Qubit Gates Research Articles

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

We describe how a universal set of dynamically-corrected quantum gates can be implemented using sequences of shaped decoupling pulses on any qubit network forming a sparse bipartite graph with always-on Ising interactions. These interactions are constantly decoupled except when they are needed for two-qubit gates. We analytically study the error operators associated with the constructed gates up to third order in the Magnus expansion, analyze these errors numerically in the unitary time evolution of small qubit clusters, and give a bound on high-order errors for qubits on a large square lattice. We prove that with a large enough toric code the present gate set can be used to implement a fault-tolerant quantum memory.

Spin-based scheme for implementing an N-qubit tunable controlled phase gate in quantum dots by interference of polarized photons

We present a scheme for direct implementation of an N-qubit tunable controlled phase gate for spin qubits in quantum dots coupled to optical cavities, resorting to spin selective dipole coupling interaction and linear optical manipulation. In the scheme, we first design a quantum entangler device to transform the operated physical qubits, which are represented by the states of the electron spins, into non-maximal hybrid entangled states with a certain probability of success via the introduction of auxiliary circularly polarized photons. Then we show that, based on this quantum entangler operation, a spin-based N-qubit tunable controlled phase gate can be probabilistically achieved by the interference and coincidence detection of polarized photons. This might lead to a useful step toward the construction of more efficient quantum circuits and quantum algorithms in solid-state qubits.

Robust two-qubit gates for exchange-coupled qubits

We present composite pulse sequences that perform fault-tolerant two-qubit gate operations on exchange-only quantum dot spin qubits in various experimentally relevant geometries. We show how to perform dynamically corrected two-qubit gates in exchange-only systems with the leading hyperfine error term cancelled. These pulse sequences are constructed to conform to the realistic experimental constraint of strictly non-negative couplings. We establish that our proposed pulse sequences lead to several orders of magnitude improvement in the gate fidelity compared with their uncorrected counterparts. Together with single-qubit dynamically corrected gates, our results enable noise-resistant universal quantum operations with exchange-only qubits.

Deterministic Hadamard gate for microwave cat-state qubits in circuit QED

We propose the implementation of a deterministic Hadamard gate for logical photonic qubits encoded in superpositions of coherent states of a harmonic oscillator. The proposed scheme builds on a recently introduced set of conditional operations in the strong dispersive regime of circuit QED [Z. Leghtas et al. Phys. Rev. A. {\bf 87} (2013)]. We further propose an architecture for coupling two such logical qubits and provide a universal set of deterministic quantum gates. Based on parameter values taken from the current state of the art, we give estimates for the achievable gate fidelities accounting for fundamental gate imperfections and finite coherence time due to photon loss.

Decomposition of quantum gates

A recurrence scheme is presented to decompose an n-qubit unitary gate to the product of no more than N(N - 1)/2 single qubit gates with small number of controls, where N = 2n. Detailed description of the recurrence steps and formulas for the number of k-controlled single qubit gates in the decomposition are given. Comparison of the result to a previous scheme is presented, and future research directions are discussed.

Analysis of a controlled phase gate using circular Rydberg states

We propose and analyze the implementation of a two qubit quantum gate using circular Rydberg states with maximum orbital angular momentum. The intrinsic quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg blockade shift. Circular states have much longer radiative lifetimes than low orbital angular momentum states and are therefore candidates for high fidelity gate operations. We analyze the dipole-dipole interaction of two circular state Rydberg atoms and present numerical simulations of quantum process tomography to find the intrinsic fidelity of a Rydberg blockade controlled phase gate. Our analysis shows that the intrinsic gate error can be less than $9 \times10^{-6}$ for circular Cs atoms in a cryogenic environment.

Quantum computer with atomic logical qubits encoded on macroscopic three-level systems in common quantum electrodynamic cavity

We propose an effective realization of the universal set of elementary quantum gates in solid state quantum computer based on macroscopic (or mesoscopic) resonance systems — multiatomic coherent ensembles, squids or quantum dots in quantum electrodynamic cavity. We exploit an encoding of logical qubits by the pairs of the macroscopic two- or three-level atoms that is working in a Hilbert subspace of all states inherent to these atomic systems. In this subspace, logical single qubit gates are realized by the controlled reversible transfer of single atomic excitation in the pair via the exchange of virtual photons and by the frequency shift of one of the atomic ensembles in a pair. In the case of two-level systems, the logical two-qubit gates are performed by the controlling of Lamb shift magnitude in one atomic ensemble, allowing/blocking the excitation transfer in a pair, respectively, that is controlled by the third atomic system of another pair. When using three-level systems, we describe the NOT-gate in the atomic pair controlled by the transfer of working atomic excitation to the additional third level caused by direct impact of the control pair excitation. Finally, we discuss advantages of the proposed physical system for accelerated computation of some useful quantum gates.

