David Poulin

Université de Sherbrooke, Sherbrooke, Quebec, Canada

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Publications (65)251.52 Total impact

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    Guillaume Duclos-Cianci, David Poulin
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    ABSTRACT: In leading fault-tolerant quantum computing schemes, accurate transformation are obtained by a two-stage process. In a first stage, a discrete, universal set of fault-tolerant operations is obtained by error-correcting noisy transformations and distilling resource states. In a second stage, arbitrary transformations are synthesized to desired accuracy by combining elements of this set into a circuit. Here, we present a scheme which merges these two stages into a single one, directly distilling complex transformations. We find that our scheme can reduce the total overhead to realize certain gates by up to a few orders of magnitude. In contrast to other schemes, this efficient gate synthesis does not require computationally intensive compilation algorithms, and a straightforward generalization of our scheme circumvents compilation and synthesis altogether.
    03/2014;
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    ABSTRACT: Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant T and control-control-Z gates. Combined with the Clifford group, either of these two gates generate a universal set. Here, we combine these two features by demonstrating how to fault-tolerantly convert between these two codes, providing a new method to realize universal fault-tolerant quantum computation. One interpretation of our result is that both codes correspond to the same subsystem code in different gauges. Our scheme extends to the entire family of quantum Reed-Muller codes.
    Physical review letters. 03/2014; 113(8).
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    Andrew J. Ferris, David Poulin
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    ABSTRACT: We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network. We perform an in-depth study of a particular example that can be thought of as an extension to Arikan's polar code. Notably, our numerical simulation show that this code polarizes the logical channels more strongly while retaining the log-linear decoding complexity using the successive cancellation decoder. These codes also display improved error-correcting capability with only a minor impact on decoding complexity. Efficient decoding is realized using powerful graphical calculus tools developed in the field of quantum many-body physics. In a companion paper, we generalize our construction to the quantum setting and describe more in-depth the relation between classical and quantum error correction and the graphical calculus of tensor networks.
    12/2013;
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    Andrew J. Ferris, David Poulin
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    ABSTRACT: We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
    Physical review letters. 12/2013; 113(3).
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    ABSTRACT: We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range between 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.
    10/2013;
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    Pavithran Iyer, David Poulin
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    ABSTRACT: In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem is known to be NP-complete, and a similar decoding problem for quantum codes is also known to be NP-complete. However, this decoding strategy is not optimal in the quantum setting as it does not take into account error degeneracy, which causes distinct errors to have the same effect on the code. Here, we show that optimal decoding of stabilizer codes is computationally much harder than optimal decoding of classical linear codes, it is #P.
    10/2013;
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    Guillaume Duclos-Cianci, David Poulin
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    ABSTRACT: We study the quantum error correction threshold of Kitaev's toric code over the group Zd subject to a generalized bit-flip noise. This problem requires special decoding techniques, and for this purpose we generalize the renormalization-group method we introduced previously [ G. Duclos-Cianci and D. Poulin Phys. Rev. Lett. 104 050504 (2010) and IEEE Information Theory Workshop, Dublin (2010), p. 1] for Z2 topological codes.
    Physical Review A 06/2013; 87(6). · 3.04 Impact Factor
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    Guillaume Duclos-Cianci, David Poulin
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    ABSTRACT: We present a three-dimensional generalization of a renormalization group decoding algorithm for topological codes with Abelian anyonic excitations that we previously introduced for two dimensions. This 3D implementation extends our previous 2D algorithm by incorporating a failure probability of the syndrome measurements, i.e., it enables fault-tolerant decoding. We report a fault-tolerant storage threshold of 1.9(4)% for Kitaev's toric code subject to a 3D bit-flip channel (i.e. including imperfect syndrome measurements). This number is to be compared with the 2.9% value obtained via perfect matching. The 3D generalization inherits many properties of the 2D algorithm, including a complexity linear in the space-time volume of the memory, which can be parallelized to logarithmic time.
    04/2013;
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    Olivier Landon-Cardinal, David Poulin
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    ABSTRACT: We study the robustness of quantum information stored in the degenerate ground space of a local, frustration-free Hamiltonian with commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier separating the distinct ground states under local transformations would protect the information from thermal fluctuations. On the other hand, local topological order would shield the ground space from static perturbations. Here we demonstrate that local topological order implies a constant energy barrier, thus inhibiting thermal stability.
    Physical Review Letters 03/2013; 110(9):090502. · 7.73 Impact Factor
  • Andrew Ferris, David Poulin
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    ABSTRACT: Studying large many-body quantum systems is difficult because the dimension of the Hilbert space grows exponentially with the number of particles/subsystems. I will present a method to approximately calculate the finite-temperature properties of an infinite, translationally invariant system by just keeping knowledge of small, local subsystems. Key to this method is the ability to (over-)estimate the global entropy, giving us access to the Gibbs free energy, and results in the property that we can find a rigorous lower-bound to the ground state energy (which compliments rigorous upper-bounds that can be found with more common, variational techniques).
    03/2013;
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    Andrew J. Ferris, David Poulin
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    ABSTRACT: The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the MED, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 XXZ model on the 2D square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact-diagonalization, we show the MED is both more accurate and significantly more flexible.
