Two-qubit Operations Research Articles

Scalable Neutral Atom Quantum Computer with Interaction on Demand: Proposal for Selective Application of Two-Qubit Gate

We propose a scalable neutral atom quantum computer with an on-demand interaction through a selective two-qubit gate operation. Atoms are trapped by a lattice of near field Fresnel diffraction lights so that each trap captures a single atom. One-qubit gate operation is implemented by a gate control laser beam which is applied to an individual atom. Two-qubit gate operation between an arbitrary pair of atoms is implemented by sending these atoms to a state-dependent optical lattice and making them collide so that a particular two-qubit state acquires a dynamical phase. We give numerical evaluations corresponding to these processes, from which we estimate the upper bound of a two-qubit gate operation time and corresponding gate fidelity. Our proposal is feasible within currently available technology developed in cold atom gas, MEMS, nanolithography, and various areas in optics.

Pulse Protocols for Quantum Computing with Electron Spins as Qubits

A method of elaborating pulse sequences performing unitary transformations on the basis of their transformation matrices has been developed. For the first time the pulse protocols performing two-qubit quantum logical operations in electron spin systems have been obtained.

Reconfigurable controlled two-qubit operation on a quantum photonic chip

Integrated quantum photonics is an appealing platform for quantum information processing, quantum communication and quantum metrology. In all these applications it is necessary not only to be able to create and detect Fock states of light but also to programme the photonic circuits that implement some desired logical operation. Here we demonstrate a reconfigurable controlled two-qubit operation on a chip using a multiwaveguide interferometer with a tunable phase shifter. We found excellent agreement between theory and experiment, with a 0.98 ± 0.02 average similarity between measured and ideal operations.

Electrically controlled quantum gates for two-spin qubits in two double quantum dots

Exchange-coupled singlet-triplet spin qubits in two gate-defined double quantum dots are considered theoretically. Using charge density operators to describe the double-dot orbital states, we calculate the Coulomb couplings between the qubits and identify optimal bias points for single- and two-qubit operations, as well as convenient idle positions. The same intuitive formulation is used to derive dephasing rates of these qubits due to the fluctuating charge environment, thereby providing the main considerations for a quantum computation architecture that is within current experimental capabilities.

Entanglement Cost of Implementing Controlled-Unitary Operations

We investigate the minimum entanglement cost of the deterministic implementation of two-qubit controlled-unitary operations using local operations and classical communication (LOCC). We show that any such operation can be implemented by a three-turn LOCC protocol, which requires at least 1 ebit of entanglement when the resource is given by a bipartite entangled state with Schmidt number 2. Our result implies that there is a gap between the minimum entanglement cost and the entangling power of controlled-unitary operations. This gap arises due to the requirement of implementing the operations while oblivious to the identity of the inputs.

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.

Optimizing entangling quantum gates for physical systems

Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive an optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.

Quantum computation over the butterfly network

In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A \textbf{76}, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.

Proposed spin-qubit controlled-not gate robust against noisy coupling

We propose an implementation of the two-qubit gate in a quantum dot spin qubit system which is immune to charge noise problems. Our proposed implementation, if it could be realized in a physical system, would have the advantage of being robust against uncertainties and fluctuations in the tunnel coupling and barrier gate voltage pulse area. The key idea is to introduce an auxiliary dot and use an analog to the stimulated Raman adiabatic passage pulse sequence in three-level atomic systems, often referred to in the context of electron transport in quantum dot systems as Coherent Tunneling by Adiabatic Passage. Spin-dependent tunneling opens the possibility of performing two-qubit gate operations by this method.

Charge-State Conditional Operation of a Spin Qubit

We report coherent operation of a singlet-triplet qubit controlled by the spatial arrangement of two confined electrons in an adjacent double quantum dot that is electrostatically coupled to the qubit. This four-dot system is the specific device geometry needed for two-qubit operations of a two-electron spin qubit. We extract the strength of the capacitive coupling between qubit and adjacent double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways toward implementation of a universal set of gates for singlet-triplet spin qubits.

Optical switching of nuclear spin–spin couplings in semiconductors

Two-qubit operation is an essential part of quantum computation. However, solid-state nuclear magnetic resonance quantum computing has not been able to fully implement this functionality, because it requires a switchable inter-qubit coupling that controls the time evolutions of entanglements. Nuclear dipolar coupling is beneficial in that it is present whenever nuclear–spin qubits are close to each other, while it complicates two-qubit operation because the qubits must remain decoupled to prevent unwanted couplings. Here we introduce optically controllable internuclear coupling in semiconductors. The coupling strength can be adjusted externally through light power and even allows on/off switching. This feature provides a simple way of switching inter-qubit couplings in semiconductor-based quantum computers. In addition, its long reach compared with nuclear dipolar couplings allows a variety of options for arranging qubits, as they need not be next to each other to secure couplings.

Constructions and noise threshold of topological subsystem codes

Topological subsystem codes proposed recently by Bombin are quantum error-correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. In this paper, we demonstrate that topological subsystem codes (TSCs) can be viewed as generalizations of Kitaev's honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. We also derive a necessary and sufficient condition under which a syndrome measurement in a subsystem code can be reduced to measurements of the gauge group generators. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-square code, has a threshold against depolarizing noise of at least 2%.

Universal quantum computing in linear nearest neighbor architectures

We introduce a scheme for realizing universal quantum computing in a linear nearest neighbor architecture with fixed couplings. We first show how to realize a controlled-NOT gate operation between two adjacent qubits without having to isolate the two qubits from qubits adjacent to them. The gate operation is implemented by applying two consecutive pulses of equal duration, but varying amplitudes, on the target qubit. Since only a single control parameter is required in implementing our scheme, it is very efficient. We next show how our scheme can be used to realize single qubit rotations and two-qubit controlled-unitary operations. As most proposals for solid state implementations of a quantum computer use a one-dimensional line of qubits, the schemes presented here will be extremely useful.

