Showing papers by "Isaac L. Chuang published in 1999"

Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations

Abstract: Algorithms such as quantum factoring1 and quantum search2 illustrate the great theoretical promise of quantum computers; but the practical implementation of such devices will require careful consideration of the minimum resource requirements, together with the development of procedures to overcome inevitable residual imperfections in physical systems3,4,5 Many designs have been proposed, but none allow a large quantum computer to be built in the near future6 Moreover, the known protocols for constructing reliable quantum computers from unreliable components can be complicated, often requiring many operations to produce a desired transformation3,4,5,7,8 Here we show how a single technique—a generalization of quantum teleportation9—reduces resource requirements for quantum computers and unifies known protocols for fault-tolerant quantum computation We show that single quantum bit (qubit) operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states10—all of which are within the reach of current technology—are sufficient to construct a universal quantum computer We also present systematic constructions for an infinite class of reliable quantum gates that make the design of fault-tolerant quantum computers much more straightforward and methodical

Quantum Teleportation is a Universal Computational Primitive

Abstract: We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

Abstract: We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.

Nuclear magnetic resonance quantum computing using liquid crystal solvents

Abstract: Liquid crystals offer several advantages as solvents for molecules used for nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a two-qubit Grover search using a molecule (13C 1HCl3) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.

Experimental realization of a two-bit phase damping quantum code

Abstract: Using nuclear-magnetic-resonance techniques, we experimentally investigated the effects of applying a two-bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without coding, and the resulting output states were compared with the originals and with each other. The theoretically expected result, net reduction of distortion and conditional error probabilities to second order, was indeed observed, despite imperfect coding operations which increased the error probabilities by approximately 5%. A systematic study of the deviations from the ideal behavior provided quantitative measures of different sources of error, and good agreement was found with a numerical model. Theoretical questions in quantum error correction in bulk nuclear spin systems including fidelity measures, signal strength, and syndrome measurements are discussed.

Simulating quantum operations with mixed environments

Abstract: We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a previous conjecture, not all quantum operations on a single-qubit can be implemented with a single-qubit environment, even if that environment is initially prepared in a mixed state. We show that a mixed single-qutrit environment is sufficient to implement a special class of operations, the generalized depolarizing channels.

Realization of Logically Labeled Effective Pure States for Bulk Quantum Computation

Abstract: We report the first use of ``logical labeling'' to perform a quantum computation with a room-temperature bulk system. This method entails the selection of a subsystem that behaves as if it were at zero temperature---except for a decrease in signal strength---conditioned upon the state of the remaining system. No averaging over differently prepared molecules is required. In order to test this concept, we execute a quantum search algorithm in a subspace of two nuclear spins, labeled by a third spin, using solution nuclear magnetic resonance and employing a novel choice of reference frame to uncouple nuclei.

Nuclear Magnetic Resonance Quantum Computing Using Liquid Crystal Solvents

Abstract: Liquid crystals offer several advantages as solvents for molecules used for nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a 2-qubit Grover search using a molecule ($^{13}$C$^{1}$HCl$_3$) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.

Nuclear magnetic resonance quantum computing method with improved solvents

Abstract: A method for nuclear magnetic resonance quantum computing (NMRQC) uses a liquid crystal solvent into which the quantum computing molecules are dissolved. The method allows implementation of more complex quantum algorithms which require execution of many logic gates over the duration of a decoherence time, allows NMRQC clock frequencies to be increased by at least an order of magnitude beyond those achievable using isotropic liquid solvents, and decreases the reinitialization times for a NMR quantum computer without decreasing the computational capability of the molecular systems.

Quantum algorithms which accept hot qubit inputs

Abstract: Realistic physical implementations of quantum computers can entail tradeoffs which depart from the ideal model of quantum computation. Although these tradeoffs have allowed successful demonstration of certain quantum algorithms, a crucial question is whether they fundamentally limit the computational capacity of such machines. We study the limitations of a quantum computation model in which only ensemble averages of measurement observables are accessible. Furthermore, we stipulate that input qubits may only be prepared in highly random, ``hot'' mixed states. In general, these limitations are believed to dramatically detract from the computational power of the system. However, we construct a class of algorithms for this limited model, which, surprisingly, are polynomially equivalent to the ideal case. This class includes the well known Deutsch-Jozsa algorithm.

Implementation of a three-quantum-bit search algorithm

Abstract: We report the experimental implementation of Grover's quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of $^{13}$C-labeled CHFBr$_2$, in which the three weakly coupled spin-1/2 nuclei behave as the bits and are initialized, manipulated, and read out using magnetic resonance techniques. This quantum computation is made possible by the introduction of two techniques which significantly reduce the complexity of the experiment and by the surprising degree of cancellation of systematic errors which have previously limited the total possible number of quantum gates.