Deterministic CNOT gate and entanglement swapping for photonic qubits using a quantum-dot spin in a double-sided optical microcavity

Abstract We propose a deterministic and scalable scheme to construct a two-qubit controlled-NOT (CNOT) gate and realize entanglement swapping between photonic qubits using a quantum-dot (QD) spin in a double-sided optical microcavity. The scheme is based on spin selective photon reflection from the cavity and can be achieved in a nondestructive and heralded way. We assess the feasibility of the scheme and show that the scheme can work in both the weak coupling and the strong coupling regimes. The scheme opens promising perspectives for long-distance photonic quantum communication and distributed quantum information processing.

Simultaneous Deterministic Control of Distant Qubits in Two Semiconductor Quantum Dots

In optimal quantum control (OQC), a target quantum state of matter is achieved by tailoring the phase and amplitude of the control Hamiltonian through femtosecond pulse-shaping techniques and powerful adaptive feedback algorithms. Motivated by recent applications of OQC in quantum information science as an approach to optimizing quantum gates in atomic and molecular systems, here we report the experimental implementation of OQC in a solid-state system consisting of distinguishable semiconductor quantum dots. We demonstrate simultaneous high-fidelity π and 2π single qubit gates in two different quantum dots using a single engineered infrared femtosecond pulse. These experiments enhance the scalability of semiconductor-based quantum hardware and lay the foundation for applications of pulse shaping to optimize quantum gates in other solid-state systems.

A quantum computer in the scheme of an atomic quantum transistor with logical encoding of qubits

A scheme of a multiqubit quantum computer on atomic ensembles using a quantum transistor implementing two qubit gates is proposed. We demonstrate how multiatomic ensembles permit one to work with a large number of qubits that are represented in a logical encoding in which each qubit is recorded on a superposition of single-particle states of two atomic ensembles. The access to qubits is implemented by appropriate phasing of quantum states of each of atomic ensembles. An atomic quantum transistor is proposed for use when executing two qubit operations. The quantum transistor effect appears when an excitation quantum is exchanged between two multiatomic ensembles located in two closely positioned QED cavities connected with each other by a gate atom. The dynamics of quantum transfer between atomic ensembles can be different depending on one of two states of the gate atom. Using the possibilities of control for of state of the gate atom, we show the possibility of quantum control for the state of atomic ensembles and, based on this, implementation of basic single and two qubit gates. Possible implementation schemes for a quantum computer on an atomic quantum transistor and their advantages in practical implementation are discussed.

A probabilistic CNOT gate for coherent state qubits

Abstract We propose a scheme for implementing a probabilistic controlled-NOT (CNOT) gate for coherent state qubits using only linear optics and a particular four-mode state. The proposed optical setup works, as a CNOT gate, near-faithful when | α | 2 ⩾ 25 and independent of the input state. The key element for realizing the proposed CNOT scheme is the entangled four-mode state.

A SWAP gate for qudits

We present a quantum SWAP gate valid for quantum systems of an arbitrary dimension. The gate generalizes the CNOT implementation of the SWAP gate for qubits and keeps its most important properties, like symmetry and simplicity. We only use three copies of the same controlled qudit gate. This gate can be built with two standard higher-dimensional operations, the quantum Fourier transform and the $$d$$ -dimensional version of the $$C\!Z$$ gate.

Complexity Analysis of Quantum Walk Based Search Algorithms

We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk search algorithm, without reference to a `black box' oracle. These circuits provide a practically implementable method to explore quantum walk based search algorithms with the aim of eventual real-world applications. We also provide a numerical analysis of a quantum walk based search along a twisted toroid family of graphs, which requires O($\sqrt{n}$ log($n$)) elementary 2-qubit quantum gate operations to find a marked node.

