It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of nontransversal, yet still fault-tolerant, gates that work directly on sma...

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This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed. We use QuRE to estimate the number of qubits, quantum gates, and amount of time needed to factor a 1024-bit number on several candidate quantum technologies ...

EEcient use of redundant computing resources is desirable in fault tolerance. To meet its fault tolerance requirements, a task may need all the computing modules; but when a lesser amount of fault tolerance is suucient, then multiple tasks should be allowed to execute concurrently. Systems supporting this type of operation usually have their fault tolerance controlled by software. Fault toleran...

The quantum logic gates used in the design of a computer should be both universal, meaning arbitrary computations can performed, and fault-tolerant, keep errors from cascading out control. A number no-go theorems constrain ways which set fault-tolerant universal. These are very restrictive, conventional wisdom holds that universal gate cannot implemented natively, requiring us to use costly dis...

A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance(NMR) under adiabatic conditions. By the adiabatic requirement, the result is inexact unless the Hamiltonian changes extremely slowly. However, in quantum computation, everything must be completed within the decoherence tim...

Given a gate set S universal for quantum computing, the problem of decomposing a unitary operator U into a circuit over S is known as the synthesis problem. This problem can be solved exactly, if U belongs to the set of circuits generated by S. Otherwise, it can be solved approximately, by finding a circuit U ′ such that ||U ′ −U || < for some chosen precision > 0. The synthesis problem is impo...

A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance(NMR) under adiabatic conditions. By the adiabatic requirement, the result is inexact unless the Hamiltonian changes extremely slowly. However, in quantum computation, everything must be completed within the decoherence tim...

We have previously 11] shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error provided each gate has error at most cc. We discuss a similar concatenation technique which can be used with fault tolerant networks to achieve any desired accuracy when computing with classical initial states, provided a minimum gate accuracy can be a...