University of Oxford, U.K.* Q.Tech.Roadmap: Quantum Computing David Lucas Ion Trap QC group University of Oxford, U.K.* (on behalf of Daniel Esteve, CEA-Saclay and QUTE working group) info taken from QT Roadmap sections 1.1 and 2.1 EU list of QT research groups has ~440 entries, many interested in QC

University of Oxford, U.K.* Q.Tech.Roadmap: Quantum Computing David Lucas Ion Trap QC group University of Oxford, U.K.* (on behalf of Daniel Esteve, CEA-Saclay and QUTE working group) info taken from QT Roadmap sections 1.1 and 2.1 EU list of QT research groups has ~440 entries, many interested in QC * full member of the E.U. until at least March 2019 !

Kaiser Wilhelm Memorial Church, Berlin

QC intro + motivation Quantum Computing in an nut U quantum register : set of quantum bits quantum bit : two basis states any arbitrary superposition is a possible state a N qubit register has 2N basis states: any arbitrary superposition of basis states can exist The register of a quantum processor evolves by applying quantum gates to qubits QM being linear the evolution can be massively parallel U I X > + I X > + I X> + ... U I X > + U I X > + U I X> + ... But readout only delivers a N bit answer The art of QC: I SOL > I X > measurement Factorization algorithm (1994) Integer N Runtime best known classical Shor Peter Shor How many qubits for overcoming a classical computer ? The most advanced classical computers & codes can simulate approx. 45 interacting qubits a QC with 50-100 ideal qubits could out-perform classical computers (for some tasks) A QC is « the most powerful computer allowed by the laws of physics » (as far as we know!). But it is *very* difficult technology, and the Universal QC is still a long-term (>10 yrs) objective.

The error correction mountain log10(no.operations) log10(scale-up) log10(gate error) Overhead and noise threshold of fault-tolerant quantum error correction, A.M.Steane, PRA 2003

Example QC hardware platforms superconducting circuits trapped atomic ions electronic semiconductor qubits linear optics impurity spins in solids (e.g. NV centres) blue: usually cryogenic red: usually room temp.

Some examples of state-of-the-art log10 (no.operations) log10 (no.qubits) log10 (error) superconducting circuits (cryo.) semiconductor qubits (cryo.) trapped ions (room temp.)

Some examples of state-of-the-art log10 (no.operations) log10 (no.qubits) log10 (error) 1-qubit gate memory initialisation, readout 1-qubit gate superconducting circuits (cryo.) semiconductor qubits (cryo.) trapped ions (room temp.) initialisation 1-qubit gate

Some examples of state-of-the-art log10 (no.operations) log10 (no.qubits) log10 (error) 1-qubit gate memory initialisation, readout 1-qubit gate 2-qubit gate 2-qubit gate (in 5-qubit device) 5 qubits, arb. control 20 qubits, limited control superconducting circuits (cryo.) semiconductor qubits (cryo.) trapped ions (room temp.) initialisation 1-qubit gate

Partial history of classical computing 1860s designs for a mechanical computer (Babbage & Lovelace) 1930s functioning mechanical computers (Zuse) 1940s electronic valve-based computers (Turing & Flowers) 1947 invention of transistor (Bardeen, Brattain & Shockley) 1959 development of first integrated circuits (Kilby) 1971 integrated circuit CPU (Intel 4004) feature size (nm) no. of transistors per chip year fs = feature size, Nt = no. transistors per chip for DRAMs From “Evolutionary Model of Moore’s Law”, Joachim Kaldasch, EBC Hochschule Berlin, ISRN Economics, 781623, (2014).

Partial history of 2-qubit gates superconducting qubits ions: laser gates Turchette et al. Sackett et al. Rowe et al. Leibfried et al. Benhelm et al. *Ballance et al. *Gaebler et al. *Steffen et al. *DiCarlo et al. *Chow et al. *Barends et al. * exclude SPAM errors

Partial history of 2-qubit gates ions: far-field m.w. superconducting qubits ions: near-field microwave ions: laser gates Near-field microwave: 100x progress is one step! (Roughly 10x from “engineering”, 10x from “physics”). Turchette et al. Sackett et al. Rowe et al. Leibfried et al. Benhelm et al. *Ballance et al. *Gaebler et al. *Steffen et al. *DiCarlo et al. *Chow et al. *Barends et al. Ospelkaus et al. *Harty et al. *Khromova et al. *Weidt et al. * exclude SPAM errors

Partial history of 2-qubit gates ions: far-field m.w. superconducting qubits ions: near-field microwave ions: laser gates Near-field microwave: 100x progress is one step! (Roughly 10x from “engineering”, 10x from “physics”). Turchette et al. Sackett et al. Rowe et al. Leibfried et al. Benhelm et al. *Ballance et al. *Gaebler et al. *Steffen et al. *DiCarlo et al. *Chow et al. *Barends et al. Ospelkaus et al. *Harty et al. *Khromova et al. *Weidt et al. * exclude SPAM errors

Quantum networking

“Climbing Mount Impossible” log10(no.operations) log10(scale-up) log10(gate error) You are here Overhead and noise threshold of fault-tolerant quantum error correction, A.M.Steane, PRA 2003

NQIT: Networked Quantum Information Technology Network of 20 ion traps each with 20 qubits “The Q20:20 Engine”

Sr/Ca Next steps: mixed-species Ca43/Sr88 Ca/Sr wobble gate laser diagnostics controllers & lock electronics diode lasers (422,1033, 1092nm) switching AOMs Rack-mount Sr+ laser system Sr-88 / Ca-40 Ca/Sr gate error scattering error heating rate error total error wobble gate P=50mW per beam, w=27um out-of-phase mode 3.07MHz heating rate 50/sec (estimate) For t_g<200us, Raman beam power constant (5mW per beam, w_0=27um) and Raman detuning varied. For t_g>200us, Raman detuning constant and power varied (as scattering error is negligible in this regime). Photon scattering error limit (from scattering to D states) is 0.5e-4 (CJB thesis).

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