scholarly journals Consequences of preserving reversibility in quantum superchannels

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 441
Author(s):  
Wataru Yokojima ◽  
Marco Túlio Quintino ◽  
Akihito Soeda ◽  
Mio Murao
Keyword(s):  
Quantum Mechanics ◽  
Physical Interpretation ◽  
Quantum Circuit ◽  
Quantum States ◽  
Quantum Circuits ◽  
Causal Order ◽  
Quantum Operations ◽  
Coherent Superposition ◽  
Physical Implementation ◽  
Quantum Objects

Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations which take independent quantum operations as inputs. While they are enforced to respect the laws of quantum mechanics, the use of input operations may lack a definite causal order, and characterizations of general superchannels in terms of quantum objects with a physical implementation have been missing. In this paper, we provide a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superchannels preserving the reversibility of quantum operations. We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a quantum circuit only consisting of unitary operations or a coherent superposition of two unitary quantum circuits where the two input operations are differently ordered. The latter may be seen as a generalization of the quantum switch, allowing a physical interpretation for pure two-slot superchannels. An immediate corollary is that purifiable bipartite processes cannot violate device-independent causal inequalities.

Quantum circuits for calculating the squared sum of the inner product of quantum states and its application

2019 ◽  
Vol 17 (05) ◽  
pp. 1950043
Author(s):  
Panchi Li ◽  
Jiahui Guo ◽  
Bing Wang ◽  
Mengqi Hao
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Experimental Results ◽  
Quantum Circuits ◽  
Inner Product ◽  
Superposition State ◽  
Initial State ◽  
Control Rules ◽  
Control Qubit ◽  
Classical Computer

In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.

scholarly journals QUANTUM AUCTIONS USING ADIABATIC EVOLUTION: THE CORRUPT AUCTIONEER AND CIRCUIT IMPLEMENTATIONS

2008 ◽  
Vol 06 (04) ◽  
pp. 815-839 ◽  
Author(s):  
SAIKAT GUHA ◽  
TAD HOGG ◽  
DAVID FATTAL ◽  
TIMOTHY SPILLER ◽  
RAYMOND G. BEAUSOLEIL
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Quantum Circuits ◽  
Adiabatic Evolution ◽  
Auction Algorithm ◽  
Final Measurement

We examine a proposed auction algorithm using quantum states to represent bids and distributed adiabatic search to find the winner.1 When the auctioneer follows the protocol, the final measurement giving the outcome of the auction also destroys the bid states, thereby preserving the privacy of losing bidders. We describe how a dishonest auctioneer could alter the protocol to violate this privacy guarantee, and present methods by which bidders can counter such attacks. We also suggest possible quantum circuit implementations of the auction protocol, and quantum circuits to perpetrate and to counter attacks by a dishonest auctioneer.

Completeness of Graphical Languages for Mixed State Quantum Mechanics

2021 ◽  
Vol 2 (4) ◽  
pp. 1-28
Author(s):  
Titouan Carette ◽  
Emmanuel Jeandel ◽  
Simon Perdrix ◽  
Renaud Vilmart
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Monoidal Category ◽  
Quantum Information Processing ◽  
Quantum Circuits ◽  
Quantum Operations ◽  
Symmetric Monoidal Category ◽  
Finite Dimensional ◽  
General Quantum ◽  
New Construction

There exist several graphical languages for quantum information processing, like quantum circuits, ZX-calculus, ZW-calculus, and so on. Each of these languages forms a †-symmetric monoidal category (†-SMC) and comes with an interpretation functor to the †-SMC of finite-dimensional Hilbert spaces. In recent years, one of the main achievements of the categorical approach to quantum mechanics has been to provide several equational theories for most of these graphical languages, making them complete for various fragments of pure quantum mechanics. We address the question of how to extend these languages beyond pure quantum mechanics to reason about mixed states and general quantum operations, i.e., completely positive maps. Intuitively, such an extension relies on the axiomatisation of a discard map that allows one to get rid of a quantum system, an operation that is not allowed in pure quantum mechanics. We introduce a new construction, the discard construction , which transforms any †-symmetric monoidal category into a symmetric monoidal category equipped with a discard map. Roughly speaking this construction consists in making any isometry causal. Using this construction, we provide an extension for several graphical languages that we prove to be complete for general quantum operations. However, this construction fails for some fringe cases like Clifford+T quantum mechanics, as the category does not have enough isometries.

