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Efficient Implementation of Multi-Controlled Quantum Gates
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We present an implementation of multi-controlled quantum gates which provides significant reductions of cost compared to state-of-the-art methods. The operator applied on the target qubit is a unitary, special unitary, or the Pauli X operator (Multi-Controlled Toffoli), and requires one clean ancilla, no ancilla, and one dirty ancilla, respectively. We generalize our methods for any number of target qubits, and provide further cost reductions if additional ancilla qubits are available. For each type of multi-controlled gate, we provide implementations for unrestricted (all-to-all) connectivity and for linear-nearest-neighbor. All of the methods use a linear cost of gates from the Clifford+T (fault-tolerant) set. In the context of linear-nearest-neighbor (LNN) architecture, the cost and depth of our circuits scale linearly irrespective of the position of the qubits on which the gate is applied. Our methods directly improve the compilation process of many quantum algorithms, providing optimized circuits. Given the scale of our improvements, for example, quadratic to linear CNOT count for LNN, they will naturally result in a large reduction of errors.
Forward citations
Cited by 7 Pith papers
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Quantum Uncomputation of Clean and Dirty Ancilla Qubits
Quantum compilers can now automatically uncompute dirty ancillas with a rewrite-based normalizer, and the existence problem is coNP-hard.
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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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Leveraging Phase Polynomials for Quantum Circuit Optimization
A quantum circuit optimizer, PhasePoly, co-optimizes phase and output parity matrices and merges phase-polynomial blocks across gate barriers, reducing total gates by 34.9% and CNOT gates by 28.5% on average.
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Multi-Controlled Quantum Gates in Linear Nearest Neighbor
Multi-controlled X and SU(2) gates on linear-nearest-neighbor qubit arrays require at most 4k+8n-16 and 4k+8n-14 CNOT gates, respectively, improving earlier bounds.
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Implementing Semiclassical Szegedy Walks in Classical-Quantum Circuits for Homomorphic Encryption
Key-updating functions for Liang's quantum homomorphic encryption are implemented as classical-quantum circuits, enabling runtime key updates and linear classically controlled S gates, and the approach is demonstrated...
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An Improved Quantum Algorithm of the Multislice Method
The authors rebuild the phase-shifting circuit of their quantum multislice algorithm using Walsh functions, removing multi-controlled gates and adding an error-controlled truncation that cuts gate count by over an ord...
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Quantum Wave Simulation with Sources and Loss Functions
A framework encodes acoustic, Maxwell, and elastic wave equations as Hamiltonian simulation, with compact or rotationally symmetric sources and l2 loss measurements, claiming a quartic speed-up in 3D.
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