arXiv subjects

Antonio Mezzacapo

Publications and source records attributed to Antonio Mezzacapo.

At least 37 records · Page 2Linked to original sources

arXiv2024

Accurate quantum-centric simulations of supramolecular interactions

We present the first quantum-centric simulations of noncovalent interactions using a supramolecular approach. We simulate the potential energy surfaces (PES) of the water and methane dimers, featuring hydrophilic and hydrophobic interactions, respectively, with a sample-based quantum diagonalization (SQD) approach. Our simulations on quantum processors, using 27- and 36-qubit circuits, are in remarkable agreement with classical methods, deviating from complete active space configuration interaction (CASCI) and coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) within 1 kcal/mol in the equilibrium regions of the PES. Finally, we test the capacity limits of the quantum methods for capturing hydrophobic interactions with an experiment on 54 qubits. These results mark significant progress in the application of quantum computing to chemical problems, paving the way for more accurate modeling of noncovalent interactions in complex systems critical to the biological, chemical and pharmaceutical sciences.

quant-ph↗

arXiv2024

Variational Benchmarks for Quantum Many-Body Problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy, and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

quant-ph↗

arXiv2024

Diagonalization of large many-body Hamiltonians on a quantum processor

The estimation of low energies of many-body systems is a cornerstone of computational quantum sciences. Variational quantum algorithms can be used to prepare ground states on pre-fault-tolerant quantum processors, but their lack of convergence guarantees and impractical number of cost function estimations prevent systematic scaling of experiments to large systems. Alternatives to variational approaches are needed for large-scale experiments on pre-fault-tolerant devices. Here, we use a superconducting quantum processor to compute eigenenergies of quantum many-body systems on two-dimensional lattices of up to 56 sites, using the Krylov quantum diagonalization algorithm, an analog of the well-known classical diagonalization technique. We construct subspaces of the many-body Hilbert space using Trotterized unitary evolutions executed on the quantum processor, and classically diagonalize many-body interacting Hamiltonians within those subspaces. These experiments show that quantum diagonalization algorithms are poised to complement their classical counterpart at the foundation of computational methods for quantum systems.

quant-ph↗

arXiv2024

Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

quant-ph↗

arXiv2024

Conditions for a quadratic quantum speedup in nonlinear transforms with applications to energy contract pricing

Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions of scenarios, largely benefiting from computational speedups. We develop a novel hybrid quantum-classical algorithm based on polynomial approximation of nonlinear functions, computed through Quantum Hadamard Products, and we rigorously assess the conditions for its end-to-end speedup for different implementation variants against classical algorithms. In our setting, a quadratic quantum speedup, up to polylogarithmic factors, can be proven only when forms are bilinear and approximating polynomials have second degree, if efficient loading unitaries are available for the input data sets. We also enhance the bidirectional encoding, that allows tuning the balance between circuit depth and width, proposing an improved version that can be exploited for the calculation of inner products. Lastly, we exploit the dynamic circuit capabilities, recently introduced on IBM Quantum devices, to reduce the average depth of the Quantum Hadamard Product circuit. A proof of principle is implemented and validated on IBM Quantum systems.

quant-ph↗

arXiv2023

Practical Benchmarking of Randomized Measurement Methods for Quantum Chemistry Hamiltonians

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on a quantum device. To guide the selection of measurement methods designed for this observable estimation problem, we propose a benchmark called CSHOREBench (Common States and Hamiltonians for ObseRvable Estimation Benchmark) that assesses the performance of these methods against a set of common molecular Hamiltonians and common states encountered during the runtime of hybrid quantum-classical algorithms. In CSHOREBench, we account for resource utilization of a quantum computer through measurements of a prepared state, and a classical computer through computational runtime spent in proposing measurements and classical post-processing of acquired measurement outcomes. We apply CSHOREBench considering a variety of measurement methods on Hamiltonians of size up to 16 qubits. Our discussion is aided by using the framework of decision diagrams which provides an efficient data structure for various randomized methods and illustrate how to derandomize distributions on decision diagrams. In numerical simulations, we find that the methods of decision diagrams and derandomization are the most preferable. In experiments on IBM quantum devices against small molecules, we observe that decision diagrams reduces the number of measurements made by classical shadows by more than 80%, that made by locally biased classical shadows by around 57%, and consistently require fewer quantum measurements along with lower classical computational runtime than derandomization. Furthermore, CSHOREBench is empirically efficient to run when considering states of random quantum ansatz with fixed depth.