Universal quantum circuit for n-qubit quantum gate: a programmable quantum gate

2007 ◽  
Vol 7 (3) ◽  
pp. 228-242
Author(s):  
P.B.M. Sousa ◽  
R.V. Ramos
Keyword(s):  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Gate ◽  
Quantum Circuits ◽  
Unitary Matrices ◽  
Quantum Operations ◽  
Universal Quantum ◽  
Np Problems ◽  
Universal Quantum Circuit ◽  
Specific Quantum

Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the basic steps is to implement the quantum circuit able to realize a given unitary operation. This task has been solved using decomposition of unitary matrices in simpler ones till reach quantum circuits having only single-qubits and CNOTs gates. Usually the goal is to find the minimal quantum circuit able to solve a given problem. In this paper we go in a different direction. We propose a general quantum circuit able to implement any specific quantum circuit by just setting correctly the parameters. In other words, we propose a programmable quantum circuit. This opens the possibility to construct a real quantum computer where several different quantum operations can be realized in the same hardware. The configuration is proposed and its optical implementation is discussed.

Determined Key Distribution Protocol Using Non-Orthogonal Quantum States

2012 ◽  
Vol 157-158 ◽  
pp. 628-631
Author(s):  
Xiao Yu Li ◽  
Lei Sheng Zhao
Keyword(s):  
Quantum Mechanics ◽  
Key Distribution ◽  
Quantum States ◽  
Entangled States ◽  
Quantum Operations

In this paper we provide an quantum determined key distribution protocol using non-orthogonal quantum states. Two parts can build a key by exchanging some qubits. The principles of quantum mechanics guarantee that the protocol is unconditionally secure. No one except the two parts can get the key. There are no entangled states and complex quantum operations except measurements needed in our protocol. So it is easier to carry out and more robust in practice.

scholarly journals Information Delay Protocol Using Non-Orthogonal Quantum States

2011 ◽  
Vol 1 ◽  
pp. 178-182
Author(s):  
De Xi Zhang ◽  
Xiao Yu Li
Keyword(s):  
Quantum Mechanics ◽  
Quantum States ◽  
The Other ◽  
Entangled States ◽  
Quantum Operations ◽  
Information Delay

In this paper we provide an information delay protocol using non-orthogonal quantum states. One person can send the other person some information which cannot be read until he or she lets the latter do. The principles of quantum mechanics guarantee that the protocol is unconditionally secure. When the sender decides to let the other get the information, he or she need only to send the latter some dictates through a public classical channel. There are no entangled states and complex quantum operations except measurements needed in our protocol. So it is easier to carry out and more robust in practice.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

scholarly journals Spacetime as a quantum circuit

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. Ramesh Chandra ◽  
Jan de Boer ◽  
Mario Flory ◽  
Michal P. Heller ◽  
Sergio Hörtner ◽  
...  
Keyword(s):  
Path Integral ◽  
Constant Scalar Curvature ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Special Role ◽  
Gravitational Action ◽  
Volume Conjecture ◽  
Interesting Connection ◽  
Kinematic Space ◽  
Boundary States

Abstract We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic $$ T\overline{T} $$ T T ¯ , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

Quantum generative adversarial networks for learning and loading quantum image in noisy environment

2021 ◽  
pp. 2150360
Author(s):  
Wanghao Ren ◽  
Zhiming Li ◽  
Yiming Huang ◽  
Runqiu Guo ◽  
Lansheng Feng ◽  
...  
Keyword(s):  
Image Processing ◽  
Quantum Circuit ◽  
Quantum Image Processing ◽  
Quantum Circuits ◽  
Generative Adversarial Networks ◽  
Channel Noise ◽  
Quantum Image ◽  
Adversarial Networks ◽  
Potential Applications ◽  
Classical Image

Quantum machine learning is expected to be one of the potential applications that can be realized in the near future. Finding potential applications for it has become one of the hot topics in the quantum computing community. With the increase of digital image processing, researchers try to use quantum image processing instead of classical image processing to improve the ability of image processing. Inspired by previous studies on the adversarial quantum circuit learning, we introduce a quantum generative adversarial framework for loading and learning a quantum image. In this paper, we extend quantum generative adversarial networks to the quantum image processing field and show how to learning and loading an classical image using quantum circuits. By reducing quantum gates without gradient changes, we reduced the number of basic quantum building block from 15 to 13. Our framework effectively generates pure state subject to bit flip, bit phase flip, phase flip, and depolarizing channel noise. We numerically simulate the loading and learning of classical images on the MINST database and CIFAR-10 database. In the quantum image processing field, our framework can be used to learn a quantum image as a subroutine of other quantum circuits. Through numerical simulation, our method can still quickly converge under the influence of a variety of noises.

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