Abstract
An encoderless quantum code is capable of connecting quantum information by replacing the encoder circuit with a fault-tolerant single-qubit gate arrangement. As a further benefit, in contrast to state preparation techniques, our encoderless scheme requires no prior knowledge of the input information, therefore totally unknown states can be encoded fault-tolerantly. Our encoderless quantum code delivers a frame error rate that is three orders of magnitude lower than that of the corresponding scheme relying on a non-fault-tolerant encoder, when the gate error probability is as high as 10−3.
Highlights
A quantum error correction code (QECC) must be implemented by a fault-tolerant circuit that is capable of avoiding avalanche-like error-proliferation1 in quantum gates
Many traditional encoding circuits are not fault-tolerant [1]–[3]. This is because these circuits have two-qubit controlled-NOT (CNOT) gate connections which have the property that a single qubit error propagates to many qubits, proliferating the errors [4]. This overwhelms the error correction capability of the [n, k, d] QECC, more errors are inflicted by the circuit than are corrected, where n is the number of encoded physical qubits, k is the number of original information qubits, d is the minimum distance and t is the error correction capability where we have t = (d − 1)/2 for the family of maximum-minimum distance codes
The arrangement of fewer single qubit gates means that the circuit is fault-tolerant leading to a FER crossover with the uncoded scheme, where Pg < Pth
Summary
A quantum error correction code (QECC) must be implemented by a fault-tolerant circuit that is capable of avoiding avalanche-like error-proliferation in quantum gates. Based on the aforementioned background, our novel contributions are: 1) We propose a technique of preparing the n-qubit encoded version of a k-qubit quantum state using imperfect quantum logic gates that are prone to the deleterious effects of decoherence both to repetition codes and to Steanes code This scheme has the added benefit that it does not require prior knowledge of the information to be encoded. We achieve this ambitious objective by proposing an additional syndrome decoding step, which prepares a code space containing the same legitimate codewords This encoderless scheme relies on a fault-tolerant circuit and as a further benefit, it requires fewer gates than the family of common state preparation techniques [1], [2].
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