Overview of quantum error prevention and leakage elimination (original) (raw)
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Combined Error Correction Techniques for Quantum Computing Architectures
2002
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing or eliminating errors, but not one, alone, will serve as a panacea. One must therefore take advantage of the strength of each of these techniques so that we may extend the coherence times of the quantum systems and create more reliable computing devices. To this end we give a general strategy for using dynamical decoupling operations on encoded subspaces. These encodings may be of any form; of particular importance are decoherence-free subspaces and quantum error correction codes. We then give means for empirically determining an appropriate set of dynamical decoupling operations for a given experiment. Using these techniques, we then propose a comprehensive encoding solution to many of the problems of quantum computing proposals which use exchange...
Overcoming leakage in quantum error correction
Nature Physics
The leakage of quantum information out of the two computational states of a qubit into other energy states represents a major challenge for quantum error correction. During the operation of an error-corrected algorithm, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of the logical error with scale, thus challenging the feasibility of quantum error correction as a path towards fault-tolerant quantum computation. Here, we demonstrate a distance-3 surface code and distance-21 bit-flip code on a quantum processor for which leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a tenfold reduction in the steady-state leakage population of the data qubits encoding the logical state and an average leakage population of less than 1 × 10−3 throughout the entire device. Our leakage removal p...
Phys Rev a, 2001
Decoherence-free subspaces (DFSs) shield quantum information from errors induced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of the Pauli group (the group of tensor products of Pauli matrices). Unlike previous studies of DFSs, this type of error does not involve any spatial symmetry assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class of DFSs. We do so by introducing a hybrid DFS quantum error-correcting-code approach, where errors that arise due to departure of the codewords from the DFS are corrected actively.
Protecting quantum information encoded in decoherence-free states against exchange errors
Physical Review A, 2000
The exchange interaction between identical qubits in a quantum information processor gives rise to unitary two-qubit errors. It is shown here that decoherence free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which however do not take the decoherence free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS-quantum error correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett. 82, 4556 (1999)].
2001
Proposals for physical systems to act as quantum computers are inevitably plagued by the unavoidable coupling with the environment (bath) that causes decoherence, and by technological difficulties connected with the controllability of quantum states. Several techniques exist for achieving reliable quantum computation by countering the effects of decoherence. At this time, however, not one, by itself, will serve as a panacea for error correction. In this paper, we introduce a method that combines system-bath decoupling operations with error avoidance or active error correction in order to address these major concerns. By using an empirical approach to error correction based on experimental data, and an efficient set of decoupling operations that will serve to protect encoded quantum information, we are able to propose a comprehensive method for reducing the adverse effects of decoherence, in particular in scalable solid state quantum computing devices. Our method has the added benefit of significantly reducing design constraints associated with certain difficult-to-implement single-qubit operations in these devices. We illustrate our results by applying them to quantum dot quantum computing proposals.
A Scheme of Concatenated Quantum Code to Protect against both Computational Error and an Erasure
Corr, 2010
We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure. Grassl et al.[4] considered a situation in which the position of the erroneous qubits is known. According to classical coding theory, they called this model the quantum erasure channel (QEC). Alterations or changes caused by the environment can be characterized as being of two types: (i) those that satisfy to certain conditions that allow their correction, i.e., that agree with the conditions established by Knill and Laflamme[2]. They are represented by Pauli matrices and are called "computational errors"[5]. Such matrices constitute the computational space, and (ii) those that lead the state encoded out of the computational space. These alterations characterize the QEC. Erasures are both detectable and locatable, which suggests that they should be easier to rectify than computational errors. In fact, quantum communication channels can tolerate a higher rate of erasure (p erasure < 0.5) than depolarization (p comp < 1/3)[6]. Dawson et al.[7] considered an error model which contains both erasure and computational errors, finding that fault-tolerant quantum computation is possible with p erasure < 3 × 10 −3 and p comp < 10 −4 .
Quantum error correction beyond qubits
Nature Physics, 2009
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by socalled decoherence noise. Indeed, the discovery of quantum error correction (QEC) 1,2 turned the field of quantum information from an academic curiosity into a developing technology. Here we present a continuous-variable experimental implementation of a QEC code, based upon entanglement among 9 optical beams 3 . In principle, this 9-wavepacket adaptation of Shor's original 9qubit scheme 1 allows for full quantum error correction against an arbitrary single-beam (singleparty) error.
Quantum error correction without measurement and an efficient recovery operation
2011
It is known that one can do quantum error correction without syndrome measurement, which is often done in operator quantum error correction (OQEC). However, the physical realization could be challenging, especially when the recovery process involves high-rank projection operators and a superoperator. We use operator theory to improve OQEC so that the implementation can always be done by unitary gates followed by a partial trace operation. Examples are given to show that our error correction scheme outperforms the existing ones in various scenarios.
Experimental Implementation of a Concatenated Quantum Error-Correcting Code
Physical Review Letters, 2005
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct against phase errors with a strong correlated component. The experiment was performed using liquid-state nuclear magnetic resonance techniques on a four spin subsystem of labeled crotonic acid. Our results show that concatenation between active and passive quantum error correcting codes offers a practical tool to handle realistic noise contributed by both independent and correlated errors.
Error tracing in linear and concatenated quantum circuits
Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance if quantum computation is to be carried out in reality. Ideally, an error correction block should be placed after every gate operation in a quantum circuit. This increases the overhead and reduced the speedup of the quantum circuit. Moreover, the error correction blocks themselves may induce errors as the gates used for error correction may be noisy. In this paper, we have proposed a procedure to trace error probability due to noisy gates and decoherence in quantum circuit and place an error correcting block only when the error probability exceeds a certain threshold. This procedure shows a drastic reduction in the required number of error correcting blocks. Furthermore, we have considered concatenated codes with tile structure layout lattice architecture[25][21],[24] and SWAP gate based qubit transport mechanism. Tracing errors in higher levels of concatenation shows that, in most cases, after 1 or 2 levels of concatenation, the number of QECC blocks required become static. However, since the gate count increases with increasing concatenation, the percentage saving in gate count is considerably high.