SESSION 12: Quantum error correction and fault tolerance

Chair: (Andrew Landahl (Sandia))
1:15pm - 2:00pmBenjamin Brown, University of Sydney (invited)
Advances in surface code quantum computation
Abstract. The surface code has emerged as one of the leading candidate quantum error-correcting codes to maintain the logical qubits of the first generation of scalable quantum computers. In this talk I will summarise my recent results that may alleviate some of the issues towards the development of a quantum computer based on a surface code architecture. I will first discuss work showing how to complete a universal set of fault-tolerant logical gates with the surface code without the need for distillation methods. This includes work showing how we can braid Majorana modes lying at the corners of the planar code to realise Clifford operations. I will also explain how the surface code can be connected to its three-dimensional generalisation to realise a non-Clifford gate using a two-dimensional system. Both of these proposals offer new routes to reduce the resource cost of scalable quantum computation as they circumvent the need for conventional distillation methods to complete a universal set of logic gates. Finally, I will briefly mention new results where we show that we can increase the threshold of a tailored variant of the surface code by specialising the decoder to deal with the common situation where the noise each qubit experiences is biased towards dephasing. This development means that the surface code can tolerate a higher rate of noise such that it is more readily constructed in the laboratory with modern hardware.
2:00pm - 2:30pmVadym Kliuchnikov, Microsoft Research
Lower bounds on the non-Clifford resources for quantum computations
Abstract. We establish lower-bounds on the number of resource states, also known as magic states, needed to perform various quantum computing tasks, treating stabilizer operations as free. Our bounds apply to adaptive computations using measurements and an arbitrary number of stabilizer ancillas. We consider (1) resource state conversion, (2) single-qubit unitary synthesis, and (3) computational tasks. To prove our resource conversion bounds we introduce two new monotones, the stabilizer nullity and the dyadic monotone, and make use of the already-known stabilizer extent. We consider conversions that borrow resource states, known as catalyst states, and return them at the end of the algorithm. We show that catalysis is necessary for many conversions and introduce new catalytic conversions, some of which are close to optimal. By finding a canonical form for post-selected stabilizer computations, we show that approximating a single-qubit unitary to within diamond-norm precision ε requires at least 1/7⋅log₂(1/ε)−4/3 T-states on average. This is the first lower bound that applies to synthesis protocols using fall-back, mixing techniques, and where the number of ancillas used can depend on ε. Up to multiplicative factors, we optimally lower bound the number of T or CCZ states needed to implement the ubiquitous modular adder and multiply-controlled-Z operations. When the probability of Pauli measurement outcomes is 1/2, some of our bounds become tight to within a small additive constant.

SQuInT Chief Organizer
Akimasa Miyake, Associate Professor

SQuInT Co-Organizer
Brian Smith, Associate Professor UO

SQuInT Program Committee
Postdoctoral Fellows:
Markus Allgaier (UO OMQ)
Sayonee Ray (UNM CQuIC)
Pablo Poggi (UNM CQuIC)
Valerian Thiel (UO OMQ)

SQuInT Event Co-Organizers (Oregon)
Jorjie Arden
Holly Lynn

SQuInT Event Administrator (Oregon)
Brandy Todd

SQuInT Administrator (CQuIC)
Gloria Cordova
505 277-1850

SQuInT Founder
Ivan Deutsch, Regents' Professor, CQuIC Director

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