Quantum operations on charge qubits with the electrostatic control in semiconductor cavities

We consider one- and two-qubit operations on charge qubits that represent double quantum dots with one electron in each of them. The dots are formed inside a high-Q semiconductor cavity (disk, toroidal, or spherical) in the antinodes of one of its optical eigenmodes; the frequencies of the transitions between the ground (logic) and excited (auxiliary) states of the discrete electron spectrum in quantum dots are close to the frequency of this mode. The precise tuning of the transition frequency is performed by applying an electric potential on the qubit control gate. Within the model of qubits coherently interacting with a cavity quantum field, a few methods for controlling their states are developed. In particular, we propose different variants for implementing two-qubit CNOT and CZ gates and generating qubit entangled states. By the example of a micro-disk cavity, we calculate the operating characteristics that ensure a high rate of quantum gate implementation.

Optically controlled phase gate and teleportation of a controlled-not gate for spin qubits in a quantum-dot–microcavity coupled system

Using linear optical manipulation, single photons, entangled photon pairs, photon measurement, and classical communication, we propose a scheme for a two-spin-qubit phase gate and the teleportation of a controlled-not gate between two electron spins from acting on local qubits to acting on remote qubits using quantum dots in optical microcavities. The scheme is based on spin selective photon reflection from the cavity and is achieved in a deterministic way by the sequential detection of photons and the single-qubit rotations of a single electron spin in a self-assembled GaAs-InAs quantum dot. The feasibility of the scheme is assessed showing that high average fidelities of the gates are achievable in the weak-coupling regime when the side leakage and cavity loss are low. The scheme opens promising possibilities for long-distance quantum communication, distributed quantum computation, and construction of remote quantum-information-processing networks.

Deterministic and cascadable conditional phase gate for photonic qubits

Previous analyses of conditional \phi-phase gates for photonic qubits that treat cross-phase modulation (XPM) in a causal, multimode, quantum field setting suggest that a large (~\pi rad) nonlinear phase shift is always accompanied by fidelity-degrading noise [J. H. Shapiro, Phys. Rev. A 73, 062305 (2006); J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)]. Using an atomic V-system to model an XPM medium, we present a conditional phase gate that, for sufficiently small nonzero \phi, has high fidelity. The gate is made cascadable by using using a special measurement, principal mode projection, to exploit the quantum Zeno effect and preclude the accumulation of fidelity-degrading departures from the principal-mode Hilbert space when both control and target photons illuminate the gate.

Quantum computation with rotational states of nonpolar ionic molecules

We propose a quantum computer architecture which is robust against decoherence and scalable. As a qubit, we adopt rotational states of a nonpolar ionic molecule trapped in an ion-trap. It is revealed that the rotational-state qubits are much more immune to decoherence than the conventional electronic-state qubits of atomic ions. A complete method set for state preparation, single-qubit gate, controlled-NOT gate, and qubit-readout suitable for the rotational-state qubits is provided. Since the ionic molecules can be transported in an array of ion traps, the rotational-state qubits are expected to be a promising candidate to build a large-scale quantum computer.

Measurement based controlled not gate for topological qubits in a Majorana fermion and quantum-dot hybrid system

We propose a scheme to implement Controlled Not-gate for topological qubits in a quantum-dot-Majorana-fermion hybrid system. Quantum information is encoded on pairs of Majorana fermions, which live on the the interface between topologically trivial and nontrivial sections of a quantum nanowire deposited on an s-wave superconductor. A measurement-based two-qubit Controlled-Not gate is produced with the help of parity measurements assisted by the quantum-dot and followed by prescribed single-qubit gates. The parity measurement, on the quantum-dot and a topological qubit, is achieved by the Aharonov-Casher effect.

Quantum control of a spin qubit coupled to a photonic crystal cavity

A key ingredient for a quantum network is an interface between stationary quantum bits and photons, which act as flying qubits for interactions and communication. Photonic crystal architectures are promising platforms for enhancing the coupling of light to solid-state qubits. Quantum dots can be integrated into a photonic crystal, with optical transitions coupling to photons and spin states forming a long-lived quantum memory. Many researchers have now succeeded in coupling these emitters to photonic crystal cavities, but there have been no demonstrations of a functional spin qubit and quantum gates in this environment. Here, we have developed a coupled cavity–quantum dot system in which the dot is controllably charged with a single electron. We perform the initialization, rotation and measurement of a single electron spin qubit using laser pulses, and find that the cavity can significantly improve these processes.

Designing quantum gates using the genetic algorithm

We demonstrate the usage of Genetic Algorithm (GA) to tailor the radio frequency pulses for producing unitary transformations in qubit systems. We find that the initial population converges to the optimal solution after 10 generations, for a one segment pulse corresponding to single qubit Hadamard gate. For a two qubit CNOT gate, we see the population convergence for a two segment pulse after 150 generations. This demonstrates that the method is suitable for designing quantum gates.