The design of new devices and experiments in science and engineering has historically relied on the intuitions of human experts. This credo, however, has changed. In many disciplines, computer-inspired design processes, also known as inverse-design, have augmented the capability of scientists. Here we visit different fields of physics in which computer-inspired designs are applied. We will meet vastly diverse computational approaches based on topological optimization, evolutionary strategies, deep learning, reinforcement learning or automated reasoning. Then we draw our attention specifically on quantum physics. In the quest for designing new quantum experiments, we face two challenges: First, quantum phenomena are unintuitive. Second, the number of possible configurations of quantum experiments explodes combinatorially. To overcome these challenges, physicists began to use algorithms for computer-designed quantum experiments. We focus on the most mature and \textit{practical} approaches that scientists used to find new complex quantum experiments, which experimentalists subsequently have realized in the laboratories. The underlying idea is a highly-efficient topological search, which allows for scientific interpretability. In that way, some of the computer-designs have led to the discovery of new scientific concepts and ideas -- demonstrating how computer algorithm can genuinely contribute to science by providing unexpected inspirations. We discuss several extensions and alternatives based on optimization and machine learning techniques, with the potential of accelerating the discovery of practical computer-inspired experiments or concepts in the future. Finally, we discuss what we can learn from the different approaches in the fields of physics, and raise several fascinating possibilities for future research.
An open question in quantum optics is how to manipulate and control complex quantum states in an experimentally feasible way. Here we present concepts for transformations of high-dimensional multi-photonic quantum systems. The proposals rely on two new ideas: (I) a novel high-dimensional quantum non-demolition measurement, (II) the encoding and decoding of the entire quantum transformation in an ancillary state for sharing the necessary quantum information between the involved parties. Many solutions can readily be performed in laboratories around the world, and identify important pathways for…
We present improved circuits intended for building a universal computer based on Random Pulse Computing (RPC) paradigm, a biologically-inspired way of computation in which variable is represented by a frequency of a Random Pulse Train (RPT) rather than a logic state. The RPC we mention here is also known as "stochastic unipolar computation" in newer literature. Unlike in previous art, where randomness is obtained from electronics noise or a pseudorandom shift register while processing circuitry is deterministic, in our approach both variable generation and signal processing rely on the random …
Inspired by non-abelian vortex anyons in spinor Bose-Einstein condensates, we consider the quantum double $\mathcal{D}(Q_8)$ anyon model as a platform to carry out a particular instance of Shor's factorization algorithm. We provide the excitation spectrum, the fusion rules, and the braid group representation for this model, and design a circuit architecture that facilitates the computation. All necessary quantum gates, less one, can be compiled exactly for this hybrid topological quantum computer, and to achieve universality the last operation can be implemented in a non-topological fashion. T…
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as low-entanglement states of the quantum register. These states can be efficiently created in a quantum computer, but they are also efficiently stored, manipulated and probed using Matrix-Product States techniques. Inspired by this idea, we present eight quantum-inspired numerical analysis algorithms, that include Fourier sampling, interpolation, differentiation and integ…
This paper presents a theory and an empirical evaluation of Higher-Order Quantum-Inspired Genetic Algorithms. Fundamental notions of the theory have been introduced, and a novel Order-2 Quantum-Inspired Genetic Algorithm (QIGA2) has been presented. Contrary to all QIGA algorithms which represent quantum genes as independent qubits, in higher-order QIGAs quantum registers are used to represent genes strings which allows modelling of genes relations using quantum phenomena. Performance comparison has been conducted on a benchmark of 20 deceptive combinatorial optimization problems. It has been p…
The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wavefunction ansatz. Compared to physically motivated ansatzes, hardware heuristic ansatzes usually lead to a shallower circuit, but it may still be too deep for an NISQ device. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where the circuit depth can be significantly reduced by introducing ancilla qubits, which makes a practical simulation of a chemical reaction with more…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show that some of these recent quantum memory-enhanced algorithms can be either implemented or approximated classically. In other words, we show that it is possible to develop quantum-inspired classical algorithms that require much less memory than the best classical algorithms known to date. Being classical, such algorithms could be implemented in state-of-the-…
Semi-quantum inspired lightweight protocol is an important research issue in realization of quantum protocols. However, the previous semi-quantum inspired lightweight mediated quantum key distribution (SQIL-MQKD) protocols need to use the Bell states or measure the Bell states. The generation and measurement of Bell states are more difficult and expensive than those of single photons. To solve this problem, a semi-quantum inspired lightweight mediated quantum key distribution with limited resource protocol is proposed. In this protocol, an untrusted third party (TP) only needs to perform the q…
We face the problem of pattern classification by proposing a quantum-inspired version of the widely used minimum distance classifier (i.e. the Nearest Mean Classifier (NMC)) already introduced in [31,33,28,27] and by applying this quantum-inspired classifier in a biomedical context. In particular, we show and compare the NMC and our quantum model performance to solve a problem related to classify the probability of survival for patients affected by idiopathic pulmonary fibrosis (IPF).
We present quantum-inspired algorithms for classification tasks inspired by the problem of quantum state discrimination. By construction, these algorithms can perform multiclass classification, prevent overfitting, and generate probability outputs. While they could be implemented on a quantum computer, we focus here on classical implementations of such algorithms. The training of these classifiers involves Semi-Definite Programming. We also present a relaxation of these classifiers that utilizes Linear Programming (but that can no longer be interpreted as a quantum measurement). Additionally, …
Quantