Quantum computation and entangled state generation via long-range off-resonant Raman coupling

A scheme is proposed to implement two-qubit controlled quantum phase gate and SWAP gate and generate two-qubit entangled state via long-range off-resonant Raman coupling between two spatially separated superconducting quantum-interference devices (SQUIDs). In the scheme each SQUID is coupled with a single-mode cavity individually and the two distant cavities are connected by an optical fiber. The two lowest levels of each SQUID are used to represent the two logical states of a qubit while the two intermediate levels of each SQUID are used to facilitate coherent coupling of quantum states of the qubits during the virtual excitation process of photon. The scheme is robust against fiber loss, cavity decay, and the effect of spontaneous decay from the higher levels and it would be an important step toward distributed quantum computation and long-distance entanglement distribution.     

Weak continuous measurements of multiqubits systems

In this review we summarize our recent experiments on the investigation on superconducting qubits. Instead of strong projective measurement used by other groups in their first pioneering experiments we have proposed and realized a weak continuous readout which belongs to the class of quantum non-demolition measurements. Moreover, our scheme enables to measure a superconducting qubit at the so called sweet (or magic) point where a qubit is in a superposition of two classical states and its sensitivity to external noise is minimized. In this scheme, which is widely used nowadays, the superconducting oscillator coupled to superconducting qubit is used as a detector of the qubit’s state. Such system is analogue to a system of a single atom interacting with photons in a cavity, which allows to study quantum electrodynamics in artificial macroscopic systems. Pushing this analogy we demonstrate Sisyphus cooling and amplification caused by energy exchange between an oscillator and a flux qubit. Using the Sisyphus effect we show consistency between the adiabatic weak continuous measurement in the ground state and the spectroscopic measurement. This allows us to characterize the more complicated system of coupled qubits by making use of the same method. We have realized and studied fixed ferromagnetic, antiferromagnetic as well as tunable qubit–qubit coupling. We argue that ground state measurements can be used for characterization of entangled states in coupled flux qubits.     

Fault-tolerant high-capacity quantum key distribution over a collective-noise channel using extended unitary operations

We propose two fault-tolerant high-capacity quantum key distribution schemes, in which an entangled pair over a collective-noise channel consisting of one logical qubit and one physical qubit can carry four bits of key information. The basic idea is to use 2-extended unitary operations from collective noises together with quantum dense coding. The key messages are encoded on logical qubits of two physical qubits with sixteen 2-extended unitary operations based on collective noises. The key can be recovered using Bell-state analysis on the logical qubit and a single-photon measurement on the physical qubit rather than three-qubit GHZ joint measurements. The proposed protocols require a collation table to be shared between Alice and Bob in advance. Consequently, the key messages carried by an entangled state, in our protocol, have doubled at the price of sharing the collation table between Alice and Bob. However, the efficiency of qubits is enhanced because a quantum bit is more expensive to prepare than a classical bit.     

Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field

We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption but no Born or Markov approximation. We write the evolution equations of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. We study two classes of states in detail: Class A is a one parameter family of states which are the superposition of the highest energy and lowest energy states, and Class B states which are the linear combinations of the symmetric and the antisymmetric Bell states. Our results for an initial Bell state are similar to those obtained before for the same model derived under the Born–Markov approximation. However, in the Class A states the behavior is qualitatively different: under the non-Markovian evolution we do not see sudden death of quantum entanglement and subsequent revivals, except when the qubits are sufficiently far apart. We provide explanations for such differences of behavior both between these two classes of states and between the predictions from the Markov and non-Markovian dynamics. We also study the decoherence of this two-qubit system.     

Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits

We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1 state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, that require nanosecond pulses. A generalization to codes with higher ratio of number of logical qubits per physical qubits is presented. Compatible decoherence and noise suppression strategies are also discussed. PACS: 03.67.Lx; 85.25.Hv; 03.67.-a; 89.70.+c     

Bell-state generation on remote superconducting qubits with dark photons

We present a scheme to generate the Bell state deterministically on remote transmon qubits coupled to different 1D superconducting resonators connected by a long superconducting transmission line. Using the coherent evolution of the entire system in the all-resonance regime, the transmission line need not to be populated with microwave photons which can robust against the long transmission line loss. This lets the scheme more applicable to the distributed quantum computing on superconducting quantum circuit. Besides, the influence from the small anharmonicity of the energy levels of the transmon qubits can be ignored safely.     

A Characterization of Global Entanglement

We define a set of 2 ⁿ⁻¹−1 entanglement monotones for n qubits and give a single measure of entanglement in terms of these. This measure is zero except on globally entangled (fully inseparable) states. This measure is compared to the Meyer–Wallach measure for two, three, and four qubits. We determine the four-qubit state, symmetric under exchange of qubit labels, which maximizes this measure. It is also shown how the elementary monotones may be computed as a function of observable quantities. We compute the magnitude of our measure for the ground state of the four-qubit superconducting experimental system investigated in [M. Grajcar et al., Phys. Rev. Lett. 96, 047006 (2006)], and thus confirm the presence of global entanglement in the ground state.      

