Session P4: Quantum Gates

Modular Entanglement of Trapped Ion Qubits Using both Phonons and Photons

Trapped atomic ions are standard qubits for the production of entangled states for applications in quantum information science, with their long coherence times and local Coulomb interactions that can be gated by external fields. However, scaling this system to large dimensions may require the addition of other interfaces such as photonic quantum information transfer. We report the experimental realization of gates combining remote and local entanglement protocols between three ions in two separate traps. Using a two-photon interference protocol with fast imaging optics, we demonstrate 4.25 Hz entangling rates between distant trapped ion qubits. Importantly, the remote and local ion entanglement generation rate is much faster than the observed entangled state decoherence rate, which is key to scaling to larger quantum networks.   

Scalable entanglement in trapped ions using optimal control of multimode couplings

We perform high fidelity multipartite entanglement of ion subsets in a chain of five Yb+ qubits using optimal pulse shaping [1]. A focused mode-locked laser beam individually addresses qubits to couple them to multiple collective transverse modes of motion to perform entangling phase gates on pairs of adjacent qubits. Pulse shaping by modulating the amplitude and phase of the laser can drive high fidelity gates for certain pulse solutions that are relatively insensitive to detuning errors. We create entangled states in the GHZ class and witness genuine tripartite entanglement using individual state detection. This method of engineering the evolution of multiple modes scales well for large qubit registers by keeping gate times short.\\[4pt] [1] T. Choi et al., arXiv:1401.1575 (2014).   

Dressed-state qubits and magnetic field gradients for multi-ion quantum gates

Strong magnetic field gradients enable multiple-qubit gates between ions without decoherence due to off-resonant excitation by laser light, however the need for qubit states to be sensitive to magnetic field gradients leads to decoherence from fluctuating magnetic fields. We demonstrate the use of dressing microwave fields to decouple an ionic qubit from magnetic field noise, significantly increasing its coherence time, and perform single-qubit gates using radiofrequency fields [1]. By integrating permanent magnets within our ion trap we generate a field gradient of 24 Tm$^{-1}$ and use this gradient to entangle a single trapped ion's internal and motional states and generate Schroedinger cat states. We also report the first realisation of driving motional sideband transitions with microwave dressed states, and demonstrate near perfect individual addressing of ions. We will also present our work creating microfabricated ion trap architectures for quantum simulation and quantum computation. \\[4pt] [1] S. C. Webster et al., Phys. Rev. Lett 111, 140501 (2013)   

Experimental realization of phonon shift operation in a trapped ion system

We report an experimental realization of phonon shift operation in a trapped ion system. The shift operation is a pure addition or subtraction without the modification of a state amplitude by $\sqrt{n}$, which transfer the state from $|n>$ to $|n+1>$ or from $|n> to |n-1>$ for any n. We implement the pure addition by applying $\pi$ pulse of a blue-sideband transition $|\downarrow,n> -> |\uparrow,n+1>$ followed by a $\pi$ pulse of resonant carrier transition of spin $|\uparrow,n+1> -> |\downarrow, n+1>$. For subtraction we exchange the order. The essence is in an adiabatic blue-sideband $\pi$ operation with high-fidelity and speed regardless of phonon number n (0 to 10) through the same operation in Ref. [1]. Although the pure shift operations are different from creation $\hat{a}^{\dagger}$ and annihilation $\hat{a}$, it produces a non-classical state of phonon [2]. We observe a negative probability in the Wigner function of a phonon state after the pure shift operation on various phonon states. The scheme can be used for the projective measurement of phonon number states and the test of boson sampling problem [3].\\[4pt] [1] Junhua, et al., PRA 89, 013608 (2014).\\[0pt] [2] Daniel K, et al., PRL 110, 210504 (2013).\\[0pt] [3] Shen, et al., arxiv:1310.4860   

Experimental recovery of a partially-collapsed qubit

We implemented and tested a process for recovering quantum information following a weak measurement whereby a qubit may spontaneously decay outside the computational basis. Alike in spirit and form to a classical spin echo, the recovery protocol and expected fidelity is, in principle, perfect and independent of the initial qubit state. To demonstrate the partial decay and recovery process, we engineered a novel qubit from the Zeeman spin-states of a single trapped $^{40}\!$Ca$^+$ ion's excited $3D_{5/2}$ electronic state. Tuning the strength of a near-resonant laser pulse allows us to realize a variable qubit decay rate. Even with a spontaneous decay probability of 0.8, we demonstrated recovery of the qubit's state vector with a fidelity of $F = 0.986$, a better result than is achievable merely by post-selection of results from un-decayed qubits.   

Single qubit gate fidelity for neutral atom qubits in a 3D optical lattice

We report on a quantum computing experiment using individual Cs atoms in a 5 $\mu$m-spaced 3D optical lattice. Single atoms in the 3D array are selected using two perpendicular far-off-resonance addressing beams. The AC Stark shift from these addressing beams shifts only the target atom into a microwave resonance, so that only the target atom participates in the gate. We will describe the gate operation, and present measurements of gate fidelity and cross talk. The measured coherence time of these qubits is 5.3 s.   

Towards a cavity electromagnetically induced transparency based quantum gate

The processing of quantum information with photons and atoms has been established as one of the strongest candidates for future quantum technologies. Photons (quantum channels) are capable of encoding quantum information and traveling long distances without decohering, whereas atoms (quantum nodes) readily interact with light and therefore provide a natural platform for mediating interactions and storing it. The development of a node in which deterministic two-qubit gates can be realized still remains an elusive goal for the quantum optics community. The success of a photonic, two-qubit gate is contingent on a photon-photon interaction generating a sufficient relative phase between the fields. This can be achieved by utilizing a combination of cavity quantum-electrodynamics and electromagnetically-induced transparency. In our newly implemented experiment based on a magneto-optical trap coupled to two optical cavities, we aim to realize strong interactions between weak quantum optical fields. We report on the current status of the experiment and discuss possible implementations of photonic quantum gates.   

Shift and swap: A method for generating Bell inequalities

A Bell inequality is a condition on measurement results, obtained in spacelike separated regions, that is obeyed by systems whose measurement probabilities all come from a single joint distribution (this is equivalent to saying that the probabilities are the result of a local, hidden-variable theory). The most well-known are the CHSH and CH inequalities in which there are 2 parties each making two possible measurements, and each measurement having two possible outcomes. We present a method based on shift and swap operators that can generate Bell inequalities. It does so by assigning high probabilities to a certain set of events, and this results in correlations that are stronger than can be obtained classically. We will present examples for several different scenarios, where a scenario is specified by the number of parties, the number of possible measurements for each party, and the number of outcomes for each measurement. We will also show how some of these scenarios can be described in terms of nonlocal games.