An electron-nucleon double spin(ENDOS) solid-state quantum computer scheme is proposed. In this scheme, the qubits are the nuclear spins of phosphorus ion implanted on the (111) surface of $^{28}$Si substrate. An $^{13}$C atom on a scanning tunnelling probe tip is used both to complete single qubit and two-qubit control-not operation, and single qubit measurement. The scheme does not require interactions between qubits, and can accomplish two qubits without the use of SWAP gate.
This scheme is scalable, and can be implemented with present-day or near-future technologies.
Here we made an analysis of the principles of a semiconductor NMR quantum computer and its developments. The known variant of an individual-access computer (B. Kane) and alternative solid-state bulk-ensemble approach versions allowing to avoid some difficulties in implementing the first variant are considered.
We propose a solid-state nuclear spin quantum computer based on application of scanning tunneling microscopy (STM) and well-developed silicon technology. It requires the measurement of tunneling current modulation caused by the Larmor precession of a single electron spin. Our envisioned STM quantum computer would operate at the high magnetic field ($\sim 10$T) and at low temperature $\sim 1$K.
We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: (a) preparation of the ground state, (b) one- and two- qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1K.
By removing a $^{12}C$ atom from the tetrahedral configuration of the diamond, replace it by a $^{13}C$ atom, and repeating this in a linear direction, it is possible to have a linear chain of nuclear spins one half and to build a solid state quantum computer. One qubit rotation and controlled-not (CNOT) quantum gates are obtained immediately from this configuration, and CNOT quantum gate is used to determined the design parameters of this quantum computer.
We examine a stochastic noise process that has a decohering effect on the average evolution of qubits in the quantum register of the solid state quantum computer proposed by Kane. We consider the effects of this process on the single qubit operations necessary to perform quantum logical gates and derive an expression for the fidelity of these gates in this system. We then calculate an upper bound on the level of this stochastic noise tolerable in a workable quantum computer.
A quantum information processing device, based on bulk solid state NMR of the quasi-one dimensional material hydroxyapatite, is proposed following the magnetic resonance force microscopy work of Yamamoto et al (quant-ph/0009122). In a macroscopic sample of hydroxyapatite, our solid state NMR model yields a limit of 10^8 qubits imposed by physics, while development of current technological considerations should allow an upper bound in the range of hundreds to thousands of qubits.
The method of iterated resolvents is used to obtain an effective Hamiltonian for neighbouring qubits in the Kane solid state quantum computer. In contrast to the adiabatic gate processes inherent in the Kane proposal we show that free evolution of the qubit-qubit system, as generated by this effective Hamiltonian, combined with single qubit operations, is sufficient to produce a controlled-NOT (c-NOT) gate. Thus the usual set of universal gates can be obtained on the Kane quantum computer without the need for adiabatic switching of the controllable parameters as prescribed by Kane. Both the fi…
The susceptibility of the transformed information to the filed and system parameters is investigated for the Kane solid state computer. It has been shown, that the field polarization and the initial state of the system play the central roles on the abrupt and gradual quench of the purity and the fidelity. If the field and the initial state are in different polarizations, then the purity and the fidelity decrease abruptly, while for the common polarization the decay is gradual and smooth. For some class of initial states one can send the information without any loss. Therefore, by controlling o…
As an ensemble scheme of solid-state NMR quantum computers the extension of Kane's many-qubits silicon scheme based on the array of 31 P donor atoms are spaced lengthwise of the strip gates is considered. The possible planar topology of such ensemble quantum computer is suggested. The estimation of the output NMR signal was performed and it was shown that for the number N>=10^5 of ensemble elements involving L~10^3 qubits each, the standard NMR methods are usable. As main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance freq…
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
We discuss the operational definition of decoherence in various solid state systems. In particular, we review, in the context of spin-based solid state quantum computation, the introduction of $T_1$ and $T_2$ to describe decoherence in a two level system. We provide a perspective on recent experiments involving the manipulation of spin coherence in semiconductors, and discuss specific decoherence and dephasing issues in electron spin-based quantum dot quantum computer architectures.
