Universal Set Of Quantum Gates Research Articles

On the photonic implementation of universal quantum gates, Bell states preparation circuit and quantum LDPC encoders and decoders based on directional couplers and HNLF

The Bell states preparation circuit is a basic circuit required in quantum teleportation. We describe how to implement it in all-fiber technology. The basic building blocks for its implementation are directional couplers and highly nonlinear optical fiber (HNLF). Because the quantum information processing is based on delicate superposition states, it is sensitive to quantum errors. In order to enable fault-tolerant quantum computing the use of quantum error correction is unavoidable. We show how to implement in all-fiber technology encoders and decoders for sparse-graph quantum codes, and provide an illustrative example to demonstrate this implementation. We also show that arbitrary set of universal quantum gates can be implemented based on directional couplers and HNLFs.

Identifying Phases of Quantum Many-Body Systems That Are Universal for Quantum Computation

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possesses a quantum (zero-temperature) phase transition between a disordered phase and an ordered "cluster phase" in which it is possible to perform a universal set of quantum gates.

Optimal quantum multiparameter estimation and application to dipole- and exchange-coupled qubits

We consider the problem of quantum multiparameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron-spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters---explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, produces a universal set of quantum gates. However, the unknown parameters must be known precisely to generate high-fidelity gates. We use the Cram\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters and present a complete analysis of the optimal experimental configuration. Our method of transforming the constrained optimal parameter estimation problem into a convex optimization is powerful and widely applicable to other systems.

Quantum computation with quantum-dot spin qubits inside a cavity

Universal set of quantum gates are realized from quantum-dot spin qubits inside a cavity via two-channel Raman interactions. Individual addressing and effective switch of the cavity mediated interaction are directly possible here. This simple realization of all wanted interaction for selective qubits makes current scenario more suitable for scalable quantum computation.

Bell’s Inequality and Universal Quantum Gates in a Cold-Atom Chiral Fermionicp-Wave Superfluid

We propose and analyze a probabilistic scheme to entangle two spatially separated topological qubits in a p{x}+ip{y} superfluid using controlled collisions between atoms in movable dipole traps and unpaired atoms inside vortex cores in the superfluid. We discuss how to test the violation of Bell's inequality with the generated entanglement. A set of universal quantum gates is shown to be implementable deterministically using the entanglement despite the fact that the entangled states can be created only probabilistically.

Simulating and Compiling Code for the Sequential Quantum Random Access Machine

We present the SQRAM architecture for quantum computing, which is based on Knill's QRAM model. We detail a suitable instruction set, which implements a universal set of quantum gates, and demonstrate the operation of the SQRAM with Deutsch's quantum algorithm. The compilation of high-level quantum programs for the SQRAM machine is considered; we present templates for quantum assembly code and a method for decomposing matrices for complex quantum operations. The SQRAM simulator and compiler are discussed, along with directions for future work.

Universal Set of Quantum Gates for Double-Dot Spin Qubits with Fixed Interdot Coupling

We propose a set of universal gate operations for the singlet-triplet qubit realized by two-electron spins in a double quantum dot, in the presence of a fixed inhomogeneous magnetic field. All gate operations are achieved by switching the potential offset between the two dots with an electrical bias, and do not require time-dependent control of the tunnel coupling between the dots. We analyze the two-electron dynamics and calculate the effective qubit rotation angle as a function of the applied electric bias. We present explicit gate sequences for single-qubit rotations about two orthogonal axes, and a CNOT gate sequence, completing the universal gate set.

Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the $\ensuremath{\pi}∕8$ gate, are also explicitly implemented by quasihole braidings. Instead of the $\ensuremath{\pi}∕8$ gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled-$Z$ precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate ${g}_{3}$.

Simulation of quantum logic via collisions of vector solitons

The polarization of a multi-component vector soliton (of the Manakov type) can be thought of as a state vector of a system of qubits (a register of quantum information). A change of this state on demand via colliding the register pulse with other solitons is shown to be possible with arbitrary accuracy. The parameters (polarization, pulse width, velocity) of the register-switching solitons corresponding to the computationally universal set of quantum gates are found. Physical realizations of information processing using effects of the self-focusing of optical media or of the self-induced transparency are considered.

Superconducting qubit network with controllable nearest-neighbour coupling

We investigate the design and functionality of a network of loop-shaped charge qubits with switchable nearest-neighbour coupling. The qubit coupling is achieved by placing large Josephson junctions (JJs) at the intersections of the qubit loops and selectively applying bias currents. The network is scalable and makes it possible to perform a universal set of quantum gates. The coupling scheme allows gate operation at the charge degeneracy point of each qubit, and also applies to charge-phase qubits. Additional JJs included in the qubit loops for qubit readout can also be employed for qubit coupling.

Classical simulability, entanglement breaking, and quantum computation thresholds

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modeled classically. This question is useful for providing upper bounds on fault-tolerant thresholds, and for understanding the nature of the quantum-classical computational transition. We refine some previously known upper bounds using two different strategies. The first one involves the introduction of bientangling operations, a class of classically simulable machines that can generate at most bipartite entanglement. Using this class we show that it is possible to sharpen previously obtained upper bounds in certain cases. As an example, we show that under depolarizing noise on the controlled-NOT gate, the previously known upper bound of 74% can be sharpened to around 67%. Another interesting consequence is that measurement-based schemes cannot work using only two-qubit nondegenerate projections. In the second strand of the work we utilize the Gottesman-Knill theorem on the classically efficient simulation of Clifford group operations. The bounds attained using this approach for the $\ensuremath{\pi}∕8$ gate can be as low as 15% for general single-gate noise, and 30% for dephasing noise.

All-electrical quantum computation with mobile spin qubits

We describe and discuss a solid state proposal for quantum computation with mobile spin qubits in one-dimensional systems, based on recent advances in spintronics. Static electric fields are used to implement a universal set of quantum gates, via the spin-orbit and exchange couplings. Initialization and measurement can be performed either by spin injection from/to ferromagnets, or by using spin filters and mesoscopic spin polarizing beam-splitters. The vulnerability of this proposal to various sources of error is estimated by numerical simulations. We also assess the suitability of various materials currently used in nanotechnology for an actual implementation of our model.

Investigation on Single-Electron Dynamics in Coupled GaAs–AlGaAs Quantum Wires

The aim of this paper is the study of the single-electron coherent propagation in a quantum-computing gate made of coupled quantum wires. The structure under investigation is based on a two-dimensional (2-D) electron gas realized in a modulation-doped GaAs-AlGaAs heterostructure. A number of surface electrodes are used to form one-dimensional channels. The profile of the conduction band at the heterojunction has been computed numerically by solving the three-dimensional Poisson equation on the whole structure at 300 mK. Finally, a single-electron wavefunction is propagated within the so-formed quantum wire geometry by means of a 2-D, time-dependent Schro/spl uml/dinger solver. Results are shown for a single-qubit rotation gate implementing a quantum-NOT transformation. This work is part of a feasibility study on a solid-state realization of a universal set of quantum gates.

Quantum Computations with Transverse Modes of an Optical FieldPropagating in Waveguides

A fully optical method to perform quantum computation with transverse modesof the optical field propagating in waveguide is proposed by supplying theprescriptions for a universal set of quantum gates. The proposal for quantumcomputation is based on implementing a quantum bit with two normal modes ofmulti-mode waveguides. The proposed C-NOT gate has the potential of beingmore compact and easily realized than some optical implementations, since itis based on planar lightwave circuit technology and can be constructed byusing Mach-Zehnder interferometer having semiconductoroptical amplifiers with very large refractive nonlinearity in its arms.

Universal Quantum Gates Based on Both Geometric and DynamicPhases in Quantum Dots

A large-scalable quantum computer model, whose qubits are represented bythe subspace subtended by the ground state and the single exciton stateon semiconductor quantum dots, is proposed. A universal set of quantumgates in this system may be achieved by a mixed approach, composed ofdynamic evolution and nonadiabatic geometric phase.

Holonomic Quantum Computation with Josephson Networks

It is well known that it is possible to build quantum gates based entirely on the action of geometric phases. This approach is called holonomic quantum computation. Here we show that it is possible to generate and detect non-Abelian geometric phases in the charge dynamics of a network of mesoscopic Josephson junctions. The scheme can be used to realize a universal set of quantum gates.

Implementation of universal quantum gates based on nonadiabatic geometric phases.

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.

Quantum Information Processing Using Electron Spins in Quantum Dots

We review the theoretical proposal for quantum computing with electron spins in quantum confined structures and discuss the essential requirements for its implementation. The quantum bit is represented by the spin of the electron, as opposed to the charge (orbital) degrees of freedom. In this context, we analyze a number of physical realizations of the elementary building blocks for quantum computation: a universal set of quantum gates, state preparation and measurement. Finally, we discuss the production, transport, and detection of electronic Einstein-Podolski-Rosen pairs, which are an important resource for quantum communication.

QUANTUM COMPUTATION WITH BALLISTIC ELECTRONS

We describe a solid state implementation of a quantum computer using ballistic single electrons as flying qubits in 1D nanowires. We show how to implement all the steps required for universal quantum computation: preparation of the initial state, measurement of the final state and a universal set of quantum gates. An important advantage of this model is the fact that we do not need ultrafast optoelectronics for gate operations. We use cold programming (or pre-programming), i.e. the gates are set before launching the electrons; all programming can be done using static electric fields only.

Quantum Computations with Polarized Photons

We propose a fully optical method to perform any quantum computation by supplying the prescriptions for a universal set of quantum gates. We also give the methods for the generation of input states and the realization of final measurements. The apparatus is scalable, and relies on high Kerr non-linearities.