scholarly journals Efficient variational simulation of non-trivial quantum states

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Wen Wei Ho ◽  
Timothy H. Hsieh
Keyword(s):  
Transverse Field ◽  
System Size ◽  
Quantum States ◽  
Quantum Simulator ◽  
Near Term ◽  
The One ◽  
Transverse Field Ising Model ◽  
Classical Computer ◽  
Model Phase ◽  
Ordered State

We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with \bm{L}𝐋 variational parameters and physical runtimes \bm{T}𝐓 that scale linearly with the system size \bm{L}𝐋. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational Ansätze as good descriptions of non-trivial states of matter.

scholarly journals All macroscopic quantum states are fragile and hard to prepare

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 118
Author(s):  
Andrea López-Incera ◽  
Pavel Sekatski ◽  
Wolfgang Dür
Keyword(s):  
Quantum State ◽  
Quantum Fisher Information ◽  
System Size ◽  
Quantum States ◽  
Initial State ◽  
Macroscopic Quantum ◽  
Effective System ◽  
Local Observables ◽  
The One ◽  
Arbitrary Quantum

We study the effect of local decoherence on arbitrary quantum states. Adapting techniques developed in quantum metrology, we show that the action of generic local noise processes --though arbitrarily small-- always yields a state whose Quantum Fisher Information (QFI) with respect to local observables is linear in system size N, independent of the initial state. This implies that all macroscopic quantum states, which are characterized by a QFI that is quadratic in N, are fragile under decoherence, and cannot be maintained if the system is not perfectly isolated. We also provide analytical bounds on the effective system size, and show that the effective system size scales as the inverse of the noise parameter p for small p for all the noise channels considered, making it increasingly difficult to generate macroscopic or even mesoscopic quantum states. In turn, we also show that the preparation of a macroscopic quantum state, with respect to a conserved quantity, requires a device whose QFI is already at least as large as the one of the desired state. Given that the preparation device itself is classical and not a perfectly isolated macroscopic quantum state, the preparation device needs to be quadratically bigger than the macroscopic target state.

scholarly journals Practical verification protocols for analog quantum simulators

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ryan Shaffer ◽  
Eli Megidish ◽  
Joseph Broz ◽  
Wei-Ting Chen ◽  
Hartmut Häffner
Keyword(s):  
System Size ◽  
Quantum Simulation ◽  
Quantum Devices ◽  
Error Sources ◽  
Trapped Ion ◽  
Quantum Simulators ◽  
Simulation Results ◽  
Quantum Simulator ◽  
Near Term ◽  
Significant Application

AbstractAnalog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits.

scholarly journals Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

2020 ◽  
Vol 9 (3) ◽  
Author(s):  
Etienne Granet ◽  
Maurizio Fagotti ◽  
Fabian Essler
Keyword(s):  
Form Factor ◽  
Form Factors ◽  
Transverse Field ◽  
Natural Generalization ◽  
Point Function ◽  
Quench Dynamics ◽  
Density Expansions ◽  
The One ◽  
Transverse Field Ising Model ◽  
Partial Fractions

We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

scholarly journals FIDELITY APPROACH TO QUANTUM PHASE TRANSITIONS

2010 ◽  
Vol 24 (23) ◽  
pp. 4371-4458 ◽  
Author(s):  
SHI-JIAN GU
Keyword(s):  
Phase Transitions ◽  
Thermal State ◽  
Quantum Phase Transitions ◽  
Transverse Field ◽  
Quantum Phase ◽  
Leading Term ◽  
Many Body Systems ◽  
The One ◽  
Definition Of ◽  
Transverse Field Ising Model

We review the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin–Meshkov–Glick model, are introduced at the graduate-student level. Besides, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.

scholarly journals A SPIN CHAIN WITH SPIRAL ORDERS: PERSPECTIVES OF QUANTUM INFORMATION AND MECHANICAL RESPONSE

2013 ◽  
Vol 27 (21) ◽  
pp. 1350106 ◽  
Author(s):  
SHI-JIAN GU ◽  
WING-CHI YU ◽  
HAI-QING LIN
Keyword(s):  
Quantum Information ◽  
Critical Point ◽  
Ground State ◽  
Information Science ◽  
Mechanical Response ◽  
Solvable Model ◽  
Transverse Field ◽  
One Dimensional ◽  
The One ◽  
Transverse Field Ising Model

In this paper, we study the ground state of a one-dimensional exactly solvable model with a spiral order. While the model's energy spectrum is the same as the one-dimensional transverse field Ising model, its ground state manifests a spiral order with various periods. The quantum phase transition from a spiral-order phase to a paramagnetic phase is investigated in the perspectives of quantum information science and mechanics. We show that the modes of the ground-state fidelity and its susceptibility can identify the change of periodicity around the critical point. We also study the spin torsion modulus which defines the coefficient of the potential energy stored under a small rotation. We find that at the critical point, it is a constant; while away from the critical point, the spin torsion modulus tends to zero.

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