arXiv subjects

Antonio Mezzacapo

Publications and source records attributed to Antonio Mezzacapo.

51 records · Page 3Linked to original sources

arXiv2021

Optimal parent Hamiltonians for time-dependent states

Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians, we find the optimal Hamiltonian once a set of realistic elementary interactions is defined. We provide three examples of this approach. We first apply the optimization protocol to the ground states of the one-dimensional Ising model and a ferromagnetic $p$-spin model but with time-dependent coefficients. We also consider a time-dependent state that interpolates between a product state and the ground state of a $p$-spin model. We determine the time-dependent optimal parent Hamiltonian for these states and analyze the capability of this Hamiltonian of generating the state evolution. Finally, we discuss the connections of our approach to shortcuts to adiabaticity.

quant-ph↗

arXiv2021

Decision Diagrams for Quantum Measurements with Shallow Circuits

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on randomised measurements, which use decision diagrams to sample from probability distributions on measurement bases. This approach generalises previously known uniform and locally-biased randomised estimators. The decision diagrams are constructed given target quantum operators and can be optimised considering different strategies. We show numerically that the estimators introduced here can produce more precise estimates on some quantum chemistry Hamiltonians, compared to previously known randomised protocols and Pauli grouping methods.

quant-ph↗

arXiv2021

Doubling the size of quantum simulators by entanglement forging

Quantum computers are promising for simulations of chemical and physical systems, but the limited capabilities of today's quantum processors permit only small, and often approximate, simulations. Here we present a method, classical entanglement forging, that harnesses classical resources to capture quantum correlations and double the size of the system that can be simulated on quantum hardware. Shifting some of the computation to classical post-processing allows us to represent ten spin-orbitals on five qubits of an IBM Quantum processor to compute the ground state energy of the water molecule in the most accurate simulation to date. We discuss conditions for applicability of classical entanglement forging and present a roadmap for scaling to larger problems.

quant-ph↗

arXiv2020

Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor

The computation of molecular excitation energies is essential for predicting photo-induced reactions of chemical and technological interest. While the classical computing resources needed for this task scale poorly, quantum algorithms emerge as promising alternatives. In particular, the extension of the variational quantum eigensolver algorithm to the computation of the excitation energies is an attractive option. However, there is currently a lack of such algorithms for correlated molecular systems that is amenable to near-term, noisy hardware. In this work, we propose an extension of the well-established classical equation of motion approach to a quantum algorithm for the calculation of molecular excitation energies on noisy quantum computers. In particular, we demonstrate the efficiency of this approach in the calculation of the excitation energies of the LiH molecule on an IBM Quantum computer.

quant-ph↗

arXiv2020

Measurements of Quantum Hamiltonians with Locally-Biased Classical Shadows

Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer. We propose a novel estimator for this task, which is locally optimised with knowledge of the Hamiltonian and a classical approximation to the underlying quantum state. Our estimator is based on the concept of classical shadows of a quantum state, and has the important property of not adding to the circuit depth for the state preparation. We test its performance numerically for molecular Hamiltonians of increasing size, finding a sizable reduction in variance with respect to current measurement protocols that do not increase circuit depths.

quant-ph↗

arXiv2020

Reducing qubit requirements for quantum simulation using molecular point group symmetries

Simulating molecules is believed to be one of the early-stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence, therefore optimizing resources to execute quantum algorithms is crucial. In this work, we develop the second quantization representation of the spatial-symmetries which are then transformed to their qubit operator representation. These qubit operator representations are used to reduce the number of qubits required for simulating molecules. We present our results for various molecules and elucidate a formal connection of this work with a previous technique that analyzed generic $Z_2$ Pauli symmetries.

quant-ph↗

arXiv2019

Precise measurement of quantum observables with neural-network estimators

The measurement precision of modern quantum simulators is intrinsically constrained by the limited set of measurements that can be efficiently implemented on hardware. This fundamental limitation is particularly severe for quantum algorithms where complex quantum observables are to be precisely evaluated. To achieve precise estimates with current methods, prohibitively large amounts of sample statistics are required in experiments. Here, we propose to reduce the measurement overhead by integrating artificial neural networks with quantum simulation platforms. We show that unsupervised learning of single-qubit data allows the trained networks to accommodate measurements of complex observables, otherwise costly using traditional post-processing techniques. The effectiveness of this hybrid measurement protocol is demonstrated for quantum chemistry Hamiltonians using both synthetic and experimental data. Neural-network estimators attain high-precision measurements with a drastic reduction in the amount of sample statistics, without requiring additional quantum resources.

quant-ph↗

arXiv2019

Fermionic neural-network states for ab-initio electronic structure

Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early research activity. Here we present an extension of neural-network quantum states to model interacting fermionic problems. Borrowing techniques from quantum simulation, we directly map fermionic degrees of freedom to spin ones, and then use neural-network quantum states to perform electronic structure calculations. For several diatomic molecules in a minimal basis set, we benchmark our approach against widely used coupled cluster methods, as well as many-body variational states. On the test molecules, we recover almost the entirety of the correlation energy. We systematically improve upon coupled cluster methods and Jastrow wave functions, reaching levels of chemical accuracy or better. Finally, we discuss routes for future developments and improvements of the methods presented.

