Variational quantum algorithm for nonequilibrium steady states

@article{Yoshioka2019VariationalQA,
  title={Variational quantum algorithm for nonequilibrium steady states},
  author={Nobuyuki Yoshioka and Yuya O Nakagawa and Kosuke Mitarai and Keisuke Fujii},
  journal={arXiv: Quantum Physics},
  year={2019}
}
We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization technique for a unitary quantum circuit, we map a mixed state into a pure state with a doubled number of qubits and design the unitary quantum circuit to fulfill the requirements for a density matrix. This allows us to define a cost function that consists of… Expand

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References

SHOWING 1-10 OF 126 REFERENCES
Variational Quantum Simulation of General Processes.
TLDR
The algorithm for generalized time evolution provides a unified framework for variational quantum simulation and shows its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalizedTime evolution. Expand
Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems.
TLDR
A variational method to efficiently simulate the nonequilibrium steady state of Markovian open quantum systems based on variational Monte Carlo methods and on a neural network representation of the density matrix is developed. Expand
Constructing neural stationary states for open quantum many-body systems
TLDR
A new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems, which is dubbed as the neural stationary state ansatz, and shown to simulate various spin systems efficiently. Expand
A quantum algorithm for evolving open quantum dynamics on quantum computing devices
TLDR
This work proposes and demonstrates a general quantum algorithm to evolve open quantum dynamics on quantum computing devices that does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models. Expand
Variational principle for steady states of dissipative quantum many-body systems.
  • H. Weimer
  • Physics, Medicine
  • Physical review letters
  • 2015
We present a novel generic framework to approximate the nonequilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of theExpand
Dissipative quantum Church-Turing theorem.
We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in theExpand
Theory of variational quantum simulation
TLDR
This work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware. Expand
Scalable Quantum Simulation of Molecular Energies
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute theExpand
Variational Neural-Network Ansatz for Steady States in Open Quantum Systems.
TLDR
A general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach is presented and applied to the dissipative quantum transverse Ising model. Expand
A variational eigenvalue solver on a photonic quantum processor
TLDR
The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future. Expand
...
1
2
3
4
5
...