Related papers: Quantum Lower Bounds for Fanout
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…
Quantum Fano inequality (QFI) in quantum information theory provides an upper bound to the entropy exchange by a function of the entanglement fidelity. We give various Fano-like upper bounds to the entropy exchange and QFI is a special case…
We study the implementation of quantum channels with quantum computers while minimizing the experimental cost, measured in terms of the number of Controlled-NOT (C-NOT) gates required (single-qubit gates are free). We consider three…
The efficient decomposition of multi-controlled gates is a significant factor in quantum compiling, both in circuit depth and T-gate count. Recent work has demonstrated that qudits have the potential to reduce resource requirements from…
While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can…
What is the minimum number of extra qubits needed to perform a large fault-tolerant quantum circuit? Working in a common model of fault-tolerance, I show that in the asymptotic limit of large circuits, the ratio of physical qubits to…
We present a computational problem with the following properties: (i) Every instance can be solved with near-certainty by a constant-depth quantum circuit using only nearest-neighbor gates in 3D even when its implementation is corrupted by…
Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the…
$ \newcommand{\cclass}[1]{{\normalfont\textsf{##1}}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there…
Quantum circuit depth minimization is critical for practical applications of circuit-based quantum computation. In this work, we present a systematic procedure to decompose multiqubit controlled unitary gates, which is essential in many…
Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…
Multi-controlled Toffoli gates are fundamental building blocks in quantum computation, with applications in quantum arithmetic, simulation, and search algorithms. In fault-tolerant architectures, their realization is constrained by the high…
Recently, Bravyi, Gosset, and K\"{o}nig (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0…
The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of…
Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…
We propose an efficiently measurable lower bound on quantum process fidelity of N-qubit controlled-Z gates. This bound is determined by average output state fidelities for N partially conjugate product bases. A distinct advantage of our…
We establish a relationship between the correlations in a many-qubit mixed state and the minimum circuit depth needed for its preparation. If the mutual information between two subsystems exceeds the mutual information between one of those…
We present a protocol to encode and decode arbitrary quantum states in the parity architecture with constant circuit depth using measurements, local nearest-neighbor and single-qubit operations only. While this procedure typically requires…