There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking an ...

Quantum machine learning

Physical Review B

Journal of Statistical Mechanics: theory and experiment

The Quantum Fisher Information (QFI) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFI matrix for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFI at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

We propose a variational quantum algorithm to study the real time dynamics of quantum systems as a ground-state problem. The method is based on the original proposal of Feynman and Kitaev to encode time into a register of auxiliary qubits. We prepare the Feynman-Kitaev Hamiltonian acting on the composed system as a qubit operator and find an approximate ground state using the Variational Quantum Eigensolver. We apply the algorithm to the study of the dynamics of a transverse field Ising chain with an increasing number of spins and time steps, proving a favorable scaling in terms of the number of two qubit gates. Through numerical experiments, we investigate its robustness against noise, showing that the method can be use to evaluate dynamical properties of quantum systems and detect the presence of dynamical quantum phase transitions by measuring Loschmidt echoes.

Variational dynamics as a ground-state problem on a quantum computer

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 ans¨atze that forge entanglement to lower quantum resource overhead. The variational ans¨atze 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.

Entanglement Forging with generative neural network models

A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating quantum systems is an important component of addressing this question. We introduce a method to simulate layered quantum circuits consisting of parametrized gates, an architecture behind many variational quantum algorithms suitable for near-term quantum computers. A neural-network parametrization of the many-qubit wave function is used, focusing on states relevant for the Quantum Approximate Optimization Algorithm (QAOA). For the largest circuits simulated, we reach 54 qubits at 4 QAOA layers, approximately implementing 324 RZZ gates and 216 RX gates without requiring large-scale computational resources. For larger systems, our approach can be used to provide accurate QAOA simulations at previously unexplored parameter values and to benchmark the next generation of experiments in the Noisy Intermediate-Scale Quantum (NISQ) era.

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Classical variational simulation of the Quantum Approximate Optimization Algorithm

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the t-V model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.

Giuseppe Carleo

Papers

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Variational dynamics as a ground-state problem on a quantum computer

Entanglement Forging with generative neural network models

Classical variational simulation of the Quantum Approximate Optimization Algorithm

Variational solutions to fermion-to-qubit mappings in two spatial dimensions