We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes a complete algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.
We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes a complete algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.
This paper presents our theoretical and nuclear magnetic resonance(NMR) experimental work on several QIPs including quantum super dense coding(QSDC),quantum algorithms,quantum error correction,and decoherence-free subspace.The main contents are,(1) Using NMR technique,we realize two kinds of QSDC.The experimental results show that QSDC only needs to transfer(N-1) qubits during transmitting N bits classical information;(2) On NMR quantum computers,we realize three kinds of quantum algorithms that include four-qubit summing algorithm,four-qubit Deutsch-like algorithm and seven-qubit Deutsch-Jozsa algorithm;(3) We present a quantum error correction scheme based on quantum cloning.This scheme shows the relationship between quantum cloning and quantum error correction;(4) To avoid decoherence in quantum algorithms,we construct a decoherence-free subspace(DFS) by using multiple quantum coherences.The validity of this DFS is also experimentally verified on our NMR quantum computers.The DFS makes the three unaddressed protons in a CH_3 group distinguished in two-dimensional(2D) NMR.It can protect against more error operators.This idea may provide new insights into extending the number of qubits in the sense that it effectively utilizes the magnetically equivalent nuclei.
This Letter presents a two-dimensional nuclear magnetic resonance (NMR) approach for constructing a two-logical-qubit decoherence-free subspace (DFS) by using four multiple-quantum coherences of a CH3 spin system as logical qubits. The three protons in this spin system are magnetically equivalent and can only be used as a single qubit in one-dimensional NMR. We have experimentally demonstrated that our DFS can protect against more types of decoherences than those of the one composed of four noisy physical qubits all with different chemical shifts. This idea may provide new insights into extending qubit systems in the sense that it effectively utilizes the magnetically equivalent nuclei.
Storing information in quantum mechanical degrees of freedom and processing it by unitary transformation promises a new class of computers that can efficiently solve problems for which no efficient classical algorithms are known. The most straightforward implementation of this type of information processing uses nuclear spins to store the information and nuclear magnetic resonance for processing it. We discuss the basics of quantum information processing by NMR, with an emphasis on two fields of research: the design and implementation of robust logical gate operations and the loss of quantum information, which is known as decoherence.
The development of quantum error correcting techniques is of paramount importance to the ultimate goal of implementing practical quantum computers. The simultaneous transmission of quantum and classical information over a quantum channel was initially investigated by Shor and since been continued by others. It was shown that there is an advantage to transmitting both quantum and classical information simultaneously, compared to independent transmissions. The characterization and construction of codes that allow to transmit both quantum and classical information, which we refer to as hybrid codes, was done from a coding theory perspective and by using the operator algebra quantum error correction (OAQEC) perspective. In this work we unify these two perspectives, showing that the coding theory formulation is a specific case of the OAQEC perspective. As a result we generalized the quantum hamming bound to the hybrid case. To date no such hybrid codes have been physically implemented. Nuclear magnetic resonance (NMR) quantum information processors (QIP) have been an excellent test bed for quantum computing. The techniques of NMR had been refined for many years and can now be applied to quantum computing. NMR techniques provides a high degree of qubit control and long decoherence times compared to other QIP. These two properties of NMR QIP make it a prime candidate for implementing hybrid codes. In this work we developed a hybrid code and designed the circuit for encoding it. We used Matlab to simulate the pulse sequence which would be used in an NMR QIP to carry out the encoding of the hybrid circuit. According to those simulations the full encoding, a single qubit Pauli error and a full decoding can be carried out without the effects of decoherence destroying the quantum information beyond retrieval.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
We demonstrate storage and manipulation of one qubit encoded into a decoherence-free subspace (DFS) of two nuclear spins using liquid state nuclear magnetic resonance (NMR) techniques. The DFS is spanned by states that are unaffected by arbitrary collective phase noise. Encoding and decoding procedures reversibly map an arbitrary qubit state from a single data spin to the DFS and back. The implementation demonstrates the robustness of the DFS memory against engineered dephasing with arbitrary strength as well as a substantial increase in the amount of quantum information retained, relative to an un-encoded qubit, under both engineered and natural noise processes. In addition, a universal set of logical manipulations over the encoded qubit is also realized. Although intrinsic limitations prevent maintaining full noise tolerance during quantum gates, we show how the use of dynamical control methods at the encoded level can ensure that computation is protected with finite distance. We demonstrate noise-tolerant control over a DFS qubit in the presence of engineered phase noise significantly stronger than observed from natural noise sources.