Abstract
Holonomic quantum computation exploits a quantum state's nontrivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through parameter space have been well researched. Discrete holonomies, on the other hand, where the state jumps from point to point in state space, have had little prior investigation. Using a sequence of incomplete projective measurements of the spin operator, we build an explicit approach to universal quantum computation. We show that quantum error correction codes integrate naturally in our scheme, providing a model for measurement-based quantum computation that combines the passive error resilience of holonomic quantum computation and active error correction techniques. In the limit of dense measurements we recover known continuous-path holonomies.
Highlights
In the circuit model of quantum computation, information is processed by using a series of quantum gates on a register of qubits
We have demonstrated that discrete holonomic quantum computation can achieve universality
We have explicitly constructed quantum gates for spin-coherent states, whereby rotation gates were achieved using a sequence of four projective measurements
Summary
In the circuit model of quantum computation, information is processed by using a series of quantum gates on a register of qubits These gates are unitary transformations, which can be realized using non-Abelian geometric phases (holonomies) [1] that make them intrinsically fault tolerant [2]. We further show that measurement-driven holonomies on SCSs can be naturally merged with active error correction techniques, such as direct implementation of the bit-flip repetition code [17] and extension into the nine-qubit Shor code [18]. In this way, our proposed scheme can be viewed as a model for measurement-based quantum computation, in the same vein as, e.g., one-way cluster state quantum computation [19] and teleportation-based quantum computation [20]. Our approach combines the passive error resilience of holonomic quantum computation and active error correction techniques, making it a promising tool for robust quantum computation
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