Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum computer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantum computing. Here we also propose a recycling computing mode in which a quantum computer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.
Quantum computers are capable of efficiently contracting unitary tensor networks, a task that is likely to remain difficult for classical computers. For instance, networks based on matrix product states or the multi-scale entanglement renormalization ansatz (MERA) can be contracted on a small quantum computer to aid the simulation of a large quantum system. However, without the ability to selectively reset qubits, the associated spatial cost can be exorbitant. In this paper, we propose a protocol that can unitarily reset qubits when the circuit has a common convolutional form, thus dramaticall…
Quantum Key Recycling (QKR) is a quantum-cryptographic primitive that allows one to re-use keys in an unconditionally secure way. By removing the need to repeatedly generate new keys it improves communication efficiency. Skoric and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate bounds on the privacy amplification. We determine optimal attacks against the …
We give the mathematical theory of duality computer in the density matrix formalism. This result complements the mathematical theory of duality computer of Gudder in the pure state formalism.
We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in classical computing. All these algorithms are polynomial in the input size.
In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Dualit…
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total nu…
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of…
We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system, with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity "triality" relation of Jakob and Bergou. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.
We present an architecture to investigate wave-particle duality in $N$-path interferometers on a universal quantum computer involving as low as $2\log N$ qubits and develop a measurement scheme which allows the efficient extraction of quantifiers of interference visibility and which-path information. We implement our algorithms for interferometers with up to $N=16$ paths in proof-of-principle experiments on a noisy intermediate-scale quantum (NISQ) device using down to $\mathcal{O}(\log N)$ gates and despite increasing noise consistently observe a complementary behavior between interference vi…
It is shown, using level-rank duality that a universal topological quantum computer based on Chern-Simons theory for SU(2)$_3$ also implies an analogous universal quantum computer based on SU(3)$_2$. Suggestions are made for the possible role of level-rank duality in entanglement from topology.
We propose an information-theoretically secure encryption scheme for classical messages with quantum ciphertexts that offers detection of eavesdropping attacks, and re-usability of the key in case no eavesdropping took place: the entire key can be securely re-used for encrypting new messages as long as no attack is detected. This is known to be impossible for fully classical schemes, where there is no way to detect plain eavesdropping attacks. This particular application of quantum techniques to cryptography was originally proposed by Bennett, Brassard and Breidbart in 1982, even before propos…
Duality quantum computing (DQC) offers the use of linear combination of unitaries (LCU), or generalized quantum gates, in designing quantum algorithms. DQC contains wave divider and wave combiner operations. The wave function of a quantum computer is split into several subwaves after the wave division operation. Then different unitary operations are performed on different subwaves in parallel. A quantum wave combiner combines the subwaves into a final wave function, so that a linear combination of the unitaries are performed on the final state. In this paper, we study of the properties of dual…
Isolated zero mode in a quantum computer from a duality twist
Western Washington University（西华盛顿大学）；IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；Advanced Materials Science and Engineering Center, Western Washington University（西华盛顿大学先进材料科学与工程中心）；Center for Quantum Phenomena, Department of Physics, New York University（纽约大学物理系量子现象中心）
Port-based teleportation (PBT) is a protocol of quantum teleportation in which a receiver does not have to apply correction to the transmitted state. In this protocol two spatially separated parties can teleport an unknown quantum state only by exploiting joint measurements on number of shared $d-$dimensional maximally entangled states (resource state) together with a state to be teleported and one way classical communication. In this paper we analyse for the first time the recycling protocol for the deterministic PBT beyond the qubit case. In the recycling protocol the main idea is to re-use …
Wave-particle duality of quantum objects is one of the most striking features of quantum physics and has been widely studied in past decades. Developments of quantum technologies enable us to experimentally realize several quantum phenomena. Observation of wave-particle morphing behavior in the context of the quantum delayed-choice experiment (QDCE) is one of them. Adopting the scheme of QDCE, we demonstrate how the coexistence of wave and particle nature emerges as a consequence of the uncertainty in the quantum controlled experimental setup, using a five-qubit cloud-based quantum processor. …
The discovery of the fact that black holes radiate particles and eventually evaporate led Hawking to pose the well-known information loss paradox. This paradox caused a long and serious debate since it claims that the fundamental laws of quantum mechanics may be violated. A possible cure appeared recently from superstring theory, a consistent theory of quantum gravity: if the holographic description of a quantum black hole based on the gauge/gravity duality is correct, the information is not lost and quantum mechanics remains valid. Here we test this gauge/gravity duality on a computer at the …
Observation of gravity-like signatures in holographic codes on a quantum computer
Duke University（杜克大学）；Virginia Tech（弗吉尼亚理工大学）；University of Maryland, College Park（马里兰大学帕克分校）；BlueQubit Inc.（BlueQubit公司）；IonQ, Inc.（IonQ公司）；California Institute of Technology（加州理工学院）
Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of gauge theories, with a suitable truncation scheme to render the Hilbert space finite-dimensional. Conventional formulations lead to a Hilbert space largely spanned by unphysical states; given the current inability to perform large scale quantum computations, we examine here how one might restrict wave function evolution entirely or mostly to the physical subs…
We present a class of hybrid classical systems using quantum co-processors and point out that unlike purely quantum computers, such hybrids can be both universal and Turing complete; we introduce such quantum-classical hybrids as "quassical." We discuss the benefits of quassical architectures from a theoretical point of view: for some classes of problems they achieve computational supremacy. From a practical point of view, quassical architectures can also reduce the overhead burden imposed by most error correction schemes and minimize the challenges of interconnecting qubits in a usefully larg…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these lattice models can be reformulated using tensorial methods where the field integrations in the path-integral formalism are replaced by discrete sums. These formulations involve various types of duality and provide exact coarse-graining formulas which can be combined with truncations to obtain practical implementations of the Wilson renormalization group progr…
