相关论文: Fermionic Hamiltonians without trivial low-energy …
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then…
Product states, unentangled tensor products of single qubits, are a ubiquitous ansatz in quantum computation, including for state-of-the-art Hamiltonian approximation algorithms. A natural question is whether we should expect to efficiently…
All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…
We study the computational complexity of the Guided Local Hamiltonian problem: given a local Hamiltonian $H$ together with a classical description of a guiding state that has non-negligible overlap with the ground state of $H$, estimate the…
A defining quantity of a physical system is its energy which is represented by the Hamiltonian. In closed quantum mechanical or/and coherent wave-based systems the Hamiltonian is introduced as a Hermitian operator which ensures real energy…
We present a cooling algorithm for ground state preparation of fermionic Hamiltonians. Our algorithm makes use of the Hamiltonian simulation of the considered system coupled to an ancillary fridge, which is regularly reset to its known…
A construction of the Coulomb-Breit Hamiltonian for a pair of fermions, considered as a quantum two-body system, immersed in an arbitrary background gravitational field described by Einstein's General Relativity is presented. Working with…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local…
A self-contained treatment of the Bogoliubov-Valatin transformation for homogeneous fermionic Hamiltonians is presented. The aim is to provide a quick reference that may also serve as supplementary material for a graduate-level course, and…
Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
Efficient simulation of interacting fermionic systems is a key application of near-term quantum computers, but is hindered by the overhead required to encode fermionic operators on qubit hardware. Here, we consider models with $N$ fermionic…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
Learning the Hamiltonian underlying a quantum many-body system in thermal equilibrium is a fundamental task in quantum learning theory and experimental sciences. To learn the Gibbs state of local Hamiltonians at any inverse temperature…
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalised set of few-body coherent states. In particular, model Hamiltonians of the FQH effect are equivalent to the…
We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…