Bell state entanglement swappings over collective noises and their applications on quantum cryptography

This work presents two robust entanglement swappings against two types of collective noises, respectively. The entanglement swapping can be achieved by performing two Bell state measurements on two logical qubits that come from two original logical Bell states, respectively. Two fault tolerant quantum secret sharing (QSS) protocols are further proposed to demonstrate the usefulness of the newly proposed entanglement swappings. The proposed QSS schemes are not only free from Trojan horse attacks but also quite efficient. Moreover, by adopting two Bell state measurements instead of four-qubit joint measurements, the proposed protocols are practical in combating collective noises. The proposed fault tolerant entanglement swapping can also be used to replace the traditional Bell-state entanglement swapping used in various quantum cryptographic protocols to provide robustness in combating collective noises.     

Efficient quantum state transfer in an engineered chain of quantum bits

We present a method of performing quantum state transfer in a chain of superconducting quantum bits. Our protocol is based on engineering the energy levels of the qubits in the chain and tuning them all simultaneously with an external flux bias. The system is designed to allow sequential adiabatic state transfers, resulting in on-demand quantum state transfer from one end of the chain to the other. Numerical simulations of the master equation using realistic parameters for capacitive nearest-neighbor coupling, energy relaxation, and dephasing show that fast, high-fidelity state transfer should be feasible using this method.     

Reservoir cross-over in entanglement dynamics

We study the effects of spontaneous emission on the entanglement dynamics of two qubits interacting with a common Lorentzian structured reservoir. We assume that the qubits are initially prepared in a Bell-like state. We focus on the strong coupling regime and study the entanglement dynamics for different regions of the spontaneous emission decay parameter. This investigation allows us to explore the cross-over between common and independent reservoirs in entanglement dynamics.     

Multipartite entangled magnon states as quantum communication channels

We investigate the entanglement properties of the two magnon states and explicate conditions under which, the two magnon state becomes useful for several quantum communication protocols. We systematically study the temporal behaviour of concurrence to find out the effect of exchange interaction on entanglement. The two magnon state, which is potentially realizable in quantum dots using Heisenberg exchange interaction, is found to be suitable for carrying out deterministic teleportation of an arbitrary two qubit composite system. Further, conditions for which the channel capacity reaches “Holevo bound”, allowing four classical bits to be transmitted through two qubits are derived. Later, an unconventional protocol is given to demonstrate that this state can be used for sharing of a two qubit entangled state among two parties.     

Quantum information processing in self-assembled crystals of cold polar molecules

We discuss the implementation of quantum gate operations in a self-assembled dipolar crystal of polar molecules. Here qubits are encoded in long-lived spin states of the molecular ground state and stabilized against collisions by repulsive dipole–dipole interactions. To overcome the single site addressability problem in this high density crystalline phase, we describe a new approach for implementing controlled single and two-qubit operations based on resonantly enhanced spin–spin interactions mediated by a localized phonon mode. This local mode is created at a specified lattice position with the help of an additional marker molecule such that individual qubits can be manipulated by using otherwise global static and microwave fields only. We present a general strategy for generating state and time dependent dipole moments to implement a universal set of gate operations for molecular qubits and we analyze the resulting gate fidelities under realistic conditions. Our analysis demonstrates the experimental feasibility of this approach for scalable quantum computing or digital quantum simulation schemes with polar molecules.     

Testing Hardy’s ladder proof of nonlocality by joint measurements of qubits

We propose an experimentally feasible scheme to test Hardy’s ladder proof of nonlocality with two qubits (two-level atoms) dispersively coupled to a driven cavity. First, we find that the required nonmaximally entangled two-qubit pure state can be prepared by only one-step two-qubit operation from the ground state $|00\rangle $ | 00 〉 , assisted by two single-qubit gates. Next, we perform two single-qubit operations to encode the local information into the prepared nonmaximally entangled state. Finally, the nonlocal correlations between the two qubits can be directly detected by the joint measurement of the two-qubit register in one of selected computational basis, implemented by probing the steady-state transmitted spectra of the driven cavity. Consequently, the Hardy’s ladder proof of nonlocality can be effectively tested. The feasibility of our proposal with the current experimental technology is also analyzed.     

Tunable interaction of superconducting flux qubits in circuit QED

We propose to implement tunable interaction of superconducting flux qubits with cavity-assisted interaction and strong driving. The qubits have a three-level Lambda configuration, and the decay of the excited state will be greatly suppressed due to the effective large detuning. The implemented interaction is insensitive to the cavity field state and can be controlled by modulating the phase difference of the driving fields of the qubits. In particular, our scheme is based on the typical circuit QED setup and thus will provide a simple method towards the tunable interaction of superconducting qubits. Finally, we consider the generation of two and four qubits entangled states with the constructed interaction under the influence of typical decoherence effects.     

