Two-qubit Operations Research Articles

Multiphoton-state-assisted entanglement purification of material qubits

We propose an entanglement purification scheme based on material qubits and ancillary coherent multiphoton states. We consider a typical QED scenario where material qubits implemented by two-level atoms fly sequentially through a cavity and interact resonantly with a single mode of the radiation field. We explore the theoretical possibilities of realizing a high-fidelity two-qubit quantum operation necessary for the purification protocol with the help of a postselective balanced homodyne photodetection. We demonstrate that the obtained probabilistic quantum operation can be used as a bilateral operation in the proposed purification scheme. It is shown that the probabilistic nature of this quantum operation is counterbalanced in the last step of the scheme where qubits are not discarded after inadequate qubit measurements. As this protocol requires present-day experimental setups and generates high-fidelity entangled pairs with high repetition rates, it may offer interesting perspectives for applications in quantum information theory.

A controllable single photon beam-splitter as a node of a quantum network

A model for a controlled single-photon beam-splitter is proposed and analyzed. It consists of two crossed optical-cavities with overlapping waists, dynamically coupled to a single flying atom. The system is shown to route a single photon with near-unity efficiency in an effective ‘weak-coupling’ regime. Furthermore, two such nodes, forming a segment of a quantum network, are shown to perform several controlled quantum operations. All one-qubit operations involve a transfer of a photon from one cavity to another in a single node, while two-qubit operations involve transfer from one node to a next one, coupled via an optical fiber. Novel timing protocols for classical optical fields are found to simplify possible experimental realizations along with achievable effective parameter regime. Though our analysis here is based on a cavity-QED scenario, basic features of the model can be extended to various other physical systems including gated quantum dots, circuit-QED or opto-mechanical elements.

Nanoelectromechanical diamond structures in quantum informatics. Part I

The second part of the review is devoted to the theoretical description of diamond nanoelectromechanical devices interacting with nitrogen-vacancy centers in diamond in the coherent mode with a certain number of quanta. The experimental data are reported that reflect the features of the dynamic and spectral properties of such hybrid structures. The possibilities of the application of the hybrid structures in implementing one- and two-qubit operations, as well as in auxiliary procedures, including cooling, measuring, and generating nonclassical states, are discussed.

Entanglement distillation using the exchange interaction

A key ingredient of quantum repeaters is entanglement distillation, i.e., the generation of high-fidelity entangled qubits from a larger set of pairs with lower fidelity. Here, we present entanglement distillation protocols based on qubit couplings that originate from exchange interaction. First, we make use of asymmetric bilateral two-qubit operations generated from anisotropic exchange interaction and show how to distill entanglement using two input pairs. We furthermore consider the case of three input pairs coupled through isotropic exchange. Here, we characterize a set of protocols which are optimizing the tradeoff between the fidelity increase and the probability of a successful run.

Spin-valley qubit in nanostructures of monolayer semiconductors: Optical control and hyperfine interaction

We investigate the optical control possibilities of spin-valley qubit carried by single electrons localized in nanostructures of monolayer TMDs, including small quantum dots formed by lateral heterojunction and charged impurities. The quantum controls are discussed when the confinement induces valley hybridization and when the valley hybridization is absent. We show that the bulk valley and spin optical selection rules can be inherited in different forms in the two scenarios, both of which allow the definition of spin-valley qubit with desired optical controllability. We also investigate nuclear spin induced decoherence and quantum control of electron-nuclear spin entanglement via intervalley terms of the hyperfine interaction. Optically controlled two-qubit operations in a single quantum dot are discussed.

Dissipative Quantum Computing with Majorana Fermions

We describe a scheme for universal quantum computation with Majorana fermions. We investigate two possible dissipative couplings of Majorana fermions to external systems, including metallic leads and local phonons. While the dissipation when coupling to metallic leads to uninteresting states for the Majorana fermions, we show that coupling the Majorana fermions to local phonons allows to generate arbitrary dissipations and therefore universal quantum operations on a single QuBit that can be enhanced by additional two-QuBit operations.

Determination of locally perfect discrimination for two-qubit unitary operations

In the study of local discrimination for multipartite unitary operations, Duan et al. (Phys Rev Lett 100(2):020503, 2008) exhibited an ingenious expression: Any two different unitary operations $$U_1$$U1 and $$U_2$$U2 are perfectly distinguishable by local operations and classical communication in the single-run scenario if and only if 0 is in the local numerical range of $$U_1^\dag U_2$$U1?U2. However, how to determine when 0 is in the local numerical range remains unclear. So it is generally hard to decide the local discrimination of nonlocal unitary operations with a single run. In this paper, for two-qubit diagonal unitary matrices V and their local unitary equivalent matrices, we present a necessary and sufficient condition for determining whether the local numerical range is a convex set or not. The result can be used to easily judge the locally perfect distinguishability of any two unitary operations $$U_1$$U1 and $$U_2$$U2 satisfying $$U_1^\dag U_2=V$$U1?U2=V. Moreover, we design the corresponding protocol of local discrimination. Meanwhile, an interesting phenomenon is discovered: Under certain conditions with a single run, $$U_1$$U1 and $$U_2$$U2 such that $$U_1^\dag U_2=V$$U1?U2=V are locally distinguishable with certainty if and only if they are perfectly distinguishable by global operations.

