying the quantum imaginary-time evolution propagator $f_β[H]=e^{-βH/{2}}$ at inverse temperature $β$ to the maximally mixed state, realized by a block-encoding of $f_β[H]$ into a unitary quantum circuit followed by a post-selection measurement. Our algorithm does not use costly subroutines such as quantum phase estimation or amplitude amplification; and the binary nature of the coin allows us to invoke tools from Bernoulli-process analysis to prove a runtime scaling as $\mathcal{O}(N/{Z_β})$, quadratically better than previous general-purpose algorithms using similar quantum resources. Moreover, since the coin is defined by a single observable, the method lends itself well to quantum error mitigation. We test this in practice with a proof-of-concept 9-qubit experiment, where we successfully mitigate errors through a simple noise-extrapolation procedure. Our findings offer an interesting alternative for quantum partition function estimation relevant to early-fault quantum hardware.

quant-ph↗

arXiv2024

Large-scale quantum annealing simulation with tensor networks and belief propagation

Quantum annealing and quantum approximate optimization algorithms hold a great potential to speed-up optimization problems. This could be game-changing for a plethora of applications. Yet, in order to hope to beat classical solvers, quantum circuits must scale up to sizes and performances much beyond current hardware. In that quest, intense experimental effort has been recently devoted to optimizations on 3-regular graphs, which are computationally hard but experimentally relatively amenable. However, even there, the amount and quality of quantum resources required for quantum solvers to outperform classical ones is unclear. Here, we show that quantum annealing for 3-regular graphs can be classically simulated even at scales of 1000 qubits and 5000000 two-qubit gates with all-to-all connectivity. To this end, we develop a graph tensor-network quantum annealer (GTQA) able of high-precision simulations of Trotterized circuits of near-adiabatic evolutions. Based on a recently proposed belief-propagation technique for tensor canonicalization, GTQA is equipped with re-gauging and truncation primitives that keep approximation errors small in spite of the circuits generating significant amounts of entanglement. As a result, even with a maximal bond dimension as low as 4, GTQA produces solutions competitive with those of state-of-the-art classical solvers. For non-degenerate instances, the unique solution can be read out from the final reduced single-qubit states. In contrast, for degenerate problems, such as MaxCut, we introduce an approximate measurement simulation algorithm for graph tensor-network states. On one hand, our findings showcase the potential of GTQA as a powerful quantum-inspired optimizer. On the other hand, they considerably raise the bar required for experimental demonstrations of quantum speed-ups in combinatorial optimizations.

quant-ph↗

arXiv2024

Randomized semi-quantum matrix processing

We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over the Chebyshev approximation of the target function while keeping the matrix oracle quantum, and is assisted by a variant of the Hadamard test that removes the need for post-selection. The resulting statistical overhead is similar to the fully quantum case and does not incur any circuit depth degradation. On the contrary, the average circuit depth is shown to get smaller, yielding equivalent reductions in noise sensitivity, as explicitly shown for depolarizing noise and coherent errors. We apply our technique to partition-function estimation, linear system solvers, and ground-state energy estimation. For these cases, we prove advantages on average depths, including quadratic speed-ups on costly parameters and even the removal of the approximation-error dependence.

quant-ph↗

arXiv2024

Towards large-scale quantum optimization solvers with few qubits

We introduce a variational quantum solver for combinatorial optimizations over $m=\mathcal{O}(n^k)$ binary variables using only $n$ qubits, with tunable $k>1$. The number of parameters and circuit depth display mild linear and sublinear scalings in $m$, respectively. Moreover, we analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature. This leads to unprecedented quantum-solver performances. For $m=7000$, numerical simulations produce solutions competitive in quality with state-of-the-art classical solvers. In turn, for $m=2000$, an experiment with $n=17$ trapped-ion qubits featured MaxCut approximation ratios estimated to be beyond the hardness threshold $0.941$. To our knowledge, this is the highest quality attained experimentally on such sizes. Our findings offer a novel heuristics for quantum-inspired solvers as well as a promising route towards solving commercially-relevant problems on near term quantum devices.

quant-ph↗

arXiv2023

Fragmented imaginary-time evolution for early-stage quantum signal processors

Simulating quantum imaginary-time evolution (QITE) is a major promise of quantum computation. However, the known algorithms are either probabilistic (repeat until success) with impractically small success probabilities or coherent (quantum amplitude amplification) but with circuit depths and ancillary-qubit numbers unrealistically large in the mid term. Our main contribution is a new generation of deterministic, high-precision QITE algorithms significantly more amenable experimentally. These are based on a surprisingly simple idea: partitioning the evolution into several fragments that are sequentially run probabilistically. This causes a huge reduction in wasted circuit depth every time a run fails. Indeed, the resulting overall runtime is asymptotically better than in coherent approaches and the hardware requirements even milder than in probabilistic ones, remarkably. More technically, we present two QITE-circuit sub-routines with excellent complexity scalings. One of them is optimal in ancillary-qubit overhead (one single ancillary qubit throughout) whereas the other one is optimal in runtime for small inverse temperature or high precision. The latter is shown by noting that the runtime saturates a cooling-speed limit that is the imaginary-time counterpart of the no fast-forwarding theorem of real-time simulations, which we prove. Moreover, we also make two technical contributions to the quantum signal processing formalism for operator-function synthesis (on which our sub-routines are based) that are useful beyond QITE. Our findings are specially relevant for the early fault-tolerance stages of quantum hardware.

