Qubit Gates Research Articles

Superlattice model for quantum gates

Probability electronic current conservation in superlattices leads to a natural connection with the qubit and quantum gate concepts of quantum information and the introduction of Bloch spheres and Hopf bundles. Superlattices or multilayer devices with coupled channels are described by sectionally constant potentials in the longitudinal direction and arbitrary lateral dependency, which allow the explicit analytic calculation of the scattering amplitudes connecting ingoing with outgoing wave functions. A superlattice with n open channels and two terminals can be seen as a quantum gate, since both can be viewed as quantum systems with n components, each of which can have two states given by input and output. Taking into account the dimensionality of the respective Hilbert spaces, it results that the one-channel or mode superlattice corresponds to a single qubit; the two-channels case to two qubits, and the three- and four-channels cases to three qubits. The coupling of modes or channels corresponds to the entanglement of qubits. As shown in this work, superlattices with interacting energy modes constitute physical systems which allow to understand and evaluate explicitly the main features used to describe entangled qubits through the study of Hopf fiber bundles on spheres. Explicit examples for superlattice gate models with coupled channels are provided.

Proof of efficient, parallelized, universal adiabatic quantum computation

We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is based on ground state quantum computation [1]. We treat both a 1-dimensional configuration in which qubits on a line undergo nearest neighbor 2-qubit gates and an all-to-all configuration in which every qubit undergoes 2-qubit gates with every other qubit in the system.

Rashba control to minimize circuit cost of quantum Fourier algorithm in ballistic nanowires

The presented work provides a new prospective of quantum computer hardware development through ballistic nanowires with Rashba effect. We address Rashba effect as a possible mechanism to realize novel qubit gates in nanowires. We apply our results to the design of a new quantum circuit for Fourier algorithm, which shows an improved quantum cost in terms of the number of gates. The current system can be successfully implemented to increase the production of quantum computer experimentally thanks to the absence of impurities. The introduced circuit will enhance the scope of experimental and theoretical research for the realization of other quantum algorithms, such as phase estimation and Shor's algorithms.

Comment on ‘Deterministic CNOT gate and entanglement swapping for photonic qubits using a quantum-dot spin in a double-sided optical microcavity’ by H.F. Wang et al. [Physics Letters A 377 (2013) 2870–2876

Comment on ‘Deterministic CNOT gate and entanglement swapping for photonic qubits using a quantum-dot spin in a double-sided optical microcavity’ by H.F. Wang et al. [Physics Letters A 377 (2013) 2870–2876

Fast three-qubit Toffoli quantum gate based on three-body Förster resonances in Rydberg atoms

We propose a scheme of fast three-qubit Toffoli quantum gate for ultracold neutral-atom qubits. The scheme is based on the Stark-tuned three-body F\"{o}rster resonances, which we have observed in our recent experiment [D.B.Tretyakov et al., Phys.Rev.Lett. 119, 173402 (2017)]. The three-body resonance corresponds to a transition when the three interacting atoms change their states simultaneously, and it occurs at a different dc electric field with respect to the two-body F\"{o}rster resonance. A combined effect of three-body and two-body F\"{o}rster interactions in external electric and magnetic fields near the three-body resonance results in complex coherent behavior of the populations and phases of collective states of a three-atom system. We have found that it is possible to obtain experimental conditions suitable to implement three-qubit Toffoli gate with 96.8\% fidelity and less than 3~$\mu$s duration.

Controlled-NOT gate for frequency-encoded qubits based on six-wave mixing

The possibility of implementing a controlled-NOT gate for frequency-encoded photonic qubits via six-wave mixing in a multilevel atomic system is shown. Starting from the Hamiltonian for six-wave mixing in a cavity, equations of motion for the amplitudes of the photonic states are derived and solved in the framework of input–output formalism. Analysis of these solutions show how to realize two-qubit gates including relevant matching conditions.

Phonon-induced decoherence of a charge quadrupole qubit

Many quantum dot qubits operate in regimes where the energy splittings between qubit states are large and phonons can be the dominant source of decoherence. The recently proposed charge quadrupole qubit, based on one electron in a triple quantum dot, employs a highly symmetric charge distribution to suppress the influence of long-wavelength charge noise. To study the effects of phonons on the charge quadrupole qubit, we consider Larmor and Ramsey pulse sequences to identify favorable operating parameters. We show that phonon-induced decoherence increases with the qubit frequency, in contrast to the effects of charge noise. We also show that there is an optimum value of the tunnel coupling of the qubit at which the decohering effects of phonons and charge noise are small enough to be consistent with single qubit gate fidelities > 99.99%.

