Quantum Computing with Very Noisy Devices

Quantum Computing with Very Noisy Devices

2 Nov 2004 | E. Knill
Quantum computing with noisy devices: This paper presents evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is higher than previously thought. However, the resources required for such high error probabilities are excessive. Fortunately, these resources decrease rapidly with lower error probabilities. If quantum resources comparable to today's digital computers are available, non-trivial quantum computations can be implemented at error probabilities as high as 1% per gate. Quantum computing is motivated by its potential for increased computational power. Experimental efforts aim to demonstrate scalable quantum computing, which requires efficient implementation of arbitrarily large computations with minimal error. DiVincenzo's criteria for scalable quantum computing include low noise in physical gates. The error model describes the type of noise affecting gates, while a fault-tolerant architecture enables scalable quantum computing in the presence of noise. The paper introduces a fault-tolerant architecture called the $ C_{4}/C_{6} $ architecture, suitable for error probabilities between $ 10^{-4} $ and $ 10^{-2} $. This architecture uses error-detecting codes and concatenation to reduce error probabilities. The threshold theorem states that if the error probability per gate is below a threshold, scalable quantum computing is possible. The $ C_{4}/C_{6} $ architecture differs from previous ones in five ways: it uses simple error-detecting codes, performs error correction in one step, uses a minimal set of operations, avoids traditional syndrome-based schemes, and introduces postselected computing with its own thresholds. The architecture uses stabilizer codes and concatenation to encode qubits and gates, reducing error probabilities. The paper also discusses the error model, assuming independent errors and using a depolarizing model for gates. It analyzes the $ C_{4}/C_{6} $ architecture's resource requirements and compares them to Steane's architecture. The $ C_{4}/C_{6} $ architecture's resource requirements are within two orders of magnitude of Steane's at $ \gamma = 10^{-4} $. The paper concludes that scalable quantum computing is possible at error probabilities above 0.01, and that fault-tolerant postselected computing can achieve higher thresholds. The work highlights the importance of fault-tolerant architectures for scalable quantum computing and the need for further research to improve resource requirements, particularly at high error probabilities.Quantum computing with noisy devices: This paper presents evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is higher than previously thought. However, the resources required for such high error probabilities are excessive. Fortunately, these resources decrease rapidly with lower error probabilities. If quantum resources comparable to today's digital computers are available, non-trivial quantum computations can be implemented at error probabilities as high as 1% per gate. Quantum computing is motivated by its potential for increased computational power. Experimental efforts aim to demonstrate scalable quantum computing, which requires efficient implementation of arbitrarily large computations with minimal error. DiVincenzo's criteria for scalable quantum computing include low noise in physical gates. The error model describes the type of noise affecting gates, while a fault-tolerant architecture enables scalable quantum computing in the presence of noise. The paper introduces a fault-tolerant architecture called the $ C_{4}/C_{6} $ architecture, suitable for error probabilities between $ 10^{-4} $ and $ 10^{-2} $. This architecture uses error-detecting codes and concatenation to reduce error probabilities. The threshold theorem states that if the error probability per gate is below a threshold, scalable quantum computing is possible. The $ C_{4}/C_{6} $ architecture differs from previous ones in five ways: it uses simple error-detecting codes, performs error correction in one step, uses a minimal set of operations, avoids traditional syndrome-based schemes, and introduces postselected computing with its own thresholds. The architecture uses stabilizer codes and concatenation to encode qubits and gates, reducing error probabilities. The paper also discusses the error model, assuming independent errors and using a depolarizing model for gates. It analyzes the $ C_{4}/C_{6} $ architecture's resource requirements and compares them to Steane's architecture. The $ C_{4}/C_{6} $ architecture's resource requirements are within two orders of magnitude of Steane's at $ \gamma = 10^{-4} $. The paper concludes that scalable quantum computing is possible at error probabilities above 0.01, and that fault-tolerant postselected computing can achieve higher thresholds. The work highlights the importance of fault-tolerant architectures for scalable quantum computing and the need for further research to improve resource requirements, particularly at high error probabilities.
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