quant-ph↗

arXiv2023

Complete quantum-inspired framework for computational fluid dynamics

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large vector dimensions required by discretized meshes. We present a full-stack method to solve for incompressible fluids with memory and runtime scaling poly-logarithmically in the mesh size. Our framework is based on matrix-product states, a powerful compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without ever passing through the expensive dense-vector representation. This machinery lays the foundations for a new generation of potentially radically more efficient solvers of real-life fluid problems.

physics.flu-dyn↗

arXiv2022

Fourier-based quantum signal processing

Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum signal processing is the state of the art for this aim, assuming that the operator to be transformed is given as a block of a unitary matrix acting on an enlarged Hilbert space. Here we present an algorithm for Hermitian-operator function design from an oracle given by the unitary evolution with respect to that operator at a fixed time. Our algorithm implements a Fourier approximation of the target function based on the iteration of a basic sequence of single-qubit gates, for which we prove the expressibility. In addition, we present an efficient classical algorithm for calculating its parameters from the Fourier series coefficients. Our algorithm uses only one qubit ancilla regardless the degree of the approximating series. This contrasts with previous proposals, which required an ancillary register of size growing with the expansion degree. Our methods are compatible with Trotterised Hamiltonian simulations schemes and hybrid digital-analog approaches.

quant-ph↗

arXiv2022

Grand Unification of continuous-variable codes

Quantum error correction codes in continuous variables (also called CV codes, or single-mode bosonic codes) have recently been identified to be a technologically viable option for building fault-tolerant quantum computers. The best-known examples are the GKP code and the cat-code, both of which were shown to have some advantageous properties over any discrete-variable, or qubit codes. It was recently shown that the cat-code, as well as other kinds of CV codes, belong to a set of codes with common properties called rotation-symmetric codes. We expand this result by giving a general description of sets of codes with common properties, and rules by which they can be mapped into one another, effectively creating a unified description of continuous-variable codes. We prove that the properties of all of these sets of codes can be obtained from the properties of the GKP code. We also show explicitly how this construction works in the case of rotation-symmetric codes, re-deriving known properties and finding new ones.

quant-ph↗

arXiv2022

Circuit connectivity boosts by quantum-classical-quantum interfaces

High-connectivity circuits are a major roadblock for current quantum hardware. We propose a hybrid classical-quantum algorithm to simulate such circuits without swap-gate ladders. As main technical tool, we introduce quantum-classical-quantum interfaces. These replace an experimentally problematic gate (e.g. a long-range one) by single-qubit random measurements followed by state-preparations sampled according to a classical quasi-probability simulation of the noiseless gate. Each interface introduces a multiplicative statistical overhead which is remarkably independent of the on-chip qubit distance. Hence, by applying interfaces to the longest range gates in a target circuit, significant reductions in circuit depth and gate infidelity can be attained. We numerically show the efficacy of our method for a Bell-state circuit for two increasingly distant qubits and a variational ground-state solver for the transverse-field Ising model on a ring. Our findings provide a versatile toolbox for error-mitigation and circuit boosts tailored for noisy, intermediate-scale quantum computation.

quant-ph↗

arXiv2021

Quasiprobabilistic state-overlap estimator for NISQ devices

As quantum technologies mature, the development of tools for benchmarking their ability to prepare and manipulate complex quantum states becomes increasingly necessary. A key concept, the state overlap between two quantum states, offers a natural tool to verify and cross-validate quantum simulators and quantum computers. Recent progress in controlling and measuring large quantum systems has motivated the development of state overlap estimators of varying efficiency and experimental complexity. Here, we demonstrate a practical approach for measuring the overlap between quantum states based on a factorable quasiprobabilistic representation of the states, and compare it with methods based on randomised measurements. Assuming realistic noisy intermediate scale quantum (NISQ) devices limitations, our quasiprobabilistic method outperforms the best circuits designed for state-overlap estimation for n-qubit states, with n > 2. For n < 7, our technique outperforms also the currently best direct estimator based on randomised local measurements, thus establishing a niche of optimality.

quant-ph↗

arXiv2021

Certification of continuous-variable gates using average channel-fidelity witnesses

