- QUANTUM ERROR CORRECTION ENCODING ISOMETRY HOW TO
- QUANTUM ERROR CORRECTION ENCODING ISOMETRY VERIFICATION
- QUANTUM ERROR CORRECTION ENCODING ISOMETRY CODE
- QUANTUM ERROR CORRECTION ENCODING ISOMETRY OFFLINE
Quantum error correction for quantum memories.
QUANTUM ERROR CORRECTION ENCODING ISOMETRY CODE
Direct measurement of Bacon–Shor code stabilizers. Logical performance of 9 qubit compass codes in ion traps with crosstalk errors. Subsystem fault tolerance with the Bacon–Shor code. Operator quantum error-correcting subsystems for self-correcting quantum memories. Benchmarking an 11-qubit quantum computer. Demonstration of a small programmable quantum computer with atomic qubits. Error correction of a logical grid state qubit by dissipative pumping. Quantum error correction of a qubit encoded in grid states of an oscillator. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Encoding a qubit in a trapped-ion mechanical oscillator. Implementing a universal gate set on a logical qubit encoded in an oscillator. Quantum teleportation of physical qubits into logical code-spaces. Quantum computations on a topologically encoded qubit.
QUANTUM ERROR CORRECTION ENCODING ISOMETRY VERIFICATION
Experimental verification of five-qubit quantum error correction with superconducting qubits. State preservation by repetitive error detection in a superconducting quantum circuit. Detecting bit-flip errors in a logical qubit using stabilizer measurements. Realization of three-qubit quantum error correction with superconducting circuits. Experimental repetitive quantum error correction. Repeated quantum error detection in a surface code. Fault-tolerant logical gates in the IBM quantum experience. Experimental demonstration of fault-tolerant state preparation with superconducting qubits. Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. PhD thesis, California Institute of Technology (1997).Ĭórcoles, A. Stabilizer Codes and Quantum Error Correction.
QUANTUM ERROR CORRECTION ENCODING ISOMETRY HOW TO
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum computing enhanced computational catalysis. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. Elucidating reaction mechanisms on quantum computers. Simulated quantum computation of molecular energies. Simulation of many-body Fermi systems on a universal quantum computer. Universal quantum computation with ideal Clifford gates and noisy ancillas. Fault-tolerant quantum computation with constant error rate. Theory of fault-tolerant quantum computation. Threshold accuracy for quantum computation. 37th Conference on Foundations of Computer Science (1996). Theory of quantum error-correcting codes. Scheme for reducing decoherence in quantum computer memory. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. In addition, we prepare magic states with fidelities that exceed the distillation threshold 7, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant control.
QUANTUM ERROR CORRECTION ENCODING ISOMETRY OFFLINE
The result of fault-tolerant design is an average state preparation and measurement error of 0.6 per cent and a Clifford gate error of 0.3 per cent after offline error correction. When we compare these fault-tolerant protocols to non-fault-tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. Here we experimentally demonstrate fault-tolerant circuits for the preparation, measurement, rotation and stabilizer measurement of a Bacon–Shor logical qubit using 13 trapped ion qubits. Although fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. Fault-tolerant circuits contain the spread of errors while controlling the logical qubit, and are essential for realizing error suppression in practice 3, 4, 5, 6. These extra degrees of freedom enable the detection and correction of errors, but also increase the control complexity of the encoded logical qubit. Quantum error correction protects fragile quantum information by encoding it into a larger quantum system 1, 2.
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