Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement ``quantum simulators.'' Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. The fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement ``quantum simulators.'' Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. The fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.

arXiv:1411.5097Physical Review AJun 2, 20164 citations

Collective treatment of the pairing Hamiltonian

Daniel R. Bes, R.A. Broglia, R.P.J. Perazzo +1 more

Nuclear Physics AMar 1, 197075 citations

Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian Using Nuclear Magnetic Resonance

Kenneth R. Brown, Robert Clark, Isaac L. Chuang

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).10.1103/PhysRevLett.89.057904] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound E. Making such simulations robust to decoherence using fault tolerance requires an additional factor of approximately 1/E gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system.Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).10.1103/PhysRevLett.89.057904] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound E. Making such simulations robust to decoherence using fault tolerance requires an additional factor of approximately 1/E gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system.

arXiv:quant-ph/0601021Physical Review LettersAug 4, 200698 citations

Photonic quantum simulations of coupled PT -symmetric Hamiltonians

Nicola Maraviglia, Patrick Yard, Ross Wakefield +9 more

Parity-time-symmetric ( $\mathcal{PT}$ -symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of $\mathcal{PT}$ -symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of $\mathcal{PT}$ -symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.Parity-time-symmetric ($\mathcal{PT}$-symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of $\mathcal{PT}$-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of $\mathcal{PT}$-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.

arXiv:2202.00358Physical Review ResearchJan 26, 202213 citations

Quantum simulation of pairing models on an NMR quantum computer

An Min Wang, Xiaodong Yang

arXiv:quant-ph/0410007Physics Letters ADec 10, 20058 citations

Parity-time-symmetric (

\mathcal{PT}

-symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of

\mathcal{PT}

-symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of

\mathcal{PT}

-symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.