The use of spin torque as a substitute for magnetic fields is now well established for classical operations like the switching of a nanomagnet. What we are describing here could be viewed as an application of spin torque like effects to quantum processes involving single qubit rotations as well as two qubit entanglement. A key ingredient of this scheme is the use of a large number of itinerant electrons whose cumulative effect is to produce the desired qubit operations on static spins. Each interaction involves entanglement and collapse of wavefunctions so that the operation is only approximately unitary. However, we show that the non-unitary component of the operations can be kept below tolerable limits with proper design. As a capstone example, we present the implementation of a complete CNOT gate using the proposed spin potential based architecture, and show that the fidelity under ideal conditions can be made acceptably close to one.
The use of spin torque as a substitute for magnetic fields is now well established for classical operations like the switching of a nanomagnet. What we are describing here could be viewed as an application of spin torque like effects to quantum processes involving single qubit rotations as well as two qubit entanglement. A key ingredient of this scheme is the use of a large number of itinerant electrons whose cumulative effect is to produce the desired qubit operations on static spins. Each interaction involves entanglement and collapse of wavefunctions so that the operation is only approximately unitary. However, we show that the non-unitary component of the operations can be kept below tolerable limits with proper design. As a capstone example, we present the implementation of a complete CNOT gate using the proposed spin potential based architecture, and show that the fidelity under ideal conditions can be made acceptably close to one.
Spin-torque-based quantum computing (QC) architecture is emerging as one of the novel technologies to meet scalability challenge due to its intra architecture spin qubit state manipulation. The existing model for spin-torque-based QC does not include the ratio of reflection barrier height to exchange interaction to the transmission coefficients. Therefore, in this paper, a modified matrix is proposed to analyze the effect of ratio of reflection barrier height to exchange interaction on electron-qubit interaction, deviation of axis of rotation for single-qubit rotation, and average error probability for two-qubit rotation in a spin-torque-based n-qubit reconfigurable architecture. In addition, the conventional and reduced quantum gates are compared for existing and modified matrices. The quantum gates performance is analyzed in terms of number of electrons required per gate for the electron-qubit interaction, gate fidelity, number of elementary quantum operations per gate, and gate execution time. Reconfigurability is accomplished through barrier height modulation to reduce the architecture hardware. Moreover, a novel nanomagnet-based spin reservoir is incorporated in the architecture for the nonlocal spin injection to facilitate only spin-based operations. High fidelity (~99%) of quantum gates is attained for the fault-tolerant QC.
We have seen how information can be encoded onto a quantum system by selecting the state in which it is prepared. Retrieving the information is achieved by performing a measurement, and the optimal measurement in any given situation is usually a generalized measurement. In between preparation and measurement, the information resides in the quantum state of the system, which evolves in a manner determined by the Hamiltonian. The associated unitary transformation may usefully be viewed as quantum information processing; if we can engineer an appropriate Hamiltonian then we can use the quantum evolution to assist in performing computational tasks. Our objective in quantum information processing is to implement a desired unitary transformation. Typically this will mean coupling together a number, perhaps a large number, of qubits and thereby generating highly entangled states. It is fortunate, although by no means obvious, that we can realize any desired multiqubit unitary transformation as a product of a small selection of simple transformations and, moreover, that each of these need only act on a single qubit or on a pair of qubits. The situation is reminiscent of digital electronics, in which logic operations are decomposed into actions on a small number of bits. If we can realize and control a very large number of such operations in a single device then we have a computer. Similar control of a large number of qubits will constitute a quantum computer. It is the revolutionary potential of quantum computers, more than any other single factor, that has fuelled the recent explosion of interest in our subject. We shall examine the remarkable properties of quantum computers in the next chapter. In digital electronics, we represent bit values by voltages: the logical value 1 is a high voltage (typically +5 V) and 0 is the ground voltage (0 V). The voltage bits are coupled and manipulated by transistor-based devices, or gates. The simplest gates act on only one bit or combine two bits to generate a single new bit, the value of which is determined by the two input bits. For a single bit, with value 0 or 1, the only possible operations are the identity (which does not require a gate) and the bit flip.
Molecular nanomagnets can be considered as serious candidates for the definition of a scalable and reliable quantum computing technology: information is encoded on their spins and they ensure relaxation and decoherence times sufficiently long for the execution of tens of quantum operations. Among these devices, Cr7Ni supramolecular complexes are extremely of interest since they implement a universal set of quantum gates, made of single-qubit gates and the two-qubit Controlled-phase gate. A model for analyzing Cr7Ni molecules and a potential quantum computer architecture are proposed: starting from the energy parameters required for spin manipulations, these systems have been proved to implement elementary quantum algorithms. Within this paper, two, three and four-qubit systems have been analyzed: the simulation of quantum operations and the analysis of dynamical non-idealities have been done in parallel. Our approach enables the definition of an operating point - in terms of magnetic driving fields and latency - in which the execution of elementary quantum algorithms is characterized by negligible errors. The proposed model has been entirely implemented in MATLAB, thus obtaining a software infrastructure for the analysis of Cr7Ni molecules that can be extended to quantum systems with analogous Hamiltonian and behavior.
Quantum information and quantum computation are emerging research areas based on the properties of quantum resources, such as superposition and entanglement. In the quantum gate array version, the use of convenient and proper gates is essential. While these gates adopt theoretically convenient forms to reproduce computational algorithms, their design and feasibility depend on specific quantum systems and physical resources used in their setup. These gates should be based on systems driven by physical interactions ruled by a quantum Hamiltonian. Then, the gate design is restricted to the properties and the limitations imposed by the interactions and the physical elements involved. This work shows how anisotropic Heisenberg-Ising interactions, written in a non-local basis, allow the reproduction of quantum computer operations based on unitary processes. We show that gates can be generated by a pulse sequence of driven magnetic fields. This fact states alternative techniques in quantum gate design for magnetic systems. A brief final discussion around associated fault tolerant extensions to the current work is included.
We model the evolving time-dependent electronic structure of a solid-state quantum gate as it performs basic quantum operations. Our time-dependent configuration-interaction method follows the evolution of two donor electron spin qubits interacting with a third, optically excited, control spin in an applied magnetic field, a possible realization of the basic component of a proposed quantum information processor. We identify unitary operations which approximately disentangle the control spin, and use them to construct high-accuracy two-electron operations that are locally equivalent to CNOT, SWAP and operations. From our evaluation of the accuracy of a set of candidate gates we estimate the residual entanglement of the control electron and overall gate operation times. These results attest to the feasibility of the silicon-based quantum gates proposed by Stoneham, Fisher and Greenland.
In Part I of this article, we introduced the notion of encoding binary bit information in the spin polarization of a single electron confined in a quantum dot and placed in a magnetic field. The spin polarization becomes bistable in a magnetic field and the spin can point either parallel to the field or antiparallel to it. These two polarizations encode the classical binary bits 0 and 1. We showed that since the bits can be switched by simply flipping the electron's spin without physically moving the electron in space and causing a current, the energy dissipated during the bit flip operation could be made very small. In Part II we discuss the notion of using a single electron's spin as a quantum bit (or qubit) that represents information in quantum computers. Just as spin is superior to charge as a vehicle to host classical bit information in classical computers it turns out that spin is superior to charge to host quantum information as well. That is why spin-based quantum information processing is gradually becoming the staple of scalable solid state versions of quantum computers.