Related papers: Classical simulation of non-Gaussian fermionic cir…

We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive…

Fermionic Gaussian unitaries are known to be efficiently learnable and simulatable. In this paper, we present a learning algorithm that learns an $n$-mode circuit containing $t$ parity-preserving non-Gaussian gates. While circuits with $t =…

Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…

Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear…

This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…

We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We…

While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of…

Classically hard to simulate quantum states, or "magic states", are prerequisites to quantum advantage, highlighting an apparent separation between classically and quantumly tractable problems. Classically simulable states such as Clifford…

Quantum generative learning is a promising application of quantum computers, but faces several trainability challenges, including the difficulty in experimental gradient estimations. For certain structured quantum generative models,…

Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems,…

Establishing the precise computational boundary between classically tractable fermionic systems and those capable of genuine quantum advantage is a central challenge in quantum simulation. While injecting non-Gaussian ``magic" inputs into…

Bosonic qubits are a promising route to building fault-tolerant quantum computers on a variety of physical platforms. Studying the performance of bosonic qubits under realistic gates and measurements is challenging with existing analytical…

To understand quantum optics experiments, we must perform calculations that consider the principal sources of noise, such as losses, spectral impurity and partial distinguishability. In both discrete and continuous variable systems, these…

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus…

Detecting when a quantum state leaves the efficiently simulable fermionic Gaussian regime is a central task for benchmarking quantum devices and certifying fermionic magic resources. We develop practical tests and witnesses based on…

A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…

As is well-known in the context of topological insulators and superconductors, short-range-correlated fermionic pure Gaussian states with fundamental symmetries are systematically classified by the periodic table. We revisit this topic from…

The coherent superposition of non-orthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We present a…

The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…