quant-ph↗

arXiv2023

Subspace methods for electronic structure simulations on quantum computers

Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrodinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the Schrodinger equation into an eigenvalue problem determined by measurements carried out on a quantum device. The eigenvalue problem is then solved on a classical computer, yielding approximations to ground- and excited-state energies and wavefunctions. QSMs are examples of hybrid quantum-classical methods, where a quantum device supported by classical computational resources is employed to tackle a problem. QSMs are rapidly gaining traction as a strategy to simulate electronic wavefunctions on quantum computers, and thus their design, development, and application is a key research field at the interface between quantum computation and electronic structure. In this review, we provide a self-contained introduction to QSMs, with emphasis on their application to the electronic structure of molecules. We present the theoretical foundations and applications of QSMs, and we discuss their implementation on quantum hardware, illustrating the impact of noise on their performance.

quant-ph↗

arXiv2023

Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group

Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up of numerical simulations. The rapid development of hardware devices with various realizations of qubits enables the execution of small scale but representative applications on quantum computers. In particular, the high-energy physics community plays a pivotal role in accessing the power of quantum computing, since the field is a driving source for challenging computational problems. This concerns, on the theoretical side, the exploration of models which are very hard or even impossible to address with classical techniques and, on the experimental side, the enormous data challenge of newly emerging experiments, such as the upgrade of the Large Hadron Collider. In this roadmap paper, led by CERN, DESY and IBM, we provide the status of high-energy physics quantum computations and give examples for theoretical and experimental target benchmark applications, which can be addressed in the near future. Having the IBM 100 x 100 challenge in mind, where possible, we also provide resource estimates for the examples given using error mitigated quantum computing.

quant-ph↗

arXiv2023

Exact and efficient Lanczos method on a quantum computer

We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians. While the classical Lanczos method has exponential cost in the system size to represent the Krylov states for quantum systems, our efficient quantum algorithm achieves this in polynomial time and memory. The construction presented is exact in the sense that the resulting Krylov space is identical to that of the Lanczos method, so the only approximation with respect to the exact method is due to finite sample noise. This is possible because, unlike previous quantum Krylov methods, our algorithm does not require simulating real or imaginary time evolution. We provide an explicit error bound for the resulting ground state energy estimate in the presence of noise. For our method to be successful efficiently, the only requirement on the input problem is that the overlap of the initial state with the true ground state must be $Ω(1/\text{poly}(n))$ for $n$ qubits.

quant-ph↗

arXiv2023

Expressivity of Variational Quantum Machine Learning on the Boolean Cube

Categorical data plays an important part in machine learning research and appears in a variety of applications. Models that can express large classes of real-valued functions on the Boolean cube are useful for problems involving discrete-valued data types, including those which are not Boolean. To this date, the commonly used schemes for embedding classical data into variational quantum machine learning models encode continuous values. Here we investigate quantum embeddings for encoding Boolean-valued data into parameterized quantum circuits used for machine learning tasks. We narrow down representability conditions for functions on the $n$-dimensional Boolean cube with respect to previously known results, using two quantum embeddings: a phase embedding and an embedding based on quantum random access codes. We show that for any real-valued function on the $n$-dimensional Boolean cube, there exists a variational linear quantum model based on a phase embedding using $n$ qubits that can represent it and an ensemble of such models using $d < n$ qubits that can express any function with degree at most $d$. Additionally, we prove that variational linear quantum models that use the quantum random access code embedding can express functions on the Boolean cube with degree $ d\leq \lceil\frac{n}{3}\rceil$ using $\lceil\frac{n}{3}\rceil$ qubits, and that an ensemble of such models can represent any function on the Boolean cube with degree $ d\leq \lceil\frac{n}{3}\rceil$. Furthermore, we discuss the potential benefits of each embedding and the impact of serial repetitions. Lastly, we demonstrate the use of the embeddings presented by performing numerical simulations and experiments on IBM quantum processors using the Qiskit machine learning framework.

quant-ph↗

arXiv2023

Analytic theory for the dynamics of wide quantum neural networks

Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.

quant-ph↗

arXiv2023

Hierarchical Clifford transformations to reduce entanglement in quantum chemistry wavefunctions

The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress in the field. So far, tools from theoretical quantum information have been not thoroughly explored for this task. Here we take a step in this direction by presenting efficiently computable Clifford similarity transformations for quantum chemistry Hamiltonians, which expose bases with reduced entanglement in the corresponding molecular ground states. These transformations are constructed via block diagonalization of a hierarchy of truncated molecular Hamiltonians, preserving the full spectrum of the original problem. We show that the bases introduced here allow for more efficient classical and quantum computation of ground state properties. First, we find a systematic reduction of bipartite entanglement in molecular ground states as compared to standard problem representations. This entanglement reduction has implications in classical numerical methods such as ones based on the density matrix renormalization group. Then, we develop variational quantum algorithms that exploit the structure in the new bases, showing again improved results when the hierarchical Clifford transformations are used.

