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Using three ancilla bits and four Toffoli gates to construct a NOT gate with 5 controls. The ancilla bits end up trashed because the effects on them were not uncomputed.

Ancilla bits are extra bits (units of information) used in computing paradigms requiring reversible operations, such as classical reversible computing and quantum computing. Unlike classical computing, where bits can be freely set to 0 or 1, reversible computation requires all operations on computer memory to be invertible. Ancilla bits, whose initial state is known, provide the necessary "workspace" for performing operations that would otherwise erase information. They play a crucial role in implementing complex logic gates and enabling universal computation within these reversible models.

In quantum computing, and unless explicitly established otherwise, the values of ancilla (qu)bits require uncomputation, as they may otherwise carry unwanted entanglement and will likely invalidate the result of the computation.

Ancilla bits can simplify complex operations. For example, an ancilla bit can be used to control a Toffoli gate, effectively turning it into a simpler gate like a controlled NOT or a NOT gate.[1]: 29 

Number of bits required

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For classical reversible computation, a constant number O(1) of ancilla bits is necessary and sufficient for universal computation.[2] While additional ancilla bits aren't strictly required, they can provide extra working space, leading to simpler circuit constructions using fewer logic gates.[1]: 131 

Ancilla qubits

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The concept of ancilla bit can be extended for quantum computing in terms of ancilla qubits, that can be used for example in quantum error correction.[3] One notable example for the use of ancilla qubits in quantum computing is the Deutsch–Jozsa algorithm.

Quantum catalysis uses ancilla qubits to store entangled states that enable tasks that would not normally be possible with local operations and classical communication (LOCC).[4]

References

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  1. ^ a b Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-1-107-00217-3.
  2. ^ Aaronson, Scott; Grier, Daniel; Schaeffer, Luke (2015). "The Classification of Reversible Bit Operations". arXiv:1504.05155 [quant-ph].
  3. ^ Shor, Peter W. (October 1, 1995). "Scheme for reducing decoherence in quantum computer memory". Physical Review A. 52 (4): R2493–R2496. Bibcode:1995PhRvA..52.2493S. doi:10.1103/PhysRevA.52.R2493. PMID 9912632. Retrieved June 6, 2015.
  4. ^ Azuma, Koji; Koashi, Masato; Imoto, Nobuyuki (2008). "Quantum catalysis of information". arXiv:0804.2426 [quant-ph].


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Ancilla

up ancilla in Wiktionary, the free dictionary. Ancilla may refer to: Maid (Latin: ancilla); see also Ancillae Ancilla College, US Ancilla bit, a bit used

Qubit

Furthermore, a set of n bits can be represented by n binary digits, simply by concatenating the representations of each of the bits, whereas a set of n qubits

Uncomputation

technique, used in reversible circuits, for cleaning up temporary effects on ancilla bits so that they can be re-used. Uncomputation is a fundamental step in quantum

Parity measurement

is encoded into 3 bits, and parity checks are performed with subsequent error correction performed based on the results of the ancilla qubits at the bottom

Five-qubit error correcting code

stabilizers, 4 ancillas will be used to measure them. The first 4 qubits in the image above are the ancillas. The resulting bits from the ancillas is the syndrome;

No-deleting theorem

state of the ancilla. One can always obtain the unknown state from the final state of the ancilla using local operation on the ancilla Hilbert space

Quantum logic gate

implement all Boolean functions, often at the cost of having to use ancilla bits. The Toffoli gate has a direct quantum equivalent, showing that quantum

Choi–Jamiołkowski isomorphism

of the standard Bell scheme. This measurement involves an extra qubit ancilla. The indirect Bell measurement is performed by applying a gate U T {\displaystyle