Robert Raußendorf

University of British Columbia
Department of Physics and Astronomy
6224 Agricultural Road, Hennings 338
Vancouver, BC, V6T 1Z1
Tel: (604) 822-3253
Email: rraussendorf[at]phas[dot]ubc[dot]ca

Research Areas

  • Quantum Information and Computation
  • Fault-tolerance
  • Foundations of Quantum Information

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Algebraic Structures in Quantum Computation IV: June 22 - 24, 2020 on Zoom

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My research interest is in quantum computation, in particular computational models, quantum fault-tolerance and foundational aspects. I have invented the one-way quantum computer (QCc) jointly with Hans Briegel (UK patent GB 2382892, US patent 7,277,872). The QCc is a scheme of universal quantum computation by local measurements on a multi-particle entangled quantum state, the so-called cluster state. Quantum information is written into the cluster state, processed and read out by one-qubit measurements only. As the computation proceeds, the entanglement in the resource cluster state is progressively destroyed. Measurements replace unitary evolution as the elementary process driving a quantum computation.


The one-way quantum computer (QCc): A universal resource for the QCc is the cluster state, a highly entangled mult-qubit quantum state that can be easily generated unitarily by the Ising interaction on a square lattice. In the figure to the left, the qubits forming the cluster state are represented by dots and arrows. The symbol used indicates the basis of local measurement. Dots represent cluster qubits measured in the eigenbasis of the Pauli operator Z, arrows denote measurement in a basis in the equator of the Bloch sphere. The pattern of measurement bases can be regarded as representing a quantum circuit, i.e., the "vertical" direction on the cluster specifies the location of a logical qubit in a quantum register, and the "horizontal" direction on the cluster represents circuit time. However, this simple picture should be taken with a grain of salt: The optimal temporal order of measurements has very little to do with the temporal sequence of gates in the corresponding circuit.

I also work in the field of fault-tolerant quantum computation. Error-correction is what a large-scale quantum computer spends most of its computation time with, and it is important to devise error-correction methods which allow for a high error threshold at a moderate operational overhead. My research interest is in fault-tolerance for quantum systems with a geometrical constraint, e.g. low-dimensional lattice systems, and in topological methods.

With my collaborators Jim Harrington and Kovid Goyal, I have presented a fault-tolerant one-way quantum computer [arXiv:quant-ph/0510135], and have described a method for fault-tolerant quantum computation in a two-dimensional lattice of qubits requiring local and translation-invariant nearest-neighbor interaction only [arXiv:quant-ph/0610082], [arXiv:quant-ph/0703143]. For our method, we have obtained by far the highest known threshold for a two-dimensional architecture with nearest-neighbor interaction, namely 0.75 percent. A high value of the error threshold is important for realization of fault-tolerant quantum computation because it relaxes the accuracy requirements of the experiment. The imposed constraint of nearest-neighbor interaction in a two-dimensional qubit array is suggested by experimental reality: Many physical systems envisioned for the realization of a quantum computer are confined to two dimensions and prefer short-range interaction, for example optical lattices, arrays of superconducting qubits and quantum dots.


Fault-tolerant topological CNOT-gate: Holes puncture a the surface of a Kitaev's surface code, creating pieces of boundary. Each pair of holes gives rise to an encoded qubit. There are two types of holes and hence qubits, primal and dual. The CNOT-gate is implemented by moving two holes around another, one being primal and the other dual. Also shown is the string corresponding to an encoded Pauli operator X on the control qubit and its evolution from the initial to the final codes surface. As expected for conjugation under the CNOT, X_c evolves into X_c X_t. The CNOT in the opposite direction - the primal qubit being the target and the dual qubit being the control - is also possible. It requires pairwise insertion and removal of holes from the code surface, i.e., the topology of the code surface for that gate changes with time.

Selected publications

Featured publication

Cohomological framework for contextual quantum computations [Published December 2019]. We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely elements of two cohomology groups. One of those invariants applies to the deterministic case, and the other to the general probabilistic case. The same invariants also witness quantumness in the form of contextuality. In result, they give rise to fundamental algebraic structures underlying quantum computation.

The Boolean algebra is at the foundation of all digital classical computation. From a quantum perspective it is thus pertinent to ask what its counterpart in quantum computation is. Which fundamental algebraic structures can quantum computation be based on? This is the question we are concerned with here. We address it for the model of measurement-based quantum computation (MBQC), in which the process of computation is driven by measurements rather than unitary evolution.


To address the above question, we introduce a generalized notion of MBQC based on symmetry. Each such H-MBQC transforms under a characteristic symmetry group H, whose action preserves the outputted function o. We establish the following properties.

We impose as minimal requirements on our description of H-MBQCs that it contains (i) a witness of quantumness, and (ii) the computed function. It turns out that this information is topological. Namely, the witness of quantumness arises as a contextuality witness, provided by the above cohomological invariants. The same invariants also characterize the outputted function.

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Brief academic bio

I obtained my PhD from the Ludwig Maximilians University in Munich, Germany in 2003. My PhD thesis [Int. J. of Quantum Information 7, 1053 - 1203 (2009).] is on measurement-based quantum computation. I was postdoc at Caltech (2003-06) and at the Perimeter Institute for Theoretical Physics (2006-07), and Sloan Research Fellow 2009 - 2011. I am Associate Professor at the Department of Physics and Astronomy of the University of British Columbia.