Entanglement generation using a controlled-phase gate for time-bin qubits

Quantum logic gates are important for quantum computation and quantum information processing in numerous physical systems. Although time-bin qubits are suitable for quantum communication over optical fiber, many essential quantum logic gates for them have not yet been realized. Here, we demonstrated a controlled-phase (C-Phase) gate for time-bin qubits that uses a 2 × 2 optical switch based on an electro-optic modulator. A Hong–Ou–Mandel interference measurement showed that the switch could work as a time-dependent beam splitter with a variable splitting ratio. We confirmed that two independent time-bin qubits were entangled as a result of C-Phase gate operation with the switch.

Two-qubit logical operations in three quantum dots system

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase (CPHASE), controlled NOT (CNOT), quantum Fourier transform (QFT) and SWAP operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the CPHASE gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: CNOT, QFT and SWAP. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations.

Controlled-Z gate for transmon qubits coupled by semiconductor junctions

We analyze the coupling of two qubits via an epitaxial semiconducting junction. In particular, we consider three configurations that include pairs of transmons or gatemons as well as gatemon-like two qubits formed by an epitaxial four-terminal junction. These three configurations provide an electrical control of the interaction between the qubits by applying voltage to a metallic gate near the semiconductor junction and can be utilized to naturally realize a controlled-Z gate (CZ). We calculate the fidelity and timing for such CZ gate. We demonstrate that in the absence of decoherence, the CZ gate can be performed under $50\ {\rm ns}$ with gate error below $10^{-4}$.

Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits

Recent progress in integrated-optics technology has made photonics a promising platform for quantum networks and quantum computation protocols. Integrated optical circuits are characterized by small device footprints and unrivalled intrinsic interferometric stability. Here, we take advantage of femtosecond-laser-written waveguides’ ability to process polarization-encoded qubits and present an implementation of a heralded controlled-NOT gate on chip. We evaluate the gate performance in the computational basis and a superposition basis, showing that the gate can create polarization entanglement between two photons. Transmission through the integrated device is optimized using thermally expanded core fibers and adiabatically reduced mode-field diameters at the waveguide facets. This demonstration underlines the feasibility of integrated quantum gates for all-optical quantum networks and quantum repeaters.

When is a product of finite order qubit gates of infinite order?

We consider a product of two finite order quantum -gates U1, U2 and ask when has an infinite order. Using the fact that is a double cover of we actually study the product of two rotations and about axes , . In particular, we focus on the case when , and are rational multiples of π and show that γ is not a rational multiple of π unless . The proof presented in this paper boils down to finding all pairs that are solutions of .

Experimental realization of quantum cheque using a five-qubit quantum computer

We demonstrate the implementation of quantum cheque, proposed by Roy Moulick and Panigrahi [Quantum Inf. Process (2016) 15: 2475], using the five-qubit IBM quantum computer. Appropriate single qubit, CNOT and Fredkin gates have been implemented for the realization of the quantum cheque transaction in a quantum networked banking system. Quantum state tomography reveals the accuracy of the implementation with comparable results from the theoretical and experimental density matrices.

Flux-tunable phase shifter for microwaves

We introduce a magnetic-flux-tunable phase shifter for propagating microwave photons, based on three equidistant superconducting quantum interference devices (SQUIDs) on a transmission line. We experimentally implement the phase shifter and demonstrate that it produces a broad range of phase shifts and full transmission within the experimental uncertainty. Together with previously demonstrated beam splitters, this phase shifter can be utilized to implement arbitrary single-qubit gates for qubits based on propagating microwave photons. These results complement previous demonstrations of on-demand single-photon sources and detectors, and hence assist in the pursuit of an all-microwave quantum computer based on propagating photons.

The complexity of translationally invariant low-dimensional spin lattices in 3D

In this theoretical paper, we consider spin systems in three spatial dimensions and consider the computational complexity of estimating the ground state energy, known as the local Hamiltonian problem, for translationally invariant Hamiltonians. We prove that the local Hamiltonian problem for 3D lattices with face-centered cubic unit cells and 4-local translationally invariant interactions between spin-3/2 particles and open boundary conditions is QMAEXP-complete, where QMAEXP is the class of problems which can be verified in exponential time on a quantum computer. We go beyond a mere embedding of past hard 1D history state constructions, for which the local spin dimension is enormous: even state-of-the-art constructions have local dimension 42. We avoid such a large local dimension by combining some different techniques in a novel way. For the verifier circuit which we embed into the ground space of the local Hamiltonian, we utilize a recently developed computational model, called a quantum ring machine, which is especially well suited for translationally invariant history state constructions. This is encoded with a new and particularly simple universal gate set, which consists of a single 2-qubit gate applied only to nearest-neighbour qubits. The Hamiltonian construction involves a classical Wang tiling problem as a binary counter which translates one cube side length into a binary description for the encoded verifier input and a carefully engineered history state construction that implements the ring machine on the cubic lattice faces. These novel techniques allow us to significantly lower the local spin dimension, surpassing the best translationally invariant result to date by two orders of magnitude (in the number of degrees of freedom per coupling). This brings our models on par with the best non-translationally invariant construction.

Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade.

We report on the first experimental realization of the controlled-not (cnot) quantum gate and entanglement for two individual atoms of different isotopes and demonstrate a negligible cross talk between two atom qubits. The experiment is based on a strong Rydberg blockade for ^{87}Rb and ^{85}Rb atoms confined in two single-atom optical traps separated by 3.8 μm. The raw fidelities of the cnot gate and entanglement are 0.73±0.01 and 0.59±0.03, respectively, without any corrections for atom loss or trace loss. Our work has applications for simulations of many-body systems with multispecies interactions, for quantum computing, and for quantum metrology.

Fault-tolerance thresholds for the surface code with fabrication errors

The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a non-trivial topology such that the quantum information is encoded in the global degrees of freedom (i.e. the topology) of the manifold. However, the manufacturing of large-scale topological devices will undoubtedly suffer from fabrication errors---permanent faulty components such as missing physical qubits or failed entangling gates---introducing permanent defects into the topology of the lattice and hence significantly reducing the distance of the code and the quality of the encoded logical qubits. In this work we investigate how fabrication errors affect the performance of topological codes, using the surface code as the testbed. A known approach to mitigate defective lattices involves the use of primitive SWAP gates in a long sequence of syndrome extraction circuits. Instead, we show that in the presence of fabrication errors the syndrome can be determined using the supercheck operator approach and the outcome of the defective gauge stabilizer generators without any additional computational overhead or the use of SWAP gates. We report numerical fault-tolerance thresholds in the presence of both qubit fabrication and gate fabrication errors using a circuit-based noise model and the minimum-weight perfect matching decoder. Our numerical analysis is most applicable to 2D chip-based technologies, but the techniques presented here can be readily extended to other topological architectures. We find that in the presence of 8% qubit fabrication errors, the surface code can still tolerate a computational error rate of up to 0.1%.

Long-range entanglement for spin qubits via quantum Hall edge modes

We propose and analyse a scheme for performing a long-range entangling gate for qubits encoded in electron spins trapped in semiconductor quantum dots. Our coupling makes use of an electrostatic interaction between the state-dependent charge configurations of a singlet-triplet qubit and the edge modes of a quantum Hall droplet. We show that distant singlet-triplet qubits can be selectively coupled, with gate times that can be much shorter than qubit dephasing times and faster than decoherence due to coupling to the edge modes. Based on parameters from recent experiments, we argue that fidelities above 99% could in principle be achieved for a two-qubit entangling gate taking as little as 20 ns.

Time-optimal control for hybrid systems based on the nitrogen-vacancy center

Fast and high fidelity quantum control is the key technology of quantum computing. The hybrid system composed of the nitrogen-vacancy center and nearby Carbon-13 nuclear spin is expected to solve this problem. The nitrogen-vacancy center electron spin enables fast operations for its strong coupling to the control field, whereas the nuclear spins preserve the coherence for their weak coupling to the environment. In this paper, we describe a strategy to achieve time-optimal control of the Carbon-13 nuclear spin qubit by alternating controlling the nitrogen-vacancy center electron spin as an actuator. We transform the qubit gate operation into a switched system. By using the maximum principle, we study the minimum time control of the switched system and obtain the time-optimal control of the qubit gate operation. We show that the X gate and Y gate operations are within 10 μs while the fidelity reaches 0.995.

Achieving high-fidelity single-qubit gates in a strongly driven silicon-quantum-dot hybrid qubit

Performing qubit gate operations as quickly as possible can be important to minimize the effects of decoherence. For resonant gates, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage to levels that lie outside the qubit subspace. Strong driving can also present theoretical challenges because preferred tools such as the rotating wave approximation can break down, resulting in complex dynamics that are difficult to control. Here we analyze resonant $X$ rotations of a silicon quantum double dot hybrid qubit within a dressed-state formalism, obtaining results beyond the rotating wave approximation. We obtain analytic formulas for the optimum driving frequency and the Rabi frequency, which both are affected by strong driving. While the qubit states exhibit fast oscillations due to counter-rotating terms and leakage, we show that they can be suppressed to the point that gate fidelities above $99.99\%$ are possible, in the absence of decoherence. Hence decoherence mechanisms, rather than strong-driving effects, should represent the limiting factor for resonant-gate fidelities in quantum dot hybrid qubits.