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
We consider a mechanism to generate controllable qudit-qudit interactions in a charge-position paradigm for a quantum computer, through the use of auxiliary states. By controlling the tunneling rates onto these auxiliaries from the qudits proper, we can controllably switch the entangling operations. We consider a practical architecture in which to realize such a computer and examine the associated Hilbert space dimension.
We demonstrate that complete set of gates can be realized in a DXD superconducting solid state quantum computer (quamputer), thereby proving its universality.
It is shown that coherent spin motion of electron-hole pairs localized in band gap states of silicon can influence charge carrier recombination. Based on this effect, a readout concept for silicon based solid-state spin--quantum computers as proposed by Kane is suggested. The 31P quantum bit (qbit) is connected via hyperfine coupling to the spin of the localized donor electron. When a second localized and singly occupied electronic state with an energy level deep within the band gap or close to the valence edge is in proximity, a gate controlled exchange between the 31P nucleus and the two ele…
We investigate the decoherence process for a quantum register composed of N qubits coupled to an environment. We consider an environment composed of one common phonon bath and several electronic baths. This environment is relevant to the implementation of a charge based solid-state quantum computer. We explicitly compute the time evolution of all off-diagonal terms of the register's reduced density matrix. We find that in realistic configurations, "superdecoherence" and "decoherence free subspaces" do not exist for an N-qubit system. This means that all off-diagonal terms decay like exp(-q(t)N…
We theoretically consider coherence times for spins in two quantum computer architectures, where the qubit is the spin of an electron bound to a P donor impurity in Si or within a GaAs quantum dot. We show that low temperature decoherence is dominated by spin-spin interactions, through spectral diffusion and dipolar flip-flop mechanisms. These contributions lead to 1-100 $μ$s calculated spin coherence times for a wide range of parameters, much higher than former estimates based on $T_{2}^{*}$ measurements.
Several solid state quantum computer schemes are based on the manipulation of electron and nuclear spins of single donor atoms in a solid matrix. The fabrication of qubit arrays requires the placement of individual atoms with nanometer precision and high efficieny. In this article we describe first results from low dose, low energy implantations and our development of a low energy (<10keV), single ion implantation scheme for 31P(q+) ions. When 31P(q+) ions impinge on a wafer surface, their potential energy (9.3 keV for P15+) is released, and about 20 secondary electrons are emitted. The emissi…
Problems in realization of silicon-based solid-state NMR quantum computer with ensemble addressing to qubits are considered. It is presented the extension of Kane's scheme to ensemble approach version with strip gates. For the initialization of nuclear quantum states it is proposed to use the solid-state effect in ENDOR technique whereby the nuclear spins can be practically fully polarized or, that is the same, indirect cooled to the spin temperature less than ~ 1 mK. It is suggested the possible planar silicon topology of such ensemble quantum computer and shown that the measurement with stan…
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.
It is proposed to map the quantum information qubit not to individual spin 1/2 states, but to the collective spin states being eigenfunctions of the Hamiltonian including spin-spin interactions, which may be not small. Such an approach allows to introduce more stable calculation basis for quantum computer based on the solid state NMR systems.
In the paper is considered stairway-like design of quantum computer, i.e., array of double quantum dots or wells. The model is quite general to include wide variety of physical systems from coupled quantum dots in experiments with solid state qubits, to very complex one, like DNA molecule. At the same time it is concrete enough, to describe main physical principles for implementation of universal set of quantum gates, initialization, measurement, decoherence, etc.
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.
A BosonSampling device is a quantum machine expected to perform tasks intractable for a classical computer, yet requiring minimal non-classical resources as compared to full-scale quantum computers. Photonic implementations to date employed sources based on inefficient processes that only simulate heralded single-photon statistics when strongly reducing emission probabilities. BosonSampling with only single-photon input has thus never been realised. Here, we report on a BosonSampling device operated with a bright solid-state source of single-photon Fock states with high photon-number purity: t…
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.
