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Quantum circuit for multi-qubit Toffoli gate with optimal resource
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abstract
Resource consumption is an important issue in quantum information processing, particularly during the present NISQ era. In this paper, we investigate resource optimization of implementing multiple controlled operations, which are fundamental building blocks in the field of quantum computing and quantum simulation. We design new quantum circuits for the $n$-Toffoli gate and general multi-controlled unitary, which have only $O(\log n)$-depth and $O(n)$-size, and only require $1$ ancillary qubit. To achieve these results, we explore the potential of ancillary qubits and discover a method to create new conditional clean qubits from existed ancillary qubits. These techniques can also be utilized to construct an efficient quantum circuit for incrementor, leading to an implementation of multi-qubit Toffoli gate with a depth of $O(\log^2n)$ and size of $O(n)$ without any ancillary qubits. Furthermore, we explore the power of ancillary qubits from the perspective of resource theory. We demonstrate that without the assistance of ancillary qubit, any quantum circuit implementation of multi-qubit Toffoli gate must employ exponential precision gates. This finding indicates a significant disparity in computational power of quantum circuits between using and not using ancillary qubits. Additionally, we discuss the comparison of the power of ancillary qubits and extra energy levels in quantum circuit design.
Forward citations
Cited by 7 Pith papers
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Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits
The authors construct relative-phase n-qubit Toffoli gates without ancillas and O(log n)-depth multi-controlled SU(2)/U(2) decompositions, improving on earlier methods.
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Preparation of cat states in many-body eigenbasis via non-local measurement
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The paper gives algorithms to decompose structured sparse matrices into polylogarithmically many sigma-basis operators and builds quantum circuits for both variational and fault-tolerant use, cutting term counts expon...
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On Exact Space-Depth Trade-Offs in Multi-Controlled Toffoli Decomposition
The paper gives exact Toffoli-depth versus ancilla-count formulas for multi-controlled Toffoli decomposition and claims a ceil(log2 n) lower bound, but the main formula is inconsistent with its own example.
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Quantum Arithmetic Circuits in Public-Key Cryptography
A structured survey of optimized quantum adders, multipliers, modular exponentiation and point-addition circuits for public-key cryptanalysis, plus fault-tolerant resource estimation techniques.
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