    Physical review. B, Condensed matter 12/2012; 87(20). · 3.77 Impact Factor
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    ABSTRACT: Topological phases can be defined in terms of local equivalence: two systems are in the same topological phase if it is possible to transform one into the other by a local reorganization of its degrees of freedom. The classification of topological phases therefore amounts to the classification of long-range entanglement. Such local transformation could result, for instance, from the adiabatic continuation of one system's Hamiltonian to the other. Here, we use this definition to study the topological phase of translationally invariant stabilizer codes in two spatial dimensions, and show that they all belong to one universal phase. We do this by constructing an explicit mapping from any such code to a number of copies of Kitaev's code. Some of our results extend to some two-dimensional (2D) subsystem codes, including topological subsystem codes. Error correction benefits from the corresponding local mappings. In particular, it enables us to use decoding algorithm developed for Kitaev's code to decode any 2D stabilizer code and subsystem code.
    New Journal of Physics 07/2012; 14(7):073048. · 4.06 Impact Factor
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    ABSTRACT: We propose a simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It inherits many favorable properties of the standard surface code such as encoding of multiple logical qubits on a planar lattice with punctured holes, efficient decoding by either minimum-weight matching or renormalization group methods, and high error threshold. The new subsystem surface code (SSC) gives rise to an exactly solvable Hamiltonian with 3-qubit interactions, topologically ordered ground state, and a constant energy gap. We construct a local unitary transformation mapping the SSC Hamiltonian to the one of the ordinary surface code thus showing that the two Hamiltonians belong to the same topological class. We describe error correction protocols for the SSC and determine its error thresholds under several natural error models. In particular, we show that the SSC has error threshold approximately 0.6% for the standard circuit-based error model studied in the literature. We also consider a model in which three-qubit parity operators can be measured directly. We show that the SSC has error threshold approximately 0.97% in this setting.
    07/2012;
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    Winton Brown, David Poulin
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    ABSTRACT: Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are therefore useful to understand the powers and limitations of certain classes of simulation algorithms. Here, we extend the characterization of quantum Markov networks and in particular prove the equivalence of positive quantum Markov networks and Gibbs states of Hamiltonians that are the sum of local commuting terms on graphs containing no triangles. For more general graphs we demonstrate the equivalence between quantum Markov networks and Gibbs states of a class of Hamiltonians of intermediate complexity between commuting and general local Hamiltonians.
    06/2012;
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    ABSTRACT: We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, to carry out multi-qubit measurements, and to perform certain recovery operations conditioned on measurement outcomes. As a consequence, the experimental benchmark of a QEC scheme is a tall order because it requires the conjuncture of many elementary components. Our scheme opens the path to experimental benchmarks of individual components of QEC. Our numerical simulations show that certain parity measurements realized in circuit quantum electrodynamics are on the verge of being useful for QEC.
    Physical Review A 04/2012; 86(3). · 3.04 Impact Factor
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    Emilie Pelchat, David Poulin
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    ABSTRACT: We present a decoding algorithm for quantum convolutional codes that finds the class of degenerate errors with the largest probability conditioned on a given error syndrome. The algorithm runs in time linear with the number of qubits. Previous decoding algorithms for quantum convolutional codes optimized the probability over individual errors instead of classes of degenerate errors. Using Monte Carlo simulations, we show that this modification to the decoding algorithm results in a significantly lower block error rate.
    IEEE Transactions on Information Theory 04/2012; · 2.62 Impact Factor
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    Olivier Landon-Cardinal, David Poulin
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    ABSTRACT: We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections.
    New Journal of Physics 04/2012; 14(8). · 4.06 Impact Factor
  • Guillaume Duclos-Cianci, David Poulin
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    ABSTRACT: 2D topological stabilizer codes have attracted a lot of attention in recent years for two main reasons. First, they provide exactly solvable models which exhibit topological order and anyonic excitations. Second, they naturally lead to quantum stabilizer error-correcting codes having macroscopic minimum distance. Although these codes are robust at zero temperature, quasi-particles appear and freely diffuse in the system at any finite temperature. If this diffusion is unchecked, errors will occur. Consequently, active error-correction is needed. We want to propose a cellular automaton that would perform this correction. It would ``manually'' confine the quasi-particles by simulating articifial attraction between them and moving them accordingly. We obtained encouraging preliminary results for error-correction and hope to generalize them to fault-tolerance.
    02/2012;
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    ABSTRACT: Quantum tomography is the main method used to assess the quality of quantum information processing devices. However, the amount of resources needed for quantum tomography is exponential in the device size. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.
    Physical Review Letters 11/2011; 107(21):210404. · 7.73 Impact Factor
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    ABSTRACT: We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.
    Physical Review Letters 04/2011; 106(17):170501. · 7.73 Impact Factor

Publication Stats

1k Citations
251.52 Total Impact Points

Institutions

  • 2009–2014
    • Université de Sherbrooke
      • Department of Physics
      Sherbrooke, Quebec, Canada
  • 2009–2013
    • Université du Québec
      Québec, Quebec, Canada
  • 2006–2008
    • California Institute of Technology
      • Institute for Quantum Information and Matter
      Pasadena, California, United States
  • 2006–2007
    • University of Queensland
      Brisbane, Queensland, Australia
  • 2003–2007
    • University of Waterloo
      • Institute for Quantum Computing
      Waterloo, Ontario, Canada
    • Perimeter Institute for Theoretical Physics
      Waterloo, Ontario, Canada
  • 2001
    • Université de Montréal
      Montréal, Quebec, Canada