quant-ph↗

arXiv2023

Quantum approximation algorithms for many-body and electronic structure problems

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems exist, although it is often challenging to establish rigorous bounds on their performances. Here we detail three algorithms that produce approximate ground states for many-body and electronic structure problems, generalizing some previously known results for 2-local Hamiltonians. Each method comes with asymptotic bounds on the energies produced. The first one produces a separable state which improves on random product states. We test it on a spinless Hubbard model, validating numerically the theoretical result. The other two algorithms produce entangled states via shallow or deep circuits, improving on the energies of given initial states. We demonstrate their performance via numerical experiments on a 2-dimensional Hubbard model, starting from a checkerboard product state, as well as on some chemistry Hamiltonians, using the Hartree-Fock state as reference. In both cases, we show that the approximate energies produced are close to the exact ones. These algorithms provide a way to systematically improve the estimation of ground state energies and can be used stand-alone or in conjunction with existing quantum algorithms for ground states.

quant-ph↗

arXiv2022

Ab-initio quantum chemistry with neural-network wavefunctions

Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific discovery. A key application of machine learning in the molecular sciences is to learn potential energy surfaces or force fields from ab-initio solutions of the electronic Schrödinger equation using datasets obtained with density functional theory, coupled cluster, or other quantum chemistry methods. Here we review a recent and complementary approach: using machine learning to aid the direct solution of quantum chemistry problems from first principles. Specifically, we focus on quantum Monte Carlo (QMC) methods that use neural network ansatz functions in order to solve the electronic Schrödinger equation, both in first and second quantization, computing ground and excited states, and generalizing over multiple nuclear configurations. Compared to existing quantum chemistry methods, these new deep QMC methods have the potential to generate highly accurate solutions of the Schrödinger equation at relatively modest computational cost.

physics.chem-ph↗

arXiv2022

Second-quantized fermionic operators with polylogarithmic qubit and gate complexity

We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes, this symmetry reduces the number of information-theoretically required qubits from $Θ(M)$ to $O(F\log M)$. In this limit, our encoding requires $O(F^2\log^4 M)$ qubits, while encoded fermionic creation and annihilation operators have cost $O(F^2\log^5 M)$ in two-qubit gates. When incorporated into randomized simulation methods, this permits simulating time-evolution with only polylogarithmic explicit dependence on $M$. This is the first second-quantized encoding of fermions in qubits whose costs in qubits and gates are both polylogarithmic in $M$, which permits studying fermionic systems in the high-accuracy regime of many modes.

quant-ph↗

arXiv2022

Entanglement Forging with generative neural network models

The optimal use of quantum and classical computational techniques together is important to address problems that cannot be easily solved by quantum computations alone. This is the case of the ground state problem for quantum many-body systems. We show here that probabilistic generative models can work in conjunction with quantum algorithms to design hybrid quantum-classical variational ansätze that forge entanglement to lower quantum resource overhead. The variational ansätze comprise parametrized quantum circuits on two separate quantum registers, and a classical generative neural network that can entangle them by learning a Schmidt decomposition of the whole system. The method presented is efficient in terms of the number of measurements required to achieve fixed precision on expected values of observables. To demonstrate its effectiveness, we perform numerical experiments on the transverse field Ising model in one and two dimensions, and fermionic systems such as the t-V Hamiltonian of spinless fermions on a lattice.

quant-ph↗

arXiv2021

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider hybrid quantum-classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum-classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine learning experiments.

quant-ph↗

arXiv2021

Approximate Solutions of Combinatorial Problems via Quantum Relaxations

Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial optimization is to date an open problem. Here we propose new methods for producing approximate solutions for the maximum cut problem and its weighted version, which are based on relaxations to local quantum Hamiltonians. These relaxations are defined through commutative maps, which in turn are constructed borrowing ideas from quantum random access codes. We establish relations between the spectra of the relaxed Hamiltonians and optimal cuts of the original problems, via two quantum rounding protocols. The first one is based on projections to random magic states. It produces average cuts that approximate the optimal one by a factor of least 0.555 or 0.625, depending on the relaxation chosen, if given access to a quantum state with energy between the optimal classical cut and the maximal relaxed energy. The second rounding protocol is deterministic and it is based on estimation of Pauli observables. The proposed quantum relaxations inherit memory compression from quantum random access codes, which allowed us to test the performances of the methods presented for 3-regular random graphs and a design problem motivated by industry for sizes up to 40 nodes, on superconducting quantum processors.

quant-ph↗