Coherent coupling between distant excitons revealed by two-dimensional nonlinear hyperspectral imaging

Coherent coupling between distant two-level systems is a fundamental process in several physical contexts, from natural photosynthesis to quantum-information processing, where it enables two-qubit operations. For quantum information, qubits based on electronic degrees of freedom in a solid-state matrix are sensible candidates for scalable, integrated implementations. Clarifying the mechanisms underlying coherent coupling in solids is therefore an essential step in the development of such technology. Here, we demonstrate the existence of a long-range coherent coupling mechanism between individual localized excitons in a 5 nm GaAs/AlGaAs quantum well, introducing the novel tool of two-dimensional nonlinear coherent hyperspectral imaging. The coupling is shown to arise due to a biexcitonic renormalization, rather than a transition dipole (Forster) interaction. The long-range nature of the coupling is attributed to the existence of spatially extended exciton states up to the micrometre range, which are admixed in the biexciton state, as revealed in nonlinear imaging.

Two-spin relaxation of P dimers in silicon

We study two-electron singlet-triplet relaxation of donor-bound electrons in Silicon. Hyperfine interaction of the electrons with the phosphorus (P) nuclei, in combination with the electron-phonon interaction, lead to relaxation of the triplet states. Within the Heitler-London and effective mass approximations, we calculate the triplet relaxation rates in the presence of an applied magnetic field. This relaxation mechanism affects the resonance peaks in current Electron Spin Resonance (ESR) experiments on P-dimers. Moreover, the estimated time scales for the spin decay put an upper bound on the gate pulses needed to perform fault-tolerant two-qubit operations in donor-spin-based quantum computers (QCs).

Bidirectional Mapping between a Biphoton Polarization State and a Single-Photon Two-Qubit State

How to manipulate (operate or measure) single photons efficiently and simply is the basic problem in optical quantum information processing. We first present an efficient scheme to transform a biphoton polarization state to a corresponding single-photon state encoded by its polarization and spatial modes. This single-photon state carries both the information of the controlled and target photons. It will make the realization of bipartite positive-operator-valued measurements efficiently and simply. Moreover, the inverse transformation from the single-photon state back to the corresponding biphoton polarization state is also proposed. Using both the transformations, the realization of the arbitrary two-qubit unitary operation is simple with an M-Z interferometer. All the schemes are feasible with the current experimental technology.

Arbitrary control of coherent dynamics for distant qubits in a quantum network

We show that the coherent coupling of atomic qubits at distant nodes of a quantum network, composed of several cavities linked by optical fibers, can be arbitrarily controlled via the selective pairing of Raman transitions. The adiabatic elimination of the atomic excited states and photonic states leads to selective qubit-qubit interactions, which would have important applications in quantum-information processing. Quantum gates between any pair of distant qubits and parallel two-qubit operations on selected qubit pairs can be implemented through suitable choices of the parameters of the external fields. Selective pairing of Raman transitions also allows the generation of spin chains and cluster states without the requirement that the cavity-fiber coupling be smaller than the detunings of the Raman transitions.

Nonlinear optical properties of a medium with M-configuration of atomic levels

Nonlinear effects related to the resonant interaction of electromagnetic fields that act on four transitions of a five-level M scheme of atomic levels in the stationary limit are studied. Eight stationary solutions that depend on the state of circular polarizations of three operating classical modes of the field are found for the atomic density matrix. To decrease the absorption of the fields on the atomic transitions, the regime of electromagnetically induced transparency is used. The conditions under which the M scheme is close in its optical properties to two- or three-level schemes are found. Based on the obtained eight solutions, the total accumulated phase shifts of the working waves are calculated. It is shown that the M scheme can perform the operation of double controlled phase shift. Alternatively to the method proposed, this operation also can be carried out using five two-qubit operations, which reduces its noise immunity.

QUANTUM STATE SPLITTING WITH YEO–CHUA GENUINE ENTANGLED STATE

Utilizing the four-qubit genuine entangled state presented by Yeo and Chua [Phys. Rev. Lett.96 (2006) 060502], we propose a tripartite quantum state splitting scheme for a sender to achieve the bipartition of his/her arbitrary two-qubit pure state between two sharers. During the scheme design, two novel and important ideas originated, respectively, from Phys. Rev. A74 (2006) 054303 and J. Phys. B41 (2008) 145506 are adopted to enhance the security and optimize resource consumption, operation complexity, and intrinsic efficiency. In the scheme, first the sender performs two Bell-state measurements and publishes the results. Afterwards, if and only if the two sharers cooperate together, they can perfectly restore the sender's quantum pure state by executing first a two-qubit collective unitary operation and then two single-qubit unitary operations.

Ancilla-driven universal quantum computation

We introduce a model of quantum computation intermediate between the gate-based and measurement-based models. A quantum register is manipulated remotely with the help of a single ancilla that ``drives'' the evolution of the register. The fully controlled ancilla qubit is coupled to the computational register only via a fixed unitary two-qubit interaction and then measured in suitable bases, driving both single- and two-qubit operations on the register. Arbitrary single-qubit operations directly on register qubits are not needed. We characterize all interactions $E$ that induce a unitary, stepwise deterministic measurement back-action on the register sufficient to implement any quantum channel. Our scheme offers experimental advantages for computation, state preparation, and generalized measurements, since no tunable control of the register is required.