# Semiconductor sources for photonic quantum computing

Photonics has emerged as an arena which holds great potential for realizing a quantum computer. The advanced technology of optical circuits allows for precision measurements and manipulations which are a crucial ingredient in any realization. More importantly, since photons are very weakly interacting, they have little sensitivity to decoherence, which poses a major challenge in most other implementations. The primary challenge facing optical quantum computation is that of building suitable photon sources. The majority of effort has been directed at single photon sources. However, the lack of interactions between photons also leads to a serious difficulty in applying two qubit entangling gates. Four single photons can be used in an interferometer to produce a maximally entangled Bell pair of photons, and given a source of Bell pairs, it is in principle possible to fuse them into larger cluster states, which can be used for performing quantum computation via the simple procedure of making individual (single-qubit) measurements on the photons involved. Bell pairs can also be produced directly, for example via a radiative cascade in quantum dots. However, even an ideal Bell-pair source would only reduce the overall resources required for a full optical quantum computation by a small factor. We study methods for utilizing semiconductor photon sources, such as quantum dots, to generate multi photon entangled states. We address important questions such as the effect of decoherence arising from the interaction of the semiconductor source with its environment, and optical circuits for utilizing and verifying these multi-photon states.

### Selected Work

#### Error distributions on large entangled states with non-Markovian dynamics

We investigate the distribution of errors on a highly entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten of errors occurs has a bound of Markovian form, and thus accuracy threshold theorems based on Markovian models should be just as effective. This is the case, for example, for a charged quantum dot emitter in a moderate to strong magnetic field. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model.

- Dara P. S. McCutcheon, N. H. Lindner, Terry Rudolph, Error distributions on large entangled states with non-Markovian dynamics, arXiv:1403.4956.

#### Entangled photon pairs from semiconductor quantum dots

Tomographic analysis demonstrates that the polarization state of pairs of photons emitted from a biexciton decay cascade becomes entangled when spectral ltering is applied. The measured density matrix of the photon pair satises the Peres criterion for entanglement by more than 3 standard deviations of the experimental uncertainty and violates Bells inequality. We show that the spectral ltering erases the which path information contained in the photons color and that the remanent information in the quantum dot degrees of freedom is negligible.

- N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M.Petro, Entangled photon pairs from semiconductor quantum dots, Phys. Rev. Lett. 96, 130501 (2006); arXiv:quant-ph/0512048

#### Proposal for pulsed on-demand sources of photonic cluster state strings

We present a method to convert certain single photon sources into devices capable of emitting large strings of photonic cluster state in a controlled and pulsed “on demand” manner. Such sources would greatly reduce the resources required to achieve linear optical quantum computation. Standard spin errors, such as dephasing, are shown to aect only 1 or 2 of the emitted photons at a time. This allows for the use of standard fault tolerance techniques, and shows that the protocol can run for arbitrarily long times. Using realistic parameters for current quantum dot sources, we conclude high entangled-photon emission rates are achievable, with Pauli-error rates per photon of less than 0:2%. For quantum dot sources the method has the added advantage of alleviating the problematic issues of obtaining identical photons from independent, non-identical quantum dots, and of exciton dephasing.

- N. H. Lindner and T. Rudolph, Proposal for pulsed on-demand sources of photonic cluster state strings, Phys. Rev. Lett. 103, 113602 (2009); Covered by the New Scientist, 2727, 23 (26 September 2009).