Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

How often must we apply syndrome measurements?

Yaakov S. Weinstein

Published May 21, 2015• 0 citations

Abstract

Quantum error correction requires encoding quantum information into a quantum error correction code and measuring error syndromes to detect and identify possible errors. Quantum fault tolerance typically assumes that syndrome measurements are applied after every logical gate at great expense both in time and number of qubits. Here we demonstrate that not only is this not necessary, but that we may achieve greater accuracy when applying syndrome measurements less often. Our simulations are performed within the [7,1,3] quantum error correction code but may be applicable to a broad range of codes.

DOI: 10.1117/12.2180288

Related papers

How Often Must We Apply Syndrome Measurements

Yaakov S. Weinstein

Quantum error correction requires encoding quantum information into a quantum error correction code and measuring error syndromes to detect and identify possible errors. Quantum fault tolerance typically assumes that syndrome measurements are applied after every logical gate at great expense both in time and number of qubits. Here we demonstrate that not only is this not necessary, but that we may achieve greater accuracy when applying syndrome measurements less often. Our simulations are performed within the [[7,1,3]] quantum error correction code but may be applicable to a broad range of codes.

Bulletin of the American Physical SocietyMar 3, 20150 citations

How Often Must Quantum Error Correction be Implemented

Yaakov S. Weinstein

Correcting errors is a vital but expensive component of fault tolerant quantum computation. Standard fault tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after every quantum gate. In fact, this is not necessary. Here we demonstrate that error correction should be applied more sparingly. We simulate encoded single qubit rotations within the [7,1,3] code and show via fidelity measures that applying error correction after every gate is not desirable. The simulations also shed light on what accuracy can be expected for noisy error correction and thus to what accuracy arbitrary single qubit rotations should be implemented.

May 13, 20130 citations

Quantum-error-correction implementation after multiple gates

Yaakov S. Weinstein

Correcting errors is a vital but expensive component of fault-tolerant quantum computation. Standard fault-tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after every quantum gate. In fact, this is not necessary. Here we demonstrate that error correction should be applied more sparingly. We simulate encoded single-qubit rotations within the [7,1,3] code and show via fidelity measures that applying error correction after every gate is not desirable.

arXiv:1305.2763Physical Review AJul 23, 201311 citations

Syndrome Measurement Strategies for the [[7,1,3]] Code

Yaakov S. Weinstein

Quantum error correction (QEC) entails the encoding of quantum information into a QEC code space, measuring error syndromes to properly locate and identify errors, and, if necessary, applying a proper recovery operation. Here we compare three syndrome measurement protocols for the [[7,1,3]] QEC code: Shor states, Steane states, and one ancilla qubit by simulating the implementation of 50 logical gates with the syndrome measurements interspersed between the gates at different intervals. We then compare the fidelities for the different syndrome measurement types. Our simulations show that the optimal syndrome measurement strategy is generally not to apply syndrome measurements after every gate but depends on the details of the error environment. Our simulations also allow a quantum computer programmer to weigh computational accuracy versus resource consumption (time and number of qubits) for a particular error environment. In addition, we show that applying syndrome measurements that are unnecessary from the standpoint of quantum fault tolerance may be helpful in achieving better accuracy or in lowering resource consumption. Finally, our simulations demonstrate that the single-qubit non-fault tolerant syndrome measurement strategy achieves comparable fidelity to those that are fault tolerant.

arXiv:1505.07390May 27, 20150 citations

Short Shor-style syndrome sequences

Nicolas Delfosse, Ben W. Reichardt

We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both code-specific and general methods, using a variety of techniques and in a variety of settings. We design new quantum error-correcting codes specifically for efficient error correction, e.g., allowing single-shot error correction. For codes with multiple logical qubits, we give methods for combining error correction with partial logical measurements. There are tradeoffs in choosing a code and error-correction technique. While to date most work has concentrated on optimizing the syndrome-extraction procedure, we show that there are also substantial benefits to optimizing how the measured syndromes are chosen and used. As an example, we design single-shot measurement sequences for fault-tolerant quantum error correction with the 16-qubit extended Hamming code. Our scheme uses 10 syndrome bit measurements, compared to 40 measurements with the Shor scheme. We design single-shot logical measurements as well: any logical Z measurement can be made together with fault-tolerant error correction using only 11 measurements. For comparison, using the Shor scheme a basic implementation of such a non-destructive logical measurement uses 63 measurements. We also offer ten open problems, the solutions of which could lead to substantial improvements of fault-tolerant error correction.

arXiv:2008.05051Aug 12, 20204 citations

Experimental demonstration of quantum fault tolerance

Norbert M. Linke, Marco Gutiérrez, K. A. Landsman +4 more

Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent detection or correction of errors without destroying the logical state itself through direct measurement. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. The advantage persists in the face of large added error rates and experimental calibration errors.

Nov 21, 20163 citations