Using high-level ab initio many-body theory, we theoretically propose that the Dy and the Ni atoms in the [Dy 2 Ni 2 (L) 4 (NO 3 ) 2 (DMF) 2 ] real molecular magnet as well as in its core, that is, the [Dy 2 Ni 2 O 6 ] system, act as two-level qubit systems. Despite their spatial proximity we can individually control each qubit in this highly correlated real magnetic system through specially designed laser-pulse combinations. This allows us to prepare any desired two-qubit state and to build several classical and quantum logic gates, such as the two-qubit (binary) CNOT gate with three distinct laser pulses. Other quantum logic gates include the single-qubit (unary) quantum X, Y, and Z Pauli gates; the Hadamard gate (which necessitates the coherent quantum superposition of two many-body electronic states); and the SWAP gate (which plays an important role in Shor’s algorithm for integer factorization). Finally, by sequentially using the achieved CNOT and Hadamard gates we are able to obtain the maximally entangled Bell states, for example, ( 1 2 )(|00⟩ + |11⟩).
Using high-level ab initio many-body theory, we theoretically propose that the Dy and the Ni atoms in the [Dy 2 Ni 2 (L) 4 (NO 3 ) 2 (DMF) 2 ] real molecular magnet as well as in its core, that is, the [Dy 2 Ni 2 O 6 ] system, act as two-level qubit systems. Despite their spatial proximity we can individually control each qubit in this highly correlated real magnetic system through specially designed laser-pulse combinations. This allows us to prepare any desired two-qubit state and to build several classical and quantum logic gates, such as the two-qubit (binary) CNOT gate with three distinct laser pulses. Other quantum logic gates include the single-qubit (unary) quantum X, Y, and Z Pauli gates; the Hadamard gate (which necessitates the coherent quantum superposition of two many-body electronic states); and the SWAP gate (which plays an important role in Shor’s algorithm for integer factorization). Finally, by sequentially using the achieved CNOT and Hadamard gates we are able to obtain the maximally entangled Bell states, for example, ( 1 2 )(|00⟩ + |11⟩).
Quantum entanglement is essential for some applications of quantum information processing such as quantum cryptography, quantum teleportation and superdence coding. A qubit is a two level quantum system and four two-qubit entangled states called Bell states can be easily obtained for two-qubit states. A qutrit is a three level quantum system and Zeeman levels of spin-1 electron or nucleus can be referred as qutrit. For SI (S=1, I=1) spin system there exist nine two-qutrit states. So nine two-qutrit entangled states can be obtained by using the Hadamard and CNOT logic gates. In this study by considering N+@C60 molecule as SI (S=1, I=1) spin system, two-qutrit entangled states are also obtained by using the magnetic resonance selective pulse sequences of Hadamard and CNOT logic gates. Then it is shown that these entangled states can be transformed into each other by the suggested transformation operators.
Molecular nanomagnets are attractive candidate qubits because of their wide inter- and intra-molecular tunability. Uniform magnetic pulses could be exploited to implement one- and two-qubit gates in presence of a properly engineered pattern of interactions, but the synthesis of suitable and potentially scalable supramolecular complexes has proven a very hard task. Indeed, no quantum algorithms have ever been implemented, not even a proof-of-principle two-qubit gate. Here we show that the magnetic couplings in two supramolecular {Cr7Ni}-Ni-{Cr7Ni} assemblies can be chemically engineered to fit the above requisites for conditional gates with no need of local control. Microscopic parameters are determined by a recently developed many-body ab-initio approach and used to simulate quantum gates. We find that these systems are optimal for proof-of-principle two-qubit experiments and can be exploited as building blocks of scalable architectures for quantum simulation.
The physical implementation of quantum information processing relies on individual modules-qubits-and operations that modify such modules either individually or in groups-quantum gates. Two examples of gates that entangle pairs of qubits are the controlled NOT-gate (CNOT) gate, which flips the state of one qubit depending on the state of another, and the gate that brings a two-qubit product state into a superposition involving partially swapping the qubit states. Here we show that through supramolecular chemistry a single simple module, molecular {Cr7Ni} rings, which act as the qubits, can be assembled into structures suitable for either the CNOT or gate by choice of linker, and we characterize these structures by electron spin resonance spectroscopy. We introduce two schemes for implementing such gates with these supramolecular assemblies and perform detailed simulations, based on the measured parameters including decoherence, to demonstrate how the gates would operate.
The intent of this study is to determine the feasibility of diatomics as molecular quantum computing candidates and shed insight into the use of such experimental laser pulse shaping methods to represent quantum logic gates. Four appropriate rovibrational states of model diatomic molecules are encoded as the qubit states. A set of 2-qubit quantum logic gates (ACNOT, CNOT, NOT, Hadamard) are represented by amplitude and phase shaped laser pulses. The combinations of amplitudes and phases that produce the optimal laser pulse representation, for each quantum logic gate, are determined by a Genetic Algorithm optimization routine. The theoretical laser pulse shaping is analogous to current experimental frequency-domain pulse shaping apparatus with amplitude and phase control at individual frequencies. A model set of diatomics is sampled in order to determine a relationship between optimal laser pulse shaping and the choice of diatomic molecule. We show that the choice of diatomic molecule greatly influences the ability to produce optimal laser pulse shapes to represent quantum logic gates. Tuneable parameters specific to laser pulse shaping instruments are varied to determine their effect on optimal pulse production. They include varying the number of amplitude and phase components, adjusting the number of frequency components, and altering the frequency resolution which is synonymous with altering the laser pulse duration. A time domain analytic form of the original frequency domain laser pulse function is derived, providing a useful means to infer the laser pulse dependencies on these parameters. Initially, we show that the appropriate choice of rovibrational state qubits of carbon monoxide (12C16O) and the use of simple shaped binary pulses, 2 amplitude and 2 phase components, can provide significant control for specific quantum gates. Further amplitude variation at each frequency component is shown to be a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We show that the generation of optimal laser pulse shapes is highly dependent upon the frequency resolution and increasing the number of frequency components provides incremental improvements to optimal laser pulses.
Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.
In NMR quantum computing, spin states of spin-1/2 nuclei are called qubits. Quantum logic gates are represented by unitary matrices. As a universal gate, controlled-NOT (CNOT) is a two-qubit gate. For the IS (I = 1/2 and S = 1/2) spin system, two-qubit CNOT gate is represented by a 4 × 4 matrix. SWAP logic gate, which exchanges two quantum states, is constructed by CNOT gates. In this study, first, four-qubit CNOT gates are constructed for the IS (I = 3/2, S = 3/2) spin system. Then, by using these CNOT gates, a four-qubit SWAP logic gate is found. As an application and verification, an obtained SWAP logic gate is applied to the matrix representation of product operators for the IS (I = 3/2, S = 3/2) spin system. SWAP logic gate can also be presented by an NMR pulse sequence. By using the product operator theory, the pulse sequence of the SWAP logic gate is applied to product operators of the IS (I = 3/2, S = 3/2) spin system. The expected exchange results are obtained for both the matrix representation and the pulse sequence of SWAP logic gate.