A two-qubit logic gate in silicon.

Quantum computation requires qubits that can be coupled in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates. Many physical realizations of qubits exist, including single photons, trapped ions, superconducting circuits, single defects or atoms in diamond and silicon, and semiconductor quantum dots, with single-qubit fidelities that exceed the stringent thresholds required for fault-tolerant quantum computing. Despite this, high-fidelity two-qubit gates in the solid state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits, owing to the difficulties of coupling qubits and dephasing in semiconductor systems. Here we present a two-qubit logic gate, which uses single spins in isotopically enriched silicon and is realized by performing single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the Loss-DiVincenzo proposal. We realize CNOT gates via controlled-phase operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is used in the two-qubit controlled-phase gate. By independently reading out both qubits, we measure clear anticorrelations in the two-spin probabilities of the CNOT gate.

Exact CNOT gates with a single nonlocal rotation for quantum-dot qubits

We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a, J_b, t)$ for which the two-qubit entanglement, in combination with appropriate single-qubit rotations, can produce an exact CNOT gate. This statement is true for practically arbitrary magnitude and form of capacitive interqubit coupling. Our findings promise a large decrease in the number of nonlocal (two-qubit) operations in quantum circuits.

Conditional rotation of two strongly coupled semiconductor charge qubits.

Universal multiple-qubit gates can be implemented by a set of universal single-qubit gates and any one kind of entangling two-qubit gate, such as a controlled-NOT gate. For semiconductor quantum dot qubits, two-qubit gate operations have so far only been demonstrated in individual electron spin-based quantum dot systems. Here we demonstrate the conditional rotation of two capacitively coupled charge qubits, each consisting of an electron confined in a GaAs/AlGaAs double quantum dot. Owing to the strong inter-qubit coupling strength, gate operations with a clock speed up to 6 GHz have been realized. A truth table measurement for controlled-NOT operation shows comparable fidelities to that of spin-based two-qubit gates, although phase coherence is not explicitly measured. Our results suggest that semiconductor charge qubits have a considerable potential for scalable quantum computing and may stimulate the use of long-range Coulomb interaction for coherent quantum control in other devices.

Geometric representation of two-qubit entanglement witnesses

Any two-qubit state can be represented geometrically by a steering ellipsoid inside the Bloch sphere. We extend this approach to represent any block positive two-qubit operator $B$. We derive a novel classification scheme based on the positivity of $\det B$ and $\det B^\mathrm{T_B}$; this shows that any ellipsoid inside the Bloch sphere must represent either a two-qubit state or a two-qubit entanglement witness. We focus on such witnesses and their corresponding ellipsoids, finding that properties such as witness optimality are naturally manifest in this geometric representation.

Multivalley effective mass theory simulation of donors in silicon

Last year, Salfi et al. made the first direct measurements of a donor wave function and found extremely good theoretical agreement with atomistic tight-binding [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multi-valley effective mass theory, applied properly, does achieve close agreement with tight-binding and hence gives reliable predictions. To demonstrate this, we variationally solve the coupled six-valley Shindo-Nara equations, including silicon's full Bloch functions. Surprisingly, we find that including the full Bloch functions necessitates a tetrahedral, rather than spherical, donor central cell correction to accurately reproduce the experimental energy spectrum of a phosphorus impurity in silicon. We cross-validate this method against atomistic tight-binding calculations, showing that the two theories agree well for the calculation of donor-donor tunnel coupling. Further, we benchmark our results by performing a statistical uncertainty analysis, confirming that derived quantities such as the wave function profile and tunnel couplings are robust with respect to variational energy fluctuations. Finally, we apply this method to exhaustively enumerate the tunnel coupling for all donor-donor configurations within a large search volume, demonstrating conclusively that the tunnel coupling has no spatially stable regions. Though this instability is problematic for reliably coupling donor pairs for two-qubit operations, we identify specific target locations where donor qubits can be placed with scanning tunneling microscopy technology to achieve reliably large tunnel couplings.

Ball-grid array architecture for microfabricated ion traps

State-of-the-art microfabricated ion traps for quantum information research are approaching nearly one hundred control electrodes. We report here on the development and testing of a new architecture for microfabricated ion traps, built around ball-grid array (BGA) connections, that is suitable for increasingly complex trap designs. In the BGA trap, through-substrate vias bring electrical signals from the back side of the trap die to the surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from the carrier. Trench capacitors fabricated into the trap die replace area-intensive surface or edge capacitors. Wirebonds in the BGA architecture are moved to the interposer. These last two features allow the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions allow tight focusing of an addressing laser beam for fast single-qubit rotations. Performance of the BGA trap as characterized with 40Ca+ ions is comparable to previous surface-electrode traps in terms of ion heating rate, mode frequency stability, and storage lifetime. We demonstrate two-qubit entanglement operations with 171Yb+ ions in a second BGA trap.