We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear s…
Some fascinating phenomena have been investigated, hence spin vortex systems are a hot subarea of solid-state physics. However, simulations of these systems require some simplifications. Quantum computers have the potential to simulate these systems without them. Therefore, we simulated the time propagation of spin vortex systems centered by small polarons by the simulator of quantum computers. As a result, we revealed that these systems have much shorter periods than XXZ models and are never be relaxed. Though there is intrinsic persistent noise, this result will affect both fundamental and a…
Correct swap action can be realized via the control of the anisotropic Heisenberg interaction in solid-state quantum systems. The conditions of performing a swap are derived by the dynamics of arbitrary bipartite pure state. It is found that swap errors can be eliminated in the presence of symmetric anisotropy. In realistic quantum computers with unavoidable fluctuations, the gate fidelity of swap action is estimated. The scheme of quantum computation via the anisotropic Heisenberg interaction is implemented in a one dimensional quantum dots. The slanting and static magnetic field can be used …
We discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a spin chain. Analytical estimates are presented for possible correlated errors caused by non-resonant transitions. A range of parameters is given in which non-resonant effects can be minimized.
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. Fidelity of the target states corresponding to each algorithm is numerically …
We study the error rate of CNOT operations in the Kane solid state quantum computer architecture. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off diagonal elements of the system's density matrix. Using available spin echo decay data, the CNOT error rate is estimated at approsimately 10^{-3}.
A scalable, high-performance quantum processor can be implemented using near-resonant dipole-dipole interacting dopants in a solid state host. In this scheme, the qubits are represented by ground and subradiant states of effective dimers formed by pairs of closely spaced two-level systems, while the two-qubit entanglement either relies on the coherent excitation exchange between the dimers or is mediated by external laser fields.
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories, and we give examples for a specific class of materials, i.e., spin defects in solids. These are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communicat…
We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. The phase and probability errors caused by unwanted transitions are minimized and computed numerically.
In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a CNOT gate is $8.3 \times 10^{-5}$. We also compute the fidelities of Z, X, Swap, and Controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.
We propose an efficient method to realize a large-scale one-way quantum computer in a two-dimensional (2D) array of coupled cavities, based on coherent displacements of an arbitrary state of cavity fields in a closed phase space. Due to the nontrivial geometric phase shifts accumulating only between the qubits in nearest-neighbor cavities, a large-scale 2D cluster state can be created within a short time. We discuss the feasibility of our method for scale solid-state quantum computation
We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states,…
A major difficulty in realizing a solid-state quantum computer is the reliable measurement of the states of the quantum registers. In this paper, we propose an efficient readout scheme making use of the resonant tunneling of a ballistic electron produced by a single electron pump. We treat the measurement interaction in detail by modeling the full spatial configuration, and show that for pumped electrons with suitably chosen energy the transmission coefficient is very sensitive to the qubit state. We further show that by using a short sequence of pumping events, coupled with a simple feedback …
The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these er…
Proposals for solid state quantum computing are extremely promising as they can be used to built room temperature quantum computers. If such a quantum computer is ever built it would require in-built sources of nonclassical states required for various quantum information processing tasks. Possibilities of generation of such nonclassical states are investigated here for a physical system composed of a monochromatic light coupled to a two-band semiconductor with direct band gap. The model Hamiltonian includes both photon-exciton and exciton-exciton interactions. Time evolution of the relevant bo…
\emph{Ab initio} computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH$^+$. Moreover, we report an energy uncertainty (given our model…
The implementation of large-scale fault-tolerant quantum computers calls for the integration of millions of physical qubits, with error rates of physical qubits significantly below 1%. This outstanding engineering challenge may benefit from emerging qubits that are protected from dominating noise sources in the qubits' environment. In addition to different noise reduction techniques, protective approaches typically encode qubits in global or local decoherence-free subspaces, or in dynamical sweet spots of driven systems. We exemplify such protective qubits by reviewing the state-of-art in prot…
We report NMR experiments using high-power, RF decoupling techniques to show that a 29-Si nuclear spin qubit in a solid silicon crystal at room temperature can preserve quantum phase for 10^9 precessional periods. The coherence times we report are longer than for any other observed solid-state qubit by more than four orders of magnitude. In high quality crystals, these times are limited by residual dipolar couplings and can be further improved by isotopic depletion. In defect-heavy samples, we provide evidence for decoherence limited by 1/f noise. These results provide insight toward proposals…
Progress toward the realization of quantum computers requires persistent advances in their constituent building blocks - qubits. Novel qubit platforms that simultaneously embody long coherence, fast operation, and large scalability offer compelling advantages in the construction of quantum computers and many other quantum information systems. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via …
I provide an introduction to quantum computers, describing how they might be realized using language accessible to a solid state physicist. A listing of the minimal requirements for creating a quantum computer is given. I also discuss several recent developments in the area of quantum error correction, a subject of importance not only to quantum computation, but also to some aspects of the foundations of quantum theory.
We describe how the spin coherence time of a localized electron spin in solids, i.e. a solid state spin qubit, can be prolonged by applying designed electron spin resonance pulse sequences. In particular, the spin echo decay due to the spectral diffusion of the electron spin resonance frequency induced by the non-Markovian temporal fluctuations of the nuclear spin flip-flop dynamics can be strongly suppressed using multiple-pulse sequences akin to the Carr-Purcell-Meiboom-Gill pulse sequence in nuclear magnetic resonance. Spin coherence time can be enhanced by factors of 4-10 in GaAs quantum d…
A solid-state quantum computer with dipolar coupling between qubits is proposed. The qubits are formed by the low-lying states of an isolated acceptor in silicon. The system has the scalability inherent to spin-based solid state systems, but the spatial separation between the qubits is an order of magnitude larger. Despite strong dipolar inter-qubit coupling, the decoherence rate, as measured by electric dipolar echoes at an energy splitting of 1.5 GHz, is less than 1 kHz at low temperatures. For inter-acceptor distances of 100 nm and for modest microwave field amplitudes (50 V/cm) the clock f…
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…
Integrated quantum photonics provides a promising route towards scalable solid-state implementations of quantum networks, quantum computers, and ultra-low power opto-electronic devices. A key component for many of these applications is the photonic quantum logic gate, where the quantum state of a solid-state quantum bit (qubit) conditionally controls the state of a photonic qubit. These gates are crucial for development of robust quantum networks, non-destructive quantum measurements, and strong photon-photon interactions. Here we experimentally realize a quantum logic gate between an optical …
Phononic quantum networks feature distinct advantages over photonic networks for on-chip quantum communications, providing a promising platform for developing quantum computers with robust solid-state spin qubits. Large mechanical networks including one-dimensional chains of trapped ions, however, have inherent and well-known scaling problems. In addition, chiral phononic processes, which are necessary for conventional phononic quantum networks, are difficult to implement in a solid-state system. To overcome these seemingly unsolvable obstacles, we have developed a new network architecture tha…
We propose a scheme for quantum information processing based on donor electron spins in semiconductors, with an architecture complementary to the original Kane proposal. We show that a naive implementation of electron spin qubits provides only modest improvement over the Kane scheme, however through the introduction of global gate control we are able to take full advantage of the fast electron evolution timescales. We estimate that the latent clock speed is 100-1000 times that of the nuclear spin quantum computer with the ratio $T_{2}/T_{ops}$ approaching the $10^{6}$ level.
We show that the edge of a two-dimensional topological insulator can be used to construct a solid state Stern-Gerlach spin-splitter. By threading such a Stern-Gerlach apparatus with a magnetic flux, Ahranov-Bohm like interference effects are introduced. Using ferromagnetic leads, the setup can be used to both measure magnetic flux and as a spintronics switch. With normal metallic leads a switchable spintronics NOT-gate can be implemented. Furthermore, we show that a sequence of such devices can be used to construct a single-qubit $SU(2)$-gate, one of the two gates required for a universal quan…
A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are Si-29 nuclear spins arranged as chains in a Si-28 (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient. No impurity dopants or electrical contacts are needed. Initialization is accomplished by optical pumping, algorithmic cooling, and pseudo-pure state techniques. Magnetic resonance force microscopy is used for readout. This proposal takes advantage of many of the successful aspects of solution NMR quantum computation, including ensemble measurement, RF contro…
