arXiv subjects

Thais de Lima Silva

Publications and source records attributed to Thais de Lima Silva.

9 recordsLinked to original sources

arXiv2026

Compilation-informed probabilistic logical-error cancellation

The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction (QEC) offers a clear path towards fault tolerance, overcoming the scalability issues will take time. Early applications will likely rely on QEC combined with quantum error mitigation (QEM). We introduce a QEM scheme against both compilation errors and logical-gate noise that is circuit-, QEC code-, and compiler-agnostic. The scheme builds on quasi-probability methods and uses information about the circuit's gates' compilations to attain an unbiased estimation of noiseless expectation values incurring a constant sample-complexity overhead. Moreover, it features maximal circuit size and code distance both independent of the target precision, in contrast to strategies based on QEC alone. We formulate the mitigation procedure as a linear program, demonstrate its efficacy through numerical simulations, and illustrate it for estimating the Jones polynomials of knots. Our method significantly reduces quantum resource requirements for high-precision estimations, offering a practical route towards fault-tolerant quantum computation with precision-independent overheads for fixed circuit size and code distance.

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arXiv2026

Robustness of Quantum Signal Processing and Resource-aware Polynomial Design

Quantum signal processing (QSP) realizes operator functions through polynomial transformations of a finite degree. In addition to function approximation errors, realistic implementations incur algorithmic errors also when encoding the input operator and in synthesizing gates into a discrete fault-tolerant gate set. We provide an end-to-end analysis of these errors and show that the input error propagation is governed by the operator-Lipschitz constant $L_\star$ of the implemented function. We then derive an efficient classical algorithm to compute tight lower and upper bounds on $L_\star$, and we show that these bounds induce in turn lower and upper bounds on the total quantum-resource cost (for instance, $T$-gate count) needed for QSP implementations compatible with a target total error. We further devise a procedure to search for a polynomial with minimum cost based solely on its coefficients, yielding a resource-aware polynomial-design procedure for QSP. We illustrate the resulting method for ground state energy estimation via eigenvalue thresholding for the H$_6$ molecular Hamiltonian. In the tested hardware profiles, the resource-aware family improves the total-error budget and reduces the modeled $T$-gate count by $51.9\%$--$56.7\%$ relative to the standard analytical polynomial obtained from an error-function approximation.

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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.

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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.

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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.

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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.

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arXiv2020

Classical and Quantum Light: Versatile tools for quantum foundations and quantum information

Light beams offer many degrees of freedom to be explored in discrete and continuous domains. In addition to the possibility of entangling photons in these many degrees of freedom, it makes light a very useful and versatile tool for quantum information and quantum foundation purposes. In this thesis, we endorse its importance and versatility by presenting novel contributions that further explore both discrete and continuous degrees of freedom. It begins with two experiments that use classical light and explore its analogous behavior to quantum systems. The first one is a classical optics simulation of the dynamics of a relativistic quantum particle. The second work is related to the theory of mutually unbiased measurements that are effectively discrete but constructed from continuous variables systems. In the second part of the thesis, three works are presented that use the polarization and path discrete degrees of freedom. The first one is a redefinition of the quantum nonlocal correlation called steering in the multipartite scenario, based on an inconsistency in the previous definition, namely the creation of this correlation from scratch using operations that supposedly would not be able to do so. We call this exposure of quantum steering. Steering exposure is observed with entangled photons. The other two works are related to the experimental implementation of quantum channels of qubits, one of them is a particular channel for which we test for non-Markovianity using a operational measure called conditional past-future (CPF) correlation. The thesis finishes with a proposal for an experimental realization of any quantum channel of a single qubit, where the qubit is realized by the polarization of single photons. The functioning of all optical devices used is didactically explained.

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arXiv2020

Detection of quantum non-Markovianity close to the Born-Markov approximation

We calculate in an exact way the conditional past-future correlation for the decay dynamics of a two-level system in a bosonic bath. Different measurement processes are considered. In contrast to quantum memory measures based solely on system propagator properties, here memory effects are related to a convolution structure involving two system propagators and the environment correlation. This structure allows to detect memory effects even close to the validity of the Born-Markov approximation. An alternative operational-based definition of environment-to-system backflow of information follows from this result. We provide experimental support to our results by implementing the dynamics and measurements in a photonic experiment.

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arXiv2019

Optical simulation of the free Dirac equation

We present a classical optics simulation of the one-dimensional Dirac equation for a free particle. Positive and negative energy components are represented by orthogonal polarizations of a free propagating beam, while the spatial profile represents the spatial wave function of the particle. Using a completely tunable time parameter, we observed the oscillation of the average value of the Dirac position operator - known as zitterbewegung (ZB). We are also able to measure the so called mean-position operator which is a single-particle observable and presents no oscillations. Our work opens the way for optical simulation of interesting phenomenon of relativistic systems, as well as condensed-matter physics, without any requirement for specially engineered medium.

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