![]() The computer scientists Dorit Aharonov and Michael Ben-Or (and other researchers working independently) proved a year later that these codes could theoretically push error rates close to zero. In 1995, Shor followed his factoring algorithm with another stunner: proof that “quantum error-correcting codes” exist. What’s more, these schemes must detect and correct errors without directly measuring the qubits, since measurements collapse qubits’ coexisting possibilities into definite realities: plain old 0s or 1s that can’t sustain quantum computations. For quantum computers to work, scientists must find schemes for protecting information even when individual qubits get corrupted. The feeblest magnetic field or stray microwave pulse causes them to undergo “bit-flips” that switch their chances of being |0 ⟩ and |1⟩ relative to the other qubits, or “phase-flips” that invert the mathematical relationship between their two states. Sustaining and manipulating this exponentially growing number of simultaneous possibilities are what makes quantum computers so theoretically powerful.īut qubits are maddeningly error-prone. The contingent possibilities proliferate as the qubits become more and more “entangled” with each operation. When qubits interact, their possible states become interdependent, each one’s chances of |0⟩ and |1⟩ hinging on those of the other. Unlike binary bits of information in ordinary computers, “qubits” consist of quantum particles that have some probability of being in each of two states, designated |0⟩ and |1⟩, at the same time. But a fundamental problem stood in the way of actually building quantum computers: the innate frailty of their physical components. 13.In 1994, a mathematician at AT&T Research named Peter Shor brought instant fame to “quantum computers” when he discovered that these hypothetical devices could quickly factor large numbers - and thus break much of modern cryptography.13 Decoherence and basic quantum error correction.12.10.9 Distinguishability and the trace distance.12.10.8 Joint probability distributions.12.10.7 Statistical distance and a special event.12.10.3 Fidelity in a trace norm inequality.12.8 Distinguishing non-orthogonal states, again.12.6 How far away are two probability distributions?.12.5 Approximating generic unitaries is hard, but…. ![]()
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