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Low-distance Surface Codes under Realistic Quantum Noise

Krysta Svore, Microsoft Research

(Session : from )

We consider three distance-3 surface code layouts (13, 17, and 25 qubits) and study their performance under several realistic noise models. We analyze the circuit resources required for these layouts and determine that a 17-qubit layout is preferable. We then compare the Pauli-twirl approximation (PTA) of quantum decoherence to a real amplitude and phase damping channel (APC). Our surface code simulation results indicate that using PTA produces a pessimistic estimate of the logical bit-flip error rate and a reliable estimate of the logical phase-flip error rate as compared to APC. This indicates that the surface code threshold under realistic noise may in fact be better than previously estimated. Finally, we study the code's performance under several realistic architectural settings and determine regimes of architectural parameters for which reliable computation is possible. We also prescribe the rate at which to error correct in a reliable quantum memory based on a small surface code.

Faster Phase Estimation

Krysta Svore, Microsoft Research

(Session : from )

We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width. We show that the use of purely random measurements requires a number of measurements that is optimal up to constant factors, albeit at the cost of exponential classical post-processing; the method can also be used to improve classical signal processing. We then develop a quantum algorithm for phase estimation that yields an asymptotic improvement in runtime, coming within a factor of log of the minimum number of measurements required while still requiring only minimal classical post-processing. The corresponding quantum circuit requires asymptotically lower depth and width (number of qubits) than quantum phase estimation.

Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries

Krysta Svore, Microsoft Research

(Session 8 : Friday from 2:30pm - 3:00pm)

We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance epsilon that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop ``Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit Z-axis rotation to within distance epsilon, where the number of T gates scales as 1.26*log_2(1/\epsilon) - 3.53, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of 2.4 * log_2(1/\epsilon) - 3.28 can be achieved for arbitrary unitaries and a small range of epsilon, which is roughly twice as good as optimal deterministic decomposition methods.