Quantum logic gates from time-dependent global magnetic field in a system with constant exchange

We propose a method that implements a universal set of one- and two-quantum-bit gates for quantum computation in a system of coupled electron pairs with constant non-diagonal exchange interaction. In our proposal, suppression of the exchange interaction is performed by the continual repetition of single-spin rotations. A small g-factor difference between the electrons allows for addressing qubits and avoiding strong magnetic field pulses. Numerical experiments were performed to show that, to implement the one- and two-qubit operations, it is sufficient to change the strength of the magnetic field by a few Gauss. This introduces one and then the other electron in a resonance. To determine the evolution of the two-qubit system, we use the algorithms of optimal control theory.

A magic state’s fidelity can be superior to the operations that created it

The leading approach to fault tolerant quantum computing requires a continual supply of magic states. When a new magic state is first encoded, its initial fidelity will be too poor for use in the computation. This necessitates a resource-intensive distillation process that occupies the majority of the computer’s hardware; creating magic states with a high initial fidelity minimizes this cost and is therefore crucial for practical quantum computing. Here we present the surprising and encouraging result that raw magic states can have a fidelity significantly better than that of the two-qubit gate operations used to construct them. Our protocol exploits post-selection without significantly slowing the rate of generation and tolerates finite error rates in initializations, measurements and single-qubit gates. This approach may dramatically reduce the size of the hardware needed for a given quantum computing task.

Experimental implementation of quantum gates through actuator qubits

Universal quantum computation requires the implementation of arbitrary control operations on the quantum register. In most cases, this is achieved by external control fields acting selectively on each qubit to drive single-qubit operations. In combination with a drift Hamiltonian containing interactions between the qubits, this allows the implementation of arbitrary gate operations. Here, we demonstrate an alternative scheme that does not require local control for all qubits: we implement one- and two-qubit gate operations on a set of target qubits indirectly, through a combination of gates on directly controlled actuator qubits with a drift Hamiltonian that couples actuator and target qubits. Experiments are performed on nuclear spins, using radio-frequency pulses as gate operations and magnetic-dipole couplings for the drift Hamiltonian.

Characterization of how dissipation and dephasing errors accumulate in quantum computers

We study the achievements of quantum circuits comprised of several one- and two-qubit gates subject to dissipation and dephasing. Quantum process matrices are determined for the basic one- and two-qubit gate operations and concatenated to yield the process matrix of the combined quantum circuit. Examples are given of process matrices obtained by a Monte Carlo wavefunction analysis of Rydberg blockade gates in neutral atoms. Our analysis is ideally suited to compare different implementations of the same process. In particular, we show that the three-qubit Toffoli gate facilitated by the simultaneous interaction between all atoms may be accomplished with higher fidelity than a concatenation of one- and two-qubit gates.

Two Quantum Direct Communication Protocols Based on Quantum Search Algorithm

Based on the properties of two-qubit Grover’s quantum search algorithm, we propose two quantum direct communication protocols, including a deterministic secure quantum communication and a quantum secure direct communication protocol. Secret messages can be directly sent from the sender to the receiver by using two-qubit unitary operations and the single photon measurement with one of the proposed protocols. Theoretical analysis shows that the security of the proposed protocols can be highly ensured.

Pairwise thermal entanglement in the Ising-XYZ diamond chain structure in an external magnetic field

Quantum entanglement is one of the most fascinating types of correlation that can be shared only among quantum systems. The Heisenberg chain is one of the simplest quantum chains which exhibits a rich entanglement feature, due to the fact that the Heisenberg interaction is quantum coupling in the spin system. The two particles were coupled trough XYZ coupling or simply called as two-qubit XYZ spin, which are the responsible for the emergence of thermal entanglement. These two-qubit operators are bonded to two nodal Ising spins, and this process is repeated infinitely resulting in a diamond chain structure. We will discuss the two-qubit thermal entanglement effect on the Ising-XYZ diamond chain structure. The concurrence could be obtained straightforwardly in terms of two-qubit density operator elements; using this result we study the thermal entanglement, as well as the threshold temperature where entangled state vanishes. The present model displays a quite unusual concurrence behavior, e.g., the boundary of two entangled regions becomes a disentangled region, and this is intrinsically related to the XY-anisotropy in the Heisenberg coupling. Although a similar property had been found for only two qubits, here we show it for the case of a diamond chain structure, which reasonably represents real materials.

Chaining property for two-qubit operator entanglement measures

The operator entanglement of two-qubit gates is quantified by Schmidt strength and linear entropy. It is known that the measures are inequivalent in capturing the nonlocal features of two-qubit operators. While Schmidt strength is known to be violating chaining property, in this paper, we show that the linear entropy also fails to satisfy the property. Further, we argue that the chaining property of the measures does not provide a tight lower bound on the number of gates required to perform a particular quantum operation.