Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userVariational preparation of finite-temperature states on a quantum computer
114
0
0.0
(
0
)
Added by
Ramiro Sagastizabal
Publication date
2020
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The preparation of thermal equilibrium states is important for the simulation of condensed-matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators, and demonstrate this technique experimentally using a gate-based quantum processor. Our method targets the generation of thermofield double states using a hybrid quantum-classical variational approach motivated by quantum-approximate optimization algorithms, without prior calculation of optimal variational parameters by numerical simulation. The fidelity of generated states to the thermal-equilibrium state smoothly varies from 99 to 75% between infinite and near-zero simulated temperature, in quantitative agreement with numerical simulations of the noisy quantum processor with error parameters drawn from experiment.
rate research
Read More
We study two different methods to prepare excited states on a quantum computer, a key initial step to study dynamics within linear response theory. The first method uses unitary evolution for a short time $T=mathcal{O}(sqrt{1-F})$ to approximate the action of an excitation operator $hat{O}$ with fidelity $F$ and success probability $Papprox1-F$. The second method probabilistically applies the excitation operator using the Linear Combination of Unitaries (LCU) algorithm. We benchmark these techniques on emulated and real quantum devices, using a toy model for thermal neutron-proton capture. Despite its larger memory footprint, the LCU-based method is efficient even on current generation noisy devices and can be implemented at a lower gate cost than a naive analysis would suggest. These findings show that quantum techniques designed to achieve good asymptotic scaling on fault tolerant quantum devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
Preparing quantum thermal states on a quantum computer is in general a difficult task. We provide a procedure to prepare a thermal state on a quantum computer with a logarithmic depth circuit of local quantum channels assuming that the thermal state correlations satisfy the following two properties: (i) the correlations between two regions are exponentially decaying in the distance between the regions, and (ii) the thermal state is an approximate Markov state for shielded regions. We require both properties to hold for the thermal state of the Hamiltonian on any induced subgraph of the original lattice. Assumption (ii) is satisfied for all commuting Gibbs states, while assumption (i) is satisfied for every model above a critical temperature. Both assumptions are satisfied in one spatial dimension. Moreover, both assumptions are expected to hold above the thermal phase transition for models without any topological order at finite temperature. As a building block, we show that exponential decay of correlation (for thermal states of Hamiltonians on all induced subgraph) is sufficient to efficiently estimate the expectation value of a local observable. Our proof uses quantum belief propagation, a recent strengthening of strong sub-additivity, and naturally breaks down for states with topological order.
It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation. In this work, we ask whether it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension whose finite-time evolution is a unitary that acts trivially in the bulk, but pumps the desired cluster state to the boundary. Examples are given for both the 1D cluster state protected by a global symmetry, and various 2D cluster states protected by subsystem symmetries. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with post-selection is sufficient to recover a cluster-like state. For a resource state of size $N$, failure to prepare the state is negligible if the size of the perturbations are much smaller than $N^{-1/2}$.
One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here, we propose variational quantum anomaly detection, an unsupervised quantum machine learning algorithm to analyze quantum data from quantum simulation. The algorithm is used to extract the phase diagram of a system with no prior physical knowledge and can be performed end-to-end on the same quantum device that the system is simulated on. We showcase its capabilities by mapping out the phase diagram of the one-dimensional extended Bose Hubbard model with dimerized hoppings, which exhibits a symmetry protected topological phase. Further, we show that it can be used with readily accessible devices nowadays and perform the algorithm on a real quantum computer.
Recent advances in qubit fidelity and hardware availability have driven efforts to simulate molecular systems of increasing complexity in a quantum computer and motivated us to to design quantum algorithms for solving the electronic structure of periodic crystalline solids. To this effect, we present a hybrid quantum-classical algorithm based on Variational Quantum Deflation [Higgott et al., Quantum, 2019, 3, 156] and Quantum Phase Estimation [Dobv{s}iv{c}ek et al., Phys. Rev. A, 2007, 76, 030306(R)] to solve the band structure of any periodic system described by an adequate tight-binding model. We showcase our algorithm by computing the band structure of a simple-cubic crystal with one $s$ and three $p$ orbitals per site (a simple model for Polonium) using simulators with increasingly realistic levels of noise and culminating with calculations on IBM quantum computers. Our results show that the algorithm is reliable in a low-noise device, functional with low precision on present-day noisy quantum computers, and displays a complexity that scales as $Omega(M^3)$ with the number $M$ of tight-binding orbitals per unit-cell, similarly to its classical counterparts. Our simulations offer a new insight into the quantum mindset applied to solid state systems and suggest avenues to explore the potential of quantum computing in materials science.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