physics.comp-ph↗

arXiv2018

Superfast encodings for fermionic quantum simulation

Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamiltonian composed of Pauli operators of weight $O(d)$. A system of $m$ fermi modes gets mapped to $n=O(md)$ qubits. We propose Generalized Superfast Encodings (GSE) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree $d\ge 6$. In contrast, we prove that the original Superfast Encoding lacks the error correction property for $d\le 6$. Secondly, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O(d)$ to $O(\log{d})$. The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.

quant-ph↗

arXiv2018

Extending the computational reach of a noisy superconducting quantum processor

Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation based off expectation values of quantum observables can be enhanced through an extrapolation of results from a collection of varying noisy experiments. Here, we demonstrate this error mitigation protocol on a superconducting quantum processor, enhancing its computational capability, with no additional hardware modifications. We apply the protocol to mitigate errors on canonical single- and two-qubit experiments and then extend its application to the variational optimization of Hamiltonians for quantum chemistry and magnetism. We effectively demonstrate that the suppression of incoherent errors helps unearth otherwise inaccessible accuracies to the variational solutions using our noisy processor. These results demonstrate that error mitigation techniques will be critical to significantly enhance the capabilities of near-term quantum computing hardware.

quant-ph↗

arXiv2018

Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework into the particle-hole (p/h) picture, which offers a better starting point for the expansion of the trial wavefunction. The state of the molecular system at study is parametrized in a way to efficiently explore the sector of the molecular Fock space that contains the desired solution. To this end, we explore several trial wavefunctions to identify the most efficient parameterization of the molecular ground state. Taking advantage of known post-Hartree Fock quantum chemistry approaches and heuristic Hilbert space search quantum algorithms, we propose a new family of quantum circuits based on exchange-type gates that enable accurate calculations while keeping the gate count (i.e., the circuit depth) low. The particle-hole implementation of the Unitary Coupled Cluster (UCC) method within the Variational Quantum Eigensolver approach gives rise to an efficient quantum algorithm, named q-UCC , with important advantages compared to the straightforward 'translation' of the classical Coupled Cluster counterpart. In particular, we show how a single Trotter step can accurately and efficiently reproduce the ground state energies of simple molecular systems.

quant-ph↗

arXiv2017

Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets

Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.

quant-ph↗

arXiv2017

Quantum optimization using variational algorithms on near-term quantum devices

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that follow a hybrid approach: the aim is to steer a highly entangled state on a quantum system to a target state that minimizes a cost function via variation of some gate parameters. This variational approach can be used both for classical optimization problems as well as for problems in quantum chemistry. The challenge is to converge to the target state given the limited coherence time and connectivity of the qubits. In this context, the quantum volume as a metric to compare the power of near-term quantum devices is discussed. With focus on chemistry applications, a general description of variational algorithms is provided and the mapping from fermions to qubits is explained. Coupled-cluster and heuristic trial wave-functions are considered for efficiently finding molecular ground states. Furthermore, simple error-mitigation schemes are introduced that could improve the accuracy of determining ground-state energies. Advancing these techniques may lead to near-term demonstrations of useful quantum computation with systems containing several hundred qubits.

quant-ph↗

arXiv2017

Tapering off qubits to simulate fermionic Hamiltonians

We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum simulations with fewer qubits. First we consider $U(1)$ symmetry describing the particle number conservation. Using a previously known encoding based on the first quantization method a system of $M$ fermi modes with $N$ particles can be simulated on a quantum computer with $Q=N\log{(M)}$ qubits. We propose a new version of this encoding tailored to variational quantum algorithms. Also we show how to improve sparsity of the simulator Hamiltonian using orthogonal arrays. Next we consider encodings based on the second quantization method. It is shown that encodings with a given filling fraction $ν=N/M$ and a qubit-per-mode ratio $η=Q/M<1$ can be constructed from efficiently decodable classical LDPC codes with the relative distance $2ν$ and the encoding rate $1-η$. A family of codes based on high-girth bipartite graphs is discussed. Graph-based encodings eliminate roughly $M/N$ qubits. Finally we consider discrete symmetries, and show how to eliminate qubits using previously known encodings, illustrating the technique for simple molecular-type Hamiltonians.

quant-ph↗

arXiv2016

A universal gate for fixed-frequency qubits via a tunable bus

A challenge for constructing large circuits of superconducting qubits is to balance addressability, coherence and coupling strength. High coherence can be attained by building circuits from fixed-frequency qubits, however, leading techniques cannot couple qubits that are far detuned. Here we introduce a method based on a tunable bus which allows for the coupling of two fixed-frequency qubits even at large detunings. By parametrically oscillating the bus at the qubit-qubit detuning we enable a resonant exchange (XX+YY) interaction. We use this interaction to implement a 183ns two-qubit iSWAP gate between qubits separated in frequency by 854MHz with a measured average fidelity of 0.9823(4) from interleaved randomized benchmarking. This gate may be an enabling technology for surface code circuits and for analog quantum simulation.

quant-ph↗