Program

SESSION 9b: Error detection, correction, and verification (Lumpkins Ballroom North)

Chair: (Travis Scholten (University of New Mexico))
3:45pm-4:15pmKarl Mayer, National Institute of Standards and Technology, Boulder
Bounding the quantum process fidelity with a minimal set of input states
Abstract. We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors, and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. Finally, we introduce a set of d+1 pure states in d dimensions which form a minimal symmetric POVM. We prove that for this set of input states the minimum fidelity scales linearly with the average output state error, providing an efficient method for estimating the process fidelity without the use of full process tomography.
4:15pm-4:45pmKenneth Rudinger, Sandia National Laboratories
Classifying and diagnosing crosstalk in quantum information processors
Abstract. Quantum information processor technology continues to progress, as illustrated by the construction and operation of devices with as many as sixteen qubits. While high-fidelity one- and two-qubit operations have been exhibited on such devices, there are a variety of errors that must be further mitigated prior to executing quantum error correction or meaningful quantum algorithms. One such error source is that of crosstalk, the process by which one or more qubits is affected by the state of, or operations on, neighboring qubits. In this talk we present a comprehensive taxonomy of crosstalk, and provide architecture-agnostic methods for detecting and characterizing such noise processes. Using experimental data taken from superconducting qubit systems, we show these protocols can be used to successfully diagnose multiple forms of crosstalk. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
4:45pm-5:15pmTomas Jochym-O'Connor, California Institute of Technology
Advantages of versatile neural-network decoders for topological codes
Abstract. Decoding of generic stabilizer codes is a computationally hard problem, even given simple noise models. While the task is simplified for codes with some structure, such as topological codes with geometrically-local stabilizer generators, finding optimal decoders remains challenging. In our work, we analyze the versatility and performance of neural network decoders. We rephrase the decoding problem as a classification task, which is well-suited for machine learning. We show versatility of the approach by studying two-dimensional variants of the toric and color codes and different error models, bit- and phase-flip, as well as nearest-neighbor depolarizing noise models. The resulting decoders have improved performance and thresholds over previously known methods. We believe that neural decoding will play a key role in error correction for near-term experiments where unknown noise sources could severely affect the performance of the code.
5:15pm-5:45pmRui Chao, University of Southern California
Fault-tolerant quantum computation with few qubits
Abstract. Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. We give space-efficient methods for fault-tolerant error correction and computation, which are promising to realize on near-term devices: 1. For many distance-three codes, two extra qubits are enough to perform fault-tolerant error correction. 2. For various small codes encoding multiple logical qubits, two ancilla qubits are also enough to apply arbitrary logical Clifford operations, and with another two ancillas we can even achieve universal computation. For example, with 19 qubits one can protect and compute universally on seven encoded qubits, fault tolerantly. Our main technique is to use circuit gadgets to catch bad faults. For space-efficient error correction, we add a “flag” ancilla to catch those faults that spread to multi-qubit data errors. For computation within a code block, multi-qubit faults are caught using flag gadgets, and are remedied before they can spread. These procedures could enable testing more sophisticated protected circuits in small-scale quantum devices, and could be used to reduce the overhead of general fault-tolerance schemes.
5:45pm-6:15pmGrant Salton, Stanford University
Approximate operator algebra quantum error correction (decoding the hologram in AdS/CFT)
Abstract. Quantum error correction -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable. In this talk, I'll mention a few examples of error correction in the wild, including the recent discovery that the AdS/CFT correspondence implements quantum error correction. We will then study the hypothesis that any local bulk operator in AdS can be reconstructed using only a causally disconnected subregion of the CFT. This hypothesis has been proven under the assumption that error correction in AdS/CFT is exact, but this assumption is not expected to be true. Fortunately, recent advances in the theory of approximate quantum error correction have emerged. We will review these results on recoverability and approximate quantum error correction, as well as AdS/CFT and the so-called entanglement wedge reconstruction hypothesis. We will then prove the entanglement wedge hypothesis robustly and find an explicit formula for reconstructed bulk operators. If time permits, we will explore a generalization of the theory of universal recovery channels to the case of finite-dimensional von Neumann algebras.

SQuInT Chief Organizer
Akimasa Miyake, Assistant Professor
amiyake@unm.edu

SQuInT Co-Organizer
Mark M. Wilde, Assistant Professor LSU
mwilde@phys.lsu.edu

SQuInT Administrator
Gloria Cordova
gjcordo1@unm.edu
505 277-1850

SQuInT Founder
Ivan Deutsch, Regents' Professor
ideutsch@unm.edu

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