Related papers: Sparse random Hamiltonians are quantumly easy
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…
Characterizing quantum systems by learning their underlying Hamiltonians is a central task in quantum information science. While recent algorithmic advances have achieved near-optimal efficiency in this task, they critically rely on…
We present several refinements and extensions of the statistical quantum phase estimation (SQPE) framework to address some of its key practical limitations, improving its applicability to realistic cases. Recently, a family of statistical…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth…
We propose new quantum algorithms for thermal and ground state preparation based on system-bath interactions. These algorithms require only forward evolution under a system-bath Hamiltonian in which the bath is a single reusable ancilla…
Preparing the thermal density matrix $\rho_{\beta} \propto e^{-\beta H}$ corresponding to a given Hamiltonian $H$ is a task of central interest across quantum many-body physics, and is particularly salient when attempting to study it with…
The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
Preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. Despite the hope for practical quantum advantage in quantum simulation, popular state preparation approaches have been challenged.…
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…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
Simulating the nonequilibrium dynamics of thermal states is a fundamental problem across scales from high energy to condensed matter physics. Quantum computers may provide a way to solve this problem efficiently. Preparing a thermal state…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
A pseudorandom quantum state (PRS) is an ensemble of quantum states indistinguishable from Haar-random states to observers with efficient quantum computers. It allows one to substitute the costly Haar-random state with efficiently…