相关论文: Quantum Circuits: Fanout, Parity, and Counting

We exhibit some simple gadgets useful in designing shallow parallel circuits for quantum algorithms. We prove that any quantum circuit composed entirely of controlled-not gates or of diagonal gates can be parallelized to logarithmic depth,…

We show that the depth of quantum circuits in the realistic architecture where a classical controller determines which local interactions to apply on the kD grid Z^k where k >= 2 is the same (up to a constant factor) as in the standard…

We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown…

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…

Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…

Executing quantum logic in cryogenic quantum computers requires a continuous energy supply from room-temperature control electronics. This dependence on external energy sources creates scalability limitations due to control channel density…

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…

What is the power of constant-depth circuits with $MOD_m$ gates, that can count modulo $m$? Can they efficiently compute MAJORITY and other symmetric functions? When $m$ is a constant prime power, the answer is well understood: Razborov and…

We present Quantum Depth Compression (QDC), a general compilation framework that utilizes dynamic circuits to reduce arbitrary quantum circuits to depth linear in the number of non-Clifford gates and to grid connectivity without the need…

We propose a mechanism for reaching pseudorandom quantum states, computationally indistinguishable from Haar random, with shallow log-n depth quantum circuits, where n is the number of qudits. We argue that $\log n$ depth 2-qubit-gate-based…

This paper concerns the problem of checking if two shallow (i.e., constant-depth) quantum circuits perform equivalent computations. Equivalence checking is a fundamental correctness question -- needed, e.g., for ensuring that…

One of the core challenges of research in quantum computing is concerned with the question whether quantum advantages can be found for near-term quantum circuits that have implications for practical applications. Motivated by this mindset,…

Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1 - o(1)$), but that any bounded fan-in constant-depth classical circuit (NC$^0$)…

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…

In parity quantum computing, multi-qubit logical gates are implemented by single-qubit rotations on a suitably encoded state involving auxiliary qubits. Consequently, there is a correspondence between qubit count and the size of the native…

It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a…

Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…

We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…

We present quantum circuits for comparison and increment operations that achieve an asymptotically optimal gate count of $\Theta(n)$ and depth of $\Theta(\log n)$ over the Clifford+Toffoli gate set, while using a provably minimal number of…

We provide an $\Omega(log(n))$ lower bound for the depth of any quantum circuit generating the unique groundstate of Kitaev's spherical code. No circuit-depth lower bound was known before on this code in the general case where the gates can…