Related papers: A Converse for Fault-tolerant Quantum Computation
Existing lower bounds on redundancy in fault-tolerant quantum circuits are applicable when both the input and the intended output are quantum states. These bounds may not necessarily hold, however, when the input and the intended output are…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
A quantum computer -- i.e., a computer capable of manipulating data in quantum superposition -- would find applications including factoring, quantum simulation and tests of basic quantum theory. Since quantum superpositions are fragile, the…
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the…
As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design,…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than…
The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a…
Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary k-qubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary…
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices…
Fault-tolerant quantum computing based on surface codes has emerged as a popular route to large-scale quantum computers capable of accurate computation even in the presence of noise. Its popularity is, in part, because the fault-tolerance…
Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…
We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a…
Errors occurring on noisy hardware pose a key challenge to reliable quantum computing. Existing techniques such as error correction, mitigation, or suppression typically separate the error handling from the algorithm analysis and design. In…
Noise is ubiquitous in quantum systems and is a major obstacle for the advancement of quantum information science. Noise-robust quantum control achieves high-fidelity operations by engineering the evolution path so that first-order noise…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…