9 research outputs found
Probing finite-temperature observables in quantum simulators with short-time dynamics
Preparing low temperature states in quantum simulators is challenging due to
their almost perfect isolation from the environment. Here, we show how
finite-temperature observables can be obtained with an algorithm that consists
of classical importance sampling of initial states and a measurement of the
Loschmidt echo with a quantum simulator. We use the method as a
quantum-inspired classical algorithm and simulate the protocol with matrix
product states to analyze the requirements on a quantum simulator. This way, we
show that a finite temperature phase transition in the long-range transverse
field Ising model can be characterized in trapped ion quantum simulators. We
propose a concrete measurement protocol for the Loschmidt echo and discuss the
influence of measurement noise, dephasing, as well as state preparation and
measurement errors. We argue that the algorithm is robust against those
imperfections under realistic conditions. The algorithm can be readily applied
to study low-temperature properties in various quantum simulation platforms.Comment: 4+3 pages, 4+1 figure
Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers
Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves non-unitary operators that render an implementation on a near-term quantum computer extremely challenging. Recently, Lu, Bañuls and Cirac \cite{Lu2021} suggested a "time-series quantum Monte Carlo method" which circumvents this problem by extracting finite temperature properties from real-time simulations via Wick's rotation and Monte Carlo sampling of easily preparable states. In this paper, we address the challenges associated with the practical applications of this method, using the two-dimensional transverse field Ising model as a testbed. We demonstrate that estimating Boltzmann weights via Wick's rotation is very sensitive to time-domain truncation and statistical shot noise. To alleviate this problem, we introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. In addition, we show how to reduce the statistical errors of Monte Carlo sampling via a reweighted version of the Wolff cluster algorithm. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems
Observation of a finite-energy phase transition in a one-dimensional quantum simulator
One of the most striking many-body phenomena in nature is the sudden change
of macroscopic properties as the temperature or energy reaches a critical
value. Such equilibrium transitions have been predicted and observed in two and
three spatial dimensions, but have long been thought not to exist in
one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out
that a phase transition in 1D can occur in the presence of long-range
interactions, but an experimental realization has so far not been achieved due
to the requirement to both prepare equilibrium states and realize sufficiently
long-range interactions. Here we report on the first experimental demonstration
of a finite-energy phase transition in 1D. We use the simple observation that
finite-energy states can be prepared by time-evolving product initial states
and letting them thermalize under the dynamics of a many-body Hamiltonian. By
preparing initial states with different energies in a 1D trapped-ion quantum
simulator, we study the finite-energy phase diagram of a long-range interacting
quantum system. We observe a ferromagnetic equilibrium phase transition as well
as a crossover from a low-energy polarized paramagnet to a high-energy
unpolarized paramagnet in a system of up to spins, in excellent agreement
with numerical simulations. Our work demonstrates the ability of quantum
simulators to realize and study previously inaccessible phases at finite energy
density.Comment: 5+9 pages, 4+14 figure
Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
Calculating the equilibrium properties of condensed matter systems is one of
the promising applications of near-term quantum computing. Recently, hybrid
quantum-classical time-series algorithms have been proposed to efficiently
extract these properties from a measurement of the Loschmidt amplitude from initial states and a
time evolution under the Hamiltonian up to short times . In this
work, we study the operation of this algorithm on a present-day quantum
computer. Specifically, we measure the Loschmidt amplitude for the
Fermi-Hubbard model on a -site ladder geometry (32 orbitals) on the
Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the
Loschmidt amplitude and implement algorithm-specific error mitigation
techniques. By using a thus-motivated error model, we numerically analyze the
influence of noise on the full operation of the quantum-classical algorithm by
measuring expectation values of local observables at finite energies. Finally,
we estimate the resources needed for scaling up the algorithm.Comment: 18 pages, 12 figure
Optically controlled entangling gates in randomly doped silicon
Donor qubits in bulk doped silicon have many competitive advantages for quantum computation in the solid state: not only do they offer a fast way to scalability, but they also show some of the longest coherence times found in any quantum computation proposal. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations of the dopants necessary for them to form exchange interaction-mediated entangling gates. Second, using nearest neighbor Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. Third, using the moving-average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of the far-from-equilibrium magnetization dynamics of one species by the orbital excitation of another. We find agreement of our results with a Monte Carlo simulation that handles multiple donor structures and scales optimally with the number of dopants. The simulator can also extract donor structures not captured by our Poisson point process theory. The combined approaches to density optimization in random distributions presented here may be useful for other condensed matter systems as well as applications outside physics