We introduce witnesses for the average channel fidelity between a known target gate and an arbitrary unknown channel, for continuous-variable (CV) systems. These are observables whose expectation value yields a tight lower bound to the average channel fidelity in question, thus constituting a practical tool for certification of experimental CV gates. Our framework applies to a broad class of target gates. Here, we focus on three specific types of targets: multi-mode Gaussian unitary channels, single-mode coherent state amplifiers, and the single-mode (non-Gaussian) cubic phase gate, which is a crucial ingredient for CV universal quantum computation. Our witnesses are experimentally-friendly as they rely exclusively on Gaussian measurements, even for the non-Gaussian-target case. Moreover, in all three cases, they can be measured efficiently in the estimation error $ε$ and failure probability $Δ$, as well as in the number of modes $m$ for the Gaussian-target case. To end up with, our approach for the Gaussian-target case relies on an improved measurement scheme for Gaussian state-fidelity witnesses, which is polynomially and exponentially more efficient in $m$ and $Δ$, respectively, than previous schemes. The latter constitutes an interesting byproduct result on its own. Our findings are relevant to the experimental validation of many-body quantum technologies.

quant-ph↗

arXiv2021

Computational advantage from quantum superposition of multiple temporal orders of photonic gates

Models for quantum computation with circuit connections subject to the quantum superposition principle have been recently proposed. There, a control quantum system can coherently determine the order in which a target quantum system undergoes $N$ gate operations. This process, known as the quantum $N$-switch, is a resource for several information-processing tasks. In particular, it provides a computational advantage -- over fixed-gate-order quantum circuits -- for phase-estimation problems involving $N$ unknown unitary gates. However, the corresponding algorithm requires an experimentally unfeasible target-system dimension (super)exponential in $N$. Here, we introduce a promise problem for which the quantum $N$-switch gives an equivalent computational speed-up with target-system dimension as small as 2 regardless of $N$. We use state-of-the-art multi-core optical-fiber technology to experimentally demonstrate the quantum $N$-switch with $N=4$ gates acting on a photonic-polarization qubit. This is the first observation of a quantum superposition of more than $N=2$ temporal orders, demonstrating its usefulness for efficient phase-estimation.

quant-ph↗

arXiv2020

Quantum process tomography with unsupervised learning and tensor networks

The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from measurement data, remains the quintessential primitive to completely characterize quantum devices. However, due to the exponential scaling of the required data and classical post-processing, its range of applicability is typically restricted to one- and two-qubit gates. Here, we present a new technique for performing quantum process tomography that addresses these issues by combining a tensor network representation of the channel with a data-driven optimization inspired by unsupervised machine learning. We demonstrate our technique through synthetically generated data for ideal one- and two-dimensional random quantum circuits of up to 10 qubits, and a noisy 5-qubit circuit, reaching process fidelities above 0.99 using only a limited set of single-qubit measurement samples and input states. Our results go far beyond state-of-the-art, providing a practical and timely tool for benchmarking quantum circuits in current and near-term quantum computers.

quant-ph↗

arXiv2020

Bipartite post-quantum steering in generalised scenarios

The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are: (i) one where Bob also has an input and operates on his subsystem, and (ii) the `instrumental steering' scenario. We show that such bipartite post-quantum steering is a genuinely new type of post-quantum nonlocality, which does not follow from post-quantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.

quant-ph↗

arXiv2019

Probabilistic Simulation of Quantum Circuits with the Transformer

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasi-stochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits with the Transformer, a powerful ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits which build GHZ and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on six qubits. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.

cond-mat.str-el↗

arXiv2019

Distributed sampling, quantum communication witnesses, and measurement incompatibility

We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully-untrusted measurement device. A distributed-sampling task naturally arises in such scenario, whose goal is for Alice and Bob to reproduce the statistics of his measurements on her quantum inputs using a fixed communication channel. Their performance at such task can certify quantum communication (QC), and this is formalised by measurement-device-independent QC witnesses. Furthermore, we prove that QC can provide an advantage (over classical communication) for distributed sampling if and only if Bob's measurements are incompatible. This gives an operational interpretation to the fundamental notion of measurement incompatibility, and motivates a generalised notion of it. Our findings have both fundamental and applied implications.

quant-ph↗

arXiv2019

Experimental device-independent certified randomness generation with an instrumental causal structure

The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the generation of bit strings whose randomness is guaranteed in a device-independent manner, i.e. without assumptions on the measurement and state-generation devices. Here, we generate this strong form of certified randomness on a new platform: the so-called instrumental scenario, which is central to the field of causal inference. First, we theoretically show that certified random bits, private against general quantum adversaries, can be extracted exploiting device-independent quantum instrumental-inequality violations. To that end, we adapt techniques previously developed for the Bell scenario. Then, we experimentally implement the corresponding randomness-generation protocol using entangled photons and active feed-forward of information. Moreover, we show that, for low levels of noise, our protocol offers an advantage over the simplest Bell-nonlocality protocol based on the Clauser-Horn-Shimony-Holt inequality.

quant-ph↗