scholarly journals Models of optical quantum computing

Nanophotonics ◽  
2017 ◽  
Vol 6 (3) ◽  
pp. 531-541 ◽  
Author(s):  
Hari Krovi
Keyword(s):  
Quantum Computing ◽  
Quantum Optics ◽  
Coherent State ◽  
Recent Work ◽  
Complexity Theory ◽  
Cluster State ◽  
Optical Computing ◽  
Circuit Model ◽  
Computational Power ◽  
Adiabatic Quantum Computing

AbstractI review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

Guest Column

2021 ◽  
Vol 52 (3) ◽  
pp. 38-59
Author(s):  
Carlo Mereghetti ◽  
Beatrice Palano
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Quantum Computer ◽  
Structural Complexity ◽  
Research Area ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Turing Machines ◽  
Computational Power ◽  
Quantum Turing Machine

Quantum computing is a prolific research area, halfway between physics and computer science [27, 29, 52]. Most likely, its origins may be dated back to 70's, when some works on quantum information began to appear (see, e.g., [34, 37]). In early 80's, R.P. Feynman suggested that the computational power of quantum mechanical processes might be beyond that of traditional computation models [25]. Almost at the same time, P. Benioff already proved that such processes are at least as powerful as Turing machines [9]. In 1985, D. Deutsch [22] proposed the notion of a quantum Turing machine as a physically realizable model for a quantum computer. From the point of view of structural complexity, E. Bernstein and U. Vazirani introduced in [20] the class BQP of problems solvable in polynomial time on quantum Turing machines, focusing attention on relations with the corresponding deterministic and probabilistic classes P and BPP, respectively. Several works in the literature explored classical issues in complexity theory from the quantum paradigm perspective (see, e.g., [7, 60, 61]).

scholarly journals Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Narendra N. Hegade ◽  
Koushik Paul ◽  
Yongcheng Ding ◽  
Mikel Sanz ◽  
F. Albarrán-Arriagada ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Adiabatic Quantum Computing ◽  
Shortcuts To Adiabaticity

scholarly journals Additive-error fine-grained quantum supremacy

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 329
Author(s):  
Tomoyuki Morimae ◽  
Suguru Tamaki
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Boolean Circuits ◽  
Exponential Time ◽  
Fine Grained ◽  
Additive Error ◽  
Universal Quantum ◽  
The One ◽  
Computing Models

It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain conjectures in classical complexity theory. Recently, these results have been improved to ``fine-grained" versions where even exponential-time classical simulations are excluded assuming certain classical fine-grained complexity conjectures. All these fine-grained results are, however, about the hardness of strong simulations or multiplicative-error sampling. It was open whether any fine-grained quantum supremacy result can be shown for a more realistic setup, namely, additive-error sampling. In this paper, we show the additive-error fine-grained quantum supremacy (under certain complexity assumptions). As examples, we consider the IQP model, a mixture of the IQP model and log-depth Boolean circuits, and Clifford+T circuits. Similar results should hold for other sub-universal models.

scholarly journals The computational power of matchgates and the XY interaction on arbitrary graphs

2014 ◽  
Vol 14 (11&12) ◽  
pp. 901-916
Author(s):  
Daniel J. Brod ◽  
Andrew M. Childs
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Connected Graph ◽  
Nearest Neighbor ◽  
Proper Subset ◽  
Computational Power ◽  
Arbitrary Graphs

Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the qubits are arranged on certain other graphs. Here we characterize the power of matchgates acting on arbitrary graphs. Specifically, we show that they are universal on any connected graph other than a path or a cycle, and that they are classically simulable on a cycle. We also prove the same dichotomy for the XY interaction, a proper subset of matchgates related to some implementations of quantum computing.

scholarly journals A linear-optical proof that the permanent is # P -hard

2011 ◽  
Vol 467 (2136) ◽  
pp. 3393-3405 ◽  
Author(s):  
Scott Aaronson
Keyword(s):  
Quantum Computing ◽  
Complexity Theory ◽  
Universality Theorem ◽  
Linear Optical ◽  
Intuitive Proof

One of the crown jewels of complexity theory is Valiant's theorem that computing the permanent of an n × n matrix is # P -hard. Here we show that, by using the model of linear-optical quantum computing —and in particular, a universality theorem owing to Knill, Laflamme and Milburn—one can give a different and arguably more intuitive proof of this theorem.

Quantum Merlin-Arthur with Clifford Arthur

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1420-1430 ◽  
Author(s):  
Tomoyuki Morimae ◽  
Masahito Hayashi ◽  
Harumichi Nishimura ◽  
Keisuke Fujii
Keyword(s):  
Quantum Computing ◽  
Computational Power ◽  
Xor Gate ◽  
Single Qubit ◽  
Qubit States

We show that the class QMA does not change even if we restrict Arthur’s computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called magic states, plus any Clifford gate operations are universal for quantum computing. If Merlin is honest, he sends the witness plus magic states to Arthur. If Merlin is malicious, he might send other states to Arthur, but Arthur can verify the correctness of magic states by himself. We also generalize the result to QIP(3): we show that the class QIP(3) does not change even if the computational power of the verifier is restricted to only Clifford gate operations (plus classical XOR gate).

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