Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows information processing tasks to be performed with interactive access to a wide variety of topological features. Topological considerations are used to suppress errors, with polarization allowing easy measurement and manipulation of qubits. We provide three examples of this approach: production of two-photon systems with entangled winding number (including topological analogs of Bell states), a topologically error-protected optical memory register, and production of entangled topologically-protected boundary states. In particular it is shown that a pair of quantum memory registers, entangled in polarization and winding number, with topologically-assisted error suppression can be made with qubits stored in superpositions of winding numbers; as a result, information processing with winding number-based qubits is a viable possibility.Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows information processing tasks to be performed with interactive access to a wide variety of topological features. Topological considerations are used to suppress errors, with polarization allowing easy measurement and manipulation of qubits. We provide three examples of this approach: production of two-photon systems with entangled winding number (including topological analogs of Bell states), a topologically error-protected optical memory register, and production of entangled topologically-protected boundary states. In particular it is shown that a pair of quantum memory registers, entangled in polarization and winding number, with topologically-assisted error suppression can be made with qubits stored in superpositions of winding numbers; as a result, information processing with winding number-based qubits is a viable possibility.

arXiv:1810.02011New Journal of PhysicsSep 14, 201814 citations

The Road to and from Quantum Entanglement Experiments

Časlav Brukner

Europhysics newsJan 1, 20230 citations

Space-efficient Quantization Method for Reversible Markov Chains

Chen-Fu Chiang, Anirban Ch Narayan Chowdhury, Paweł Wocjan

In a seminal paper, Szegedy showed how to construct a quantum walk $W(P)$ for any reversible Markov chain $P$ such that its eigenvector with eigenphase $0$ is a quantum sample of the limiting distribution of the random walk and its eigenphase gap is quadratically larger than the spectral gap of $P$ . The standard construction of Szegedy's quantum walk requires an ancilla register of Hilbert-space dimension equal to the size of the state space of the Markov chain. We show that it is possible to avoid this doubling of state space for certain Markov chains that employ a symmetric proposal probability and a subsequent accept/reject probability to sample from the Gibbs distribution. For such Markov chains, we give a quantization method which requires an ancilla register of dimension equal to only the number of different energy values, which is often significantly smaller than the size of the state space. To accomplish this, we develop a technique for block encoding Hadamard products of matrices which may be of wider interest.In a seminal paper, Szegedy showed how to construct a quantum walk $W(P)$ for any reversible Markov chain $P$ such that its eigenvector with eigenphase $0$ is a quantum sample of the limiting distribution of the random walk and its eigenphase gap is quadratically larger than the spectral gap of $P$. The standard construction of Szegedy's quantum walk requires an ancilla register of Hilbert-space dimension equal to the size of the state space of the Markov chain. We show that it is possible to avoid this doubling of state space for certain Markov chains that employ a symmetric proposal probability and a subsequent accept/reject probability to sample from the Gibbs distribution. For such Markov chains, we give a quantization method which requires an ancilla register of dimension equal to only the number of different energy values, which is often significantly smaller than the size of the state space. To accomplish this, we develop a technique for block encoding Hadamard products of matrices which may be of wider interest.

arXiv:2206.06886Jun 14, 20220 citations

Quantum entanglement and quantum computing

F. J. Duarte

Institute of Physics eBooksSep 1, 20220 citations

Entanglement swapping via three-step quantum walk-like protocol

Xiaoman Li, Ming Yang, Nikola Paunković +2 more

arXiv:1710.09981Physics Letters AOct 18, 20179 citations

Phonon Random Walks: Using Classical Chains to Simulate Quantum Dynamics

Daxing Xiong, Eli Barkai

Inspired by quantum walks (QW), we propose the concept of classical phonon random walks (PRW). With this we show a correspondence between classical and quantum dynamics. To be specific, we explain how a classical chain of particles with linear interactions can be used to simulate a quantum like wave function $\psi_{m}(t)$ . In particular, the real (imaginary) part of $\psi_{m}(t)$ is the normalized classical momentum (a new $\pi/2$ shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared $\left|\psi_{m}(t)\right|^{2}$ . We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.Inspired by quantum walks (QW), we propose the concept of classical phonon random walks (PRW). With this we show a correspondence between classical and quantum dynamics. To be specific, we explain how a classical chain of particles with linear interactions can be used to simulate a quantum like wave function $\psi_{m}(t)$. In particular, the real (imaginary) part of $\psi_{m}(t)$ is the normalized classical momentum (a new $\pi/2$ shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared $\left|\psi_{m}(t)\right|^{2}$. We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.

Jun 15, 20160 citations

In a seminal paper, Szegedy showed how to construct a quantum walk

W(P)

for any reversible Markov chain

P

such that its eigenvector with eigenphase

0

is a quantum sample of the limiting distribution of the random walk and its eigenphase gap is quadratically larger than the spectral gap of

P

. The standard construction of Szegedy's quantum walk requires an ancilla register of Hilbert-space dimension equal to the size of the state space of the Markov chain. We show that it is possible to avoid this doubling of state space for certain Markov chains that employ a symmetric proposal probability and a subsequent accept/reject probability to sample from the Gibbs distribution. For such Markov chains, we give a quantization method which requires an ancilla register of dimension equal to only the number of different energy values, which is often significantly smaller than the size of the state space. To accomplish this, we develop a technique for block encoding Hadamard products of matrices which may be of wider interest.

\psi_{m}(t)

. In particular, the real (imaginary) part of

\psi_{m}(t)

is the normalized classical momentum (a new

\pi/2

shifted momentum) correlation function of the thermalized many-body system. Energy and heat densities are directly analogous to wave function's modulus squared

\left|\psi_{m}(t)\right|^{2}

. We also propose a formula predicting the non-universal spreading of these energy packets in terms of the phonon dispersion of the system. Our equilibrium molecular dynamics simulations of several linear chains perfectly verify these relations. The extension of the concept to integrable Toda chain is also discussed.