Robust calibration of a universal single-qubit gate set via robust phase estimation

An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors but is both time consuming (when one wants to learn only a few key parameters) and usually inaccurate without resources such as perfect state preparation and measurement, which might not be available. With the goal of efficiently and accurately estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge key systematic parameters (specifically, amplitude and off-resonance errors) in a universal single-qubit gate set with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling, and do so without entanglement and entirely within a single-qubit Hilbert space. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins et al., New J. Phys. 11, 073023 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073023].United States. Dept. of DefenseUnited States. Army Research Office. Quantum Algorithms ProgramAmerican Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Fixed-point adiabatic quantum search

Fixed-point quantum search algorithms succeed at finding one of M target items among N total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property—the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014)] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002)] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.American Society for Engineering Education. National Defense Science and Engineering Graduate FellowshipMIT-Harvard Center for Ultracold Atoms MIT International Science and Technology InitiativeNational Science Foundation (U.S.) (RQCC Project 1111337)Massachusetts Institute of Technology. Undergraduate Research Opportunities Program (Paul E. Gray Endowed Fund

Encoding a magic state with beyond break-even fidelity

We distill magic states to complete a universal set of fault-tolerant logic gates that is needed for large-scale quantum computing. By encoding better quality input states for our distillation procedure, we can reduce the considerable resource cost of producing magic states. We demonstrate an error-suppressed encoding scheme for a two-qubit input magic state, that we call the CZ state, on an array of superconducting qubits. Using a complete set of projective logical Pauli measurements, that are also tolerant to a single circuit error, we propose a circuit that demonstrates a magic state prepared with infidelity $(1.87 \pm 0.16) \times 10^{-2}$. Additionally, the yield of our scheme increases with the use of adaptive circuit elements that are conditioned in real time on mid-circuit measurement outcomes. We find our results are consistent with variations of the experiment, including where we use only post-selection in place of adaptive circuits, and where we interrogate our output state using quantum state tomography on the data qubits of the code. Remarkably, the error-suppressed preparation experiment demonstrates a fidelity exceeding that of the preparation of the same unencoded magic-state on any single pair of physical qubits on the same device.Comment: 10 pages, 7 figures, comments welcom

Big Data: Managing the Future\u27s Agriculture and Natural Resource Systems

Big Data: Managing the Future\u27s Agriculture and Natural Resource Systems Big data is the incredible flow of information that surrounds each of us, every day. Big data tools identify patterns and habits, not only in research, but in manufacturing, logistics–even ordering items online

Error rates and resource overheads of encoded three-qubit gates

A non-Clifford gate is required for universal quantum computation, and, typically, this is the most error-prone and resource-intensive logical operation on an error-correcting code. Small, single-qubit rotations are popular choices for this non-Clifford gate, but certain three-qubit gates, such as Toffoli or controlled-controlled-Z (ccz), are equivalent options that are also more suited for implementing some quantum algorithms, for instance, those with coherent classical subroutines. Here, we calculate error rates and resource overheads for implementing logical ccz with pieceable fault tolerance, a nontransversal method for implementing logical gates. We provide a comparison with a nonlocal magic-state scheme on a concatenated code and a local magic-state scheme on the surface code. We find the pieceable fault-tolerance scheme particularly advantaged over magic states on concatenated codes and in certain regimes over magic states on the surface code. Our results suggest that pieceable fault tolerance is a promising candidate for fault tolerance in a near-future quantum computer