Related papers: Jordan-Wigner formalism for arbitrary 2-input 2-ou…
Based on a multimode multilevel Jaynes-Cummings model and multiphoton resonance theory, a set of universal two- and three-qubit gates, namely the iSWAP and the Fredkin gates, has been realized where dual-rail qubits are encoded in cavities.…
We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest. The correspondence between fermionic and bosonic operators…
This work proposes numerical tests which determine whether a two-qubit operator has an atypically simple quantum circuit. Specifically, we describe formulae, written in terms of matrix coefficients, characterizing operators implementable…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex…
The infinite series of logarithmic minimal models LM(1,p) is considered in the W-extended picture where they are denoted by WLM(1,p). As in the rational models, the fusion algebra of WLM(1,p) is described by a simple graph fusion algebra.…
The quantum Fourier transform (QFT) is sometimes said to be the source of various exponential quantum speed-ups. In this paper we introduce a class of quantum circuits which cannot outperform classical computers even though the QFT…
Any quantum computational network can be constructed with a sequence of the two-qubit diagonal quantum gates and one-qubit gates in two-state quantum systems. The universal construction of these quantum gates in the quantum systems and of…
Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these…
Seniority is a useful way of organizing Hilbert space for strongly correlated systems. The exact zero-seniority wave function, doubly-occupied configuration interaction (DOCI), provides accurate results (given the right orbitals) for many…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…
Quantum simulation of fermionic systems is a promising application of quantum computers, but in order to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as…
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the…
An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions. We find such mappings using only the frustration graph $G$ of a Hamiltonian $H$, i.e., the network of…
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct…
Widely used in atomic and superconducting qubit systems, the Jaynes-Cummings (JC) Hamiltonian is a simple, yet powerful model for a two-level system interacting with a quantum harmonic oscillator. In this paper, we focus on a system of n…
In this paper, we prove that any two birational projective varieties with finite quotient singularities can be realized as two geometric GIT quotients of a non-singular projective variety by a reductive algebraic group. Then, by applying…
The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of…
Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose…
The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation…