Osama Moussa

Symmetrized characterization of noisy quantum processes.

A major goal of developing high-precision control of many-body quantum systems is to realize their potential as quantum computers. A substantial obstacle to this is the extreme fragility of quantum systems to “decoherence” from environmental noise and other control limitations. Although quantum computation is possible if the noise affecting the quantum system satisfies certain conditions, existing methods for noise characterization are intractable for present multibody systems. We introduce a technique based on symmetrization that enables direct experimental measurement of some key properties of the decoherence affecting a quantum system. Our method reduces the number of experiments required from exponential to polynomial in the number of subsystems. The technique is demonstrated for the optimization of control over nuclear spins in the solid state.

Experimental implementation of heat-bath algorithmic cooling using solid-state nuclear magnetic resonance

The counter-intuitive properties of quantum mechanics have the potential to revolutionize information processing by enabling the development of efficient algorithms with no known classical counterparts. Harnessing this power requires the development of a set of building blocks, one of which is a method to initialize the set of quantum bits (qubits) to a known state. Additionally, fresh ancillary qubits must be available during the course of computation to achieve fault tolerance. In any physical system used to implement quantum computation, one must therefore be able to selectively and dynamically remove entropy from the part of the system that is to be mapped to qubits. One such method is an ‘open-system’ cooling protocol in which a subset of qubits can be brought into contact with an external system of large heat capacity. Theoretical efforts have led to an implementation-independent cooling procedure, namely heat-bath algorithmic cooling. These efforts have culminated with the proposal of an optimal algorithm, the partner-pairing algorithm, which was used to compute the physical limits of heat-bath algorithmic cooling. Here we report the experimental realization of multi-step cooling of a quantum system via heat-bath algorithmic cooling. The experiment was carried out using nuclear magnetic resonance of a solid-state ensemble three-qubit system. We demonstrate the repeated repolarization of a particular qubit to an effective spin-bath temperature, and alternating logical operations within the three-qubit subspace to ultimately cool a second qubit below this temperature. Demonstration of the control necessary for these operations represents an important step forward in the manipulation of solid-state nuclear magnetic resonance qubits.

Testing contextuality on quantum ensembles with one clean qubit.

We present a protocol to evaluate the expectation value of the correlations of measurement outcomes for ensembles of quantum systems, and use it to experimentally demonstrate--under an assumption of fair sampling--the violation of an inequality that is satisfied by any noncontextual hidden-variables theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established nuclear magnetic resonance techniques for quantum-information processing.

Experimental approximation of the Jones polynomial with one quantum bit.

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.

Spin based heat engine: demonstration of multiple rounds of algorithmic cooling.

We experimentally demonstrate multiple rounds of heat-bath algorithmic cooling in a 3 qubit solid-state nuclear magnetic resonance quantum information processor. By pumping entropy into a heat bath, we are able to surpass the closed system limit of the Shannon bound and purify a single qubit to 1.69 times the heat-bath polarization. The algorithm combines both high fidelity coherent control and a deliberate interaction with the environment. Given this level of quantum control in systems with larger reset polarizations, nearly pure qubits should be achievable.

Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule

The Born rule is at the foundation of quantum mechanics and transforms the classical understanding of probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three-way (or three-path) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three-path interference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance. As a measure of the consistency, we evaluate the ratio of three-way interference to two-way interference. Our experiment bounded the ratio to the order of 10?3???10?3, and hence it is consistent with Borns rule.

Practical experimental certification of computational quantum gates using a twirling procedure.

Because of the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the computation process via quantum process tomography requires an exponential amount of resources, and thus is not practical even for relatively small devices. We solve this problem by demonstrating that twirling experiments previously used to characterize the average fidelity of quantum memories efficiently can be easily adapted to estimate the average fidelity of the experimental implementation of important quantum computation processes, such as unitaries in the Clifford group, in a practical and efficient manner with applicability in current quantum devices. Using this procedure, we demonstrate state-of-the-art coherent control of an ensemble of magnetic moments of nuclear spins in a single crystal solid by implementing the encoding operation for a 3-qubit code with only a 1% degradation in average fidelity discounting preparation and measurement errors. We also highlight one of the advances that was instrumental in achieving such high fidelity control.

Measuring geometric quantum discord using one bit of quantum information

We describe an efficient DQC1-algorithm to quantify the amount of Geometric Quantum Discord present in the output state of a DQC1 computation. DQC1 is a model of computation that utilizes separable states to solve a problem with no known efficient classical algorithm and is known to contain quantum correlations as measured by the discord. For the general case of a (1+n)-qubit DQC1-state we provide an analytical expression for the Geometric Quantum Discord and find that its typical (and maximum) value decreases exponentially with n. This is in contrast to the standard Quantum Discord whose value for typical DQC1-states is known to be independent of n. We experimentally demonstrate the proposed algorithm on a four-qubit liquid-state nuclear magnetic resonance quantum information processor. In the special case of a two-qubit DQC1 model, we also provide an expression for the Quantum Discord that only requires the outcome of the DQC1 algorithm.

Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor.

We report the implementation of a 3-qubit quantum error-correction code on a quantum information processor realized by the magnetic resonance of carbon nuclei in a single crystal of malonic acid. The code corrects for phase errors induced on the qubits due to imperfect decoupling of the magnetic environment represented by nearby spins, as well as unwanted evolution under the internal Hamiltonian. We also experimentally demonstrate sufficiently high-fidelity control to implement two rounds of quantum error correction. This is a demonstration of state-of-the-art control in solid state nuclear magnetic resonance, a leading test bed for the implementation of quantum algorithms.

Quantum Error Correction with Mixed Ancilla Qubits

Institute for Quantum Computing, University of WaterlooPerimeter Institute for Theoretical Physics, Waterloo, Ontario andDepartment of Physics and Astronomy, University of Waterloo(Dated: January 10, 2012)Most quantum error correcting codes are predicated on the assumption that there exists a reservoirof qubits in the state j0i, which can be used as ancilla qubits to prepare multi-qubit logical states.In this report, we examine the consequences of relaxing this assumption, and propose a method toincrease the delity produced by a given code when the ancilla qubits are initialized in mixed states,using the same number of qubits, at most doubling the number of gates. The procedure implementedconsists of altering the encoding operator to include the inverse of the unitary operation used tocorrect detected errors after decoding. This augmentation will be especially useful in quantumcomputing architectures that do not possess projective measurement, such as solid state NMRQIP.