Maximum density of quantum information in a scalable CMOS implementation of the hybrid qubit architecture

Scalability from single-qubit operations to multi-qubit circuits for quantum information processing requires architecture-specific implementations. Semiconductor hybrid qubit architecture is a suitable candidate to realize large-scale quantum information processing, as it combines a universal set of logic gates with fast and all-electrical manipulation of qubits. We propose an implementation of hybrid qubits, based on Si metal-oxide-semiconductor (MOS) quantum dots, compatible with the CMOS industrial technological standards. We discuss the realization of multi-qubit circuits capable of fault-tolerant computation and quantum error correction, by evaluating the time and space resources needed for their implementation. As a result, the maximum density of quantum information is extracted from a circuit including eight logical qubits encoded by the [[7, 1, 3]] Steane code. The corresponding surface density of logical qubits is 2.6 Mqubit/cm\(^2\).     

Can quantum discord increase in a quantum communication task?

Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver’s state has more quantum discord than the sender’s state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob’s qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting feature in this scenario, when the quantum discord of Alice’s qubits increases, then the quantum discord of Bob’s prepared qubits decreases. Furthermore, we show that the fidelity of one-qubit quantum teleportation using Bob’s prepared qubits as the channel is higher than using Alice’s qubits.     

An Explicit Universal Gate-Set for Exchange-Only Quantum Computation

A single physical interaction might not be universal for quantum computation in general. It has been shown, however, that in some cases it can achieve universal quantum computation over a subspace. For example, by encoding logical qubits into arrays of multiple physical qubits, a single isotropic or anisotropic exchange interaction can generate a universal logical gate-set. Recently, encoded universality for the exchange interaction was explicitly demonstrated on three-qubit arrays, the smallest nontrivial encoding. We now present the exact specification of a discrete universal logical gate-set on four-qubit arrays. We show how to implement the single qubit operations exactly with at most 3 nearest neighbor exchange operations and how to generate the encoded controlled-NOT with 27 parallel nearest neighbor exchange interactions or 50 serial gates, obtained from extensive numerical optimization using genetic algorithms and Nelder–Mead searches. We also give gate-switching times for the three-qubit encoding to much higher accuracy than previously and provide the full speci.cation for exact CNOT for this encoding. Our gate-sequences are immediately applicable to implementations of quantum circuits with the exchange interaction. PACS: 03.67.Lx, 03.65.Ta, 03.65.Fd, 89.70.+c     

Lyapunov-based States Transfer for Open System with Superconducting Qubits

We design control fields to realize states transfer for open quantum system by Lyapunov stability theory, and investigate the states transfer of superconducting qubits in Markovian channels with phase relaxation and energy dissipative relaxation. The numerical simulations indicate that arbitrary state (eigenstate, superposition state or mixed state) transfer and maintenance for Markovian system can be realized under Lyapunov control function by an external steady control field of proper amplitude. Moreover, proper increase of proportional coefficients can accelerate the qubits flip and reduce the vibration frequency of control function.     

Fault-tolerant asymmetric quantum dialogue protocols against collective noise

In this paper, we propose two kinds of fault-tolerant asymmetric quantum dialogue (AQD) protocols and investigate the effect of collective noise on the proposed AQD protocols. In our work, logical qubits have been selected to build traveling blocks for constructing a decoherence-free subspace. Both communicants can encode each bit of secret message in the logical qubit with unitary logical operator. Compared with the previous quantum dialogue protocols, the proposed AQD protocols not only enable two users to transmit different amount of classical information to each other, but also can provide higher communication fidelity under the interference of collective noise. Furthermore, we will demonstrate the security of the AQD protocols against information leakage problem and Eve’s active eavesdropping attack.     

Quantum computing and quantum simulation with group-II atoms

Recent experimental progress in controlling neutral group-II atoms for optical clocks, and in the production of degenerate gases with group-II atoms has given rise to novel opportunities to address challenges in quantum computing and quantum simulation. In these systems, it is possible to encode qubits in nuclear spin states, which are decoupled from the electronic state in the ¹S₀ ground state and the long-lived ³P₀ metastable state on the clock transition. This leads to quantum computing scenarios where qubits are stored in long lived nuclear spin states, while electronic states can be accessed independently, for cooling of the atoms, as well as manipulation and readout of the qubits. The high nuclear spin in some fermionic isotopes also offers opportunities for the encoding of multiple qubits on a single atom, as well as providing an opportunity for studying many-body physics in systems with a high spin symmetry. Here we review recent experimental and theoretical progress in these areas, and summarise the advantages and challenges for quantum computing and quantum simulation with group-II atoms.