A new universal and fault-tolerant quantum basis
Information Processing Letters
Fast parallel circuits for the quantum Fourier transform
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Polynomial simulations of decohered quantum computers
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
New Limits on Fault-Tolerant Quantum Computation
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Error-detection-based quantum fault tolerance against discrete pauli noise
Error-detection-based quantum fault tolerance against discrete pauli noise
Error-Detection-Based Quantum Fault-Tolerance Threshold
Algorithmica - Special Issue: Quantum Computation; Guest Editors: Frédéric Magniez and Ashwin Nayak
Both Toffoli and controlled-NOT need little help to do universal quantum computing
Quantum Information & Computation
An upper bound on the threshold quantum decoherence rate
Quantum Information & Computation
Accuracy threshold for postselected quantum computation
Quantum Information & Computation
Fault-tolerance threshold for a distance-three quantum code
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
A comparative code study for quantum fault tolerance
Quantum Information & Computation
Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle
Quantum Information & Computation
Quantum binary field inversion: improved circuit depth via choice of basis representation
Quantum Information & Computation
The robustness of magic state distillation against errors in Clifford gates
Quantum Information & Computation
Abstract resource cost derivation for logical quantum circuit descriptions
Proceedings of the 1st annual workshop on Functional programming concepts in domain-specific languages
Efficient quantum circuits for binary elliptic curve arithmetic: reducing T-gate complexity
Quantum Information & Computation
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Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give universality, by using a simple parity-checking operation. For applications to proving threshold lower bounds, certain practical stability characteristics are often required, and we also show a stable distillation procedure. No distillation upper bounds are known beyond those given by the Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce to upper bounds for single-qubit ancilla states. For multi-qubit pure states and previously considered two-qubit ancilla states, the answer is yes. However, we exhibit two-qubit mixed states that are not mixtures of stabilizer states, but for which every postselected stabilizer reduction from two qubits to one outputs a mixture of stabilizer states. Distilling such states would require true multi-qubit state distillation methods.