Related papers: Optimizing Strongly Interacting Fermionic Hamilton…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic…
The problem of testing low-degree polynomials has received significant attention over the years due to its importance in theoretical computer science, and in particular in complexity theory. The problem is specified by three parameters:…
Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are…
The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…
We introduce $k$-local quasi-quantum states: a superset of the regular quantum states, defined by relaxing the positivity constraint. We show that a $k$-local quasi-quantum state on $n$ qubits can be 1-1 mapped to a distribution of…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Identifying unknown Hamiltonians from their quantum dynamics is a pivotal challenge in quantum technologies. In this paper, we introduce Hamiltonian recognition, a framework that bridges quantum hypothesis testing and quantum metrology,…
We study the 2D fermionic SYK model with Majorana fermions, featuring a quartic kinetic term and a $2q$-body interaction with Gaussian disorder. By minimizing the effective action or solving the SD equation for $q=1$, we determine that the…
Fermionic Gaussian states (FGSs) and the associated matchgate circuits play a central role in quantum information theory and condensed matter physics. Despite being possibly highly entangled, they can still be efficiently simulated on…
Large-scale optimization problems are prevalent in several fields, including engineering, finance, and logistics. However, most optimization problems cannot be efficiently encoded onto a physical system because the existing quantum samplers…
We present an exact ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schr\"odinger equation (CSE), our approach guides a…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
We study the preparation of thermal states of the dense and sparse Sachdev-Ye-Kitaev (SYK) model using a variational quantum algorithm for $6 \le N \le 12$ Majorana fermions over a wide range of temperatures. Utilizing IBM's 127-qubit…
The Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm intending to find the ground state of a target Hamiltonian. Theoretically, QAOA can obtain the approximate solution if the quantum circuit is deep…
The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation. [S. Bravyi and D. Gosset, Comm. Math. Phys. 356, 451 (2017)]. It is…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…
We argue the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte-Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from Quantum Chromodynamics…
Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum…