The dynamics of the nuclear-spin quantum computer with large number (L=1000) of qubits is considered using a perturbation approach, based on approximate diagonalization of exponentially large sparse matrices. Small parameters are introduced and used to compute the error in implementation of entanglement between remote qubits, by applying a sequence of resonant radio-frequency pulses. The results of the perturbation theory are tested using exact numerical solutions for small number of qubits.
We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.
Cluster states are entangled multipartite states which enable to do universal quantum computation with local measurements only. We show that these states have a very simple interpretation in terms of valence bond solids, which allows to understand their entanglement properties in a transparent way. This allows to bridge the gap between the differences of the measurement-based proposals for quantum computing, and we will discuss several features and possible extensions.
The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation of quantum gates in the computational model. We introduce a new universal set of qudit gates and use it to give a constructive proof of the universality of d1WQC. We characterise the set of gates that can be performed in one parallel time step in this model.
Holonomic quantum computation is a quantum computation strategy that promises some built-in noise-resilience features. Here, we propose a scheme for nonadiabatic holonomic quantum computation with nitrogen-vacancy center electron spins, which are characterized by fast quantum gates and long qubit coherence times. By varying the detuning, amplitudes, and phase difference of lasers applied to a nitrogen-vacancy center, one can directly realize an arbitrary single-qubit holonomic gate on the spin. Meanwhile, with the help of cavity-assisted interactions, a nontrivial two-qubit holonomic quantum g…
A scheme for decoupling and selectively recoupling large networks of dipolar-coupled spins is proposed. The scheme relies on a combination of broadband, decoupling pulse sequences applied to all the nuclear spins with a band-selective pulse sequence for single spin rotations or recoupling. The evolution-time overhead required for selective coupling is independent of the number of spins, subject to time-scale constraints, for which we discuss the feasibility. This scheme may improve the scalability of solid-state-NMR quantum computing architectures.
We propose a decoherence-free subspaces (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent Coulomb interaction is exploited, and the universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for the ion array system is demonstrated, either by an adiabatic way of switching on and off the interactions, or by a fast gate scheme with comprehensive DFS encoding and noise decoupling techniques.
Experimental realization of a universal set of quantum logic gates with high-fidelity is critical to quantum information processing, which is always challenging by inevitable interaction between the quantum system and environment. Geometric quantum computation is noise immune, and thus offers a robust way to enhance the control fidelity. Here, we experimentally implement the recently proposed extensible nonadiabatic holonomic quantum computation with solid spins in diamond at room-temperature, which maintains both flexibility and resilience against decoherence and system control errors. Compar…
The response of a quadrupolar nucleus (nuclear spin with I>1/2) to an oscillating radio-frequency (RF) pulse/field is delicately dependent on the ratio of the quadrupolar coupling constant to the amplitude of the pulse in addition to its duration and oscillating frequency. Consequently, analytic description of the excitation process in the density operator formalism has remained less transparent within existing theoretical frameworks. As an alternative, the utility of the "concept of effective Floquet Hamiltonians" is explored in the present study to explicate the nuances of the excitation pro…
The high-speed implementation and robustness against of non-adiabatic holonomic quantum computation provide a new idea for overcoming the difficulty of quantum system interacting with the environment easily decoherence, which realizing large-scale quantum computer construction. Here, we show that a high-fidelity quantum gates to implement non-adiabatic holonomic quantum computation under solid-state spin in Nitrogen-Vacancy(NV) centers, providing an extensible experimental platform that has the potential for room-temperature quantum computing, which has increased attention recent years. Compar…
We present the constructon and detailed analysis of highly-optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order. This allows a semi-analytical analysis of the performance of the constructed shapes in sequences and composite pulses by computing the corresponding leading-order error operators. Higher orders can be analyzed with the numerical technique suggested by us previously. We illustrate the technique by analysing several composite pulses designed to protect against…
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi …
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. By far, there is no experimental realization of adiabatic quantum computation on a single solid spin system under ambient conditions, which has been proved to be a compatible candidate for scalable quantum computation. In this letter, we report on the first experimental realization of an adiab…
Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. The procedures for realizing state labeling, state transformation and coherence selection in Floquet space are given. It suggests that by this method, the largest number of qubits can easily surpass that achievable with other techniques. Unlike other modalities proposed for…
Metal atoms in solid and liquid helium-4 have attracted some interest either as a way to keep the atoms in a weakly perturbing matrix, or using them as a probe for the helium host medium. Laser sputtering with nanosecond pulsed lasers is the most often used method for atom production, resulting however in a substantial perturbation of the matrix. We show that a much weaker perturbation can be obtained by using femtosecond laser pulses with energy as low as 10 $μ$J. As an unexpected benefit, the atomic density produced is much higher.
We review our work on the interplay between non-resonant gates and solid state environment in various solid state quantum computer architectures and the resulting gate errors. Particular, we show that adiabatic condition can be satisfied in small quantum dots, while higher energy excited states can play important role in the evolution of a Cooper-pair-box based quantum computer model. We also show that complicated bandstructure such as that of Si can pose a severe gate control problem.
In this paper we analyze the dynamics in a spin-model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no any danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to…
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa al…
Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the spin-qubits in solids with the accuracy required by fault-tolerant quantum computation under ambient conditions remains elusive. Here, we quantitatively characterize the source of noise during quantum gate operation and demonstrate strategies to suppress the effect of these. A universal set of logic gates in a nitrogen-vacancy centre in diamond are reported w…
An adiabatic cyclic evolution of control parameters of a quantum system ends up with a holonomic operation on the system, determined entirely by the geometry in the parameter space. The operation is given either by a simple phase factor (a Berry phase) or a non-Abelian unitary operator depending on the degeneracy of the eigenspace of the Hamiltonian. Geometric quantum computation is a scheme to use such holonomic operations rather than the conventional dynamic operations to manipulate quantum states for quantum information processing. Here we propose a geometric quantum computation scheme whic…
Solid state quantum computing proposals rely on adiabatic operations of the exchange gate among localized spins in nanostructures. We study corrections to the Heisenberg interaction between lateral semiconductor quantum dots in an external magnetic field. Using exact diagonalization we obtain the regime of validity of the adiabatic approximation. We also find qualitative corrections to the Heisenberg model at high magnetic fields and in looped arrays of spins. Looped geometries of localized spins generate flux dependent, multi-spin terms which go beyond the basic Heisenberg model.
The solid effect is one of the simplest and most effective mechanisms for Dynamic Nuclear Polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches which differ in the way the hyperfine interaction i…
Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations artificially. Here we show theoretically that quantum correlations exhibited in the two-dimensional valence bond solid phase of a quantum antiferromagnet, modeled by Affleck, Kennedy, Lieb, and Tasaki as a precursor of spin liquids and topological orders, are sufficiently complex yet structured enough to simulate universal quantum computation when every single s…
We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transi…
We investigate the sensitivity of nonintegrable large-spin quantum lattices to small perturbations with a particular focus on the time reversal experiments known in statistical physics as "Loschmidt echoes" and in nuclear magnetic resonance (NMR) as "magic echoes". Our numerical simulations of quantum spin-$7\frac{1}{2}$ clusters indicate that there is a regime, where Loschmidt echoes exhibit nearly exponential sensitivity to small perturbations with characteristic constant approximately equal to twice the value of the largest Lyapunov exponent of the corresponding classical spin clusters. The…
Establishing a predictive ab initio method for solid systems is one of the fundamental goals in condensed matter physics and computational materials science. The central challenge is how to encode a highly-complex quantum-many-body wave function compactly. Here, we demonstrate that artificial neural networks, known for their overwhelming expressibility in the context of machine learning, are excellent tool for first-principles calculations of extended periodic materials. We show that the ground-state energies in real solids in one-, two-, and three-dimensional systems are simulated precisely, …
