To balance a pencil on its tip : on the passive approach to quantum error correction

Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many proofs of concept (also known as the ‘threshold theorems’, e.g., Aharonov & Ben–Or, 1996; Knill & Laflamme, 1996; Knill et al., 1996; Knill et al., 1998), the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists still struggle to maintain useful quantum coherence in QIP devices with more than a pair of qubits (e.g., Blatt & Wineland, 2008). This slow progress has prompted debates on the feasibility of quantum computers, yet the quantum information community has dismissed the skepticism as “ideology” (Aaronson, 2004), claiming that, given the threshold theorems, the obstacles are merely technological (Kaye et al., 2007, p. 240). A recent analysis (Alicki et al., 2006), however, has shown that the threshold theorems, originally proven for a Markovian noise model, are physically suspect, and that once non–Markovian noise is considered, the feasibility question is still open. Analogies from the foundations of classical statistical mechanics (SM) suggest further (Hagar, 2009), that for this question to be well–posed, a shift in perspective is required. Instead of active error correction, the appropriate framework for debating this question is the project of passive error correction, or error avoidance: rather than trying to constantly ‘cool down’ the QIP device and prevent its thermalization, one should try to locate those regions in the device’s state space which are thermodynamically abnormal, i.e., those regions in the device’s state space which resist thermalization regardless of external noise. This paper is intended as a further contribution to the debate on the feasibility of large–scale, fault–tolerant and computationally superior quantum computers. Relying again on analogies from the foundations of classical SM, it suggests a skeptical conjecture and frames it in the passive, error avoidance, context. To be clear, while I do hint at various routes in which such a conjecture could be proven, in doing so I do not pretend to present a ‘no–go’ argument nor a definitive skeptical attack; my sole intention is to make the debate more precise. Moreover, even if this skeptical conjecture turned out to be true, this would not render QIP devices useless; one might still use them to outperform existing classical computers for certain designated tasks that require only few qubits. It would mean, however, that the aforementioned threshold theorems that support the feasibility of an arbitrarily scalable computationally superior quantum computation were misleading. The paper is structured as follows. In section 2 I sketch the passive approach to quantum error correction. Section 3 presents the main background for the statistical mechanical analogy that drives my argument, namely, Boltzmann’s combinatorial approach to the problem of the thermodynamic arrow in time. In section 4 I present the skeptical conjecture I believe can (and should) be made precise using this analogy, and give several hints how to pursue a possible proof thereof. Limited conclusions are given in Section 5.