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arXiv:quant-ph/9605009

Error symmetrization in quantum computers

Asher Peres

Published May 13, 1996• 3 citations
arXivHTMLPDF

Abstract

It is possible to reduce some types of quantum computation errors by symmetrizing the quantum state of a redundant array. Various models are discussed.
DOI
10.48550/arxiv.quant-ph/9605009

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Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the computer, and forcing their joint quantum state to be completely symmetric. On the other hand, isolated errors can be corrected by quantum codewords that represent a logical qubit in a redundant way, by several physical qubits. If one of the physical qubits is perturbed, for example if it gets entangled with an unknown environment, there still is enough information encoded in the other physical qubits to restore the logical qubit, and disentangle it from the environment. The recovery procedure may consist of unitary operations, without the need of actually identifying the error.
We propose a method for the stabilization of quantum computations (including quantum state storage). The method is based on the operation of projection into SYM\cal SYMSYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting SYM\cal SYMSYM--projection and discuss the stabilizing effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.
A broad effort is currently underway to develop quantum computers that can outperform classical counterparts for certain computational or simulation tasks. Suppressing errors is one of the central challenges for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected “logical” qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. In this talk, we will discuss the recent advances involving programmable, coherent manipulation of quantum systems based on neutral atom arrays excited into Rydberg states, allowing the control over several hundred qubits in two dimensions. Optical control techniques are central to this approach. In particular, we use this platform to explore quantum algorithms with encoded logical qubits and quantum error correction techniques. Using this logical processor with various types of error-correcting codes, we demonstrate that we can improve logical two-qubit gates by increasing code size, outperform physical qubit fidelities, create logical GHZ states, and perform computationally complex scrambling circuits using 48 logical qubits and hundreds of logical gates. These results herald the advent of early error-corrected quantum computation, enabling new applications and inspiring a shift in addressing both the challenges and opportunities that lay ahead.
In this paper, we develop a system with redundant splicing topology by studying the ET (error-tolerant) system, and study its unique advantages in topology. And tapped the potential of application in quantum computing. Through theoretical analysis and modeling, it reveals various possibilities for the design of two-dimensional and even three-dimensional quantum computing systems, which are widely neglected in the field of quantum computing, and combines some features of the previous ET system design. And the design methodology is discussed; the network design of the novel quantum computing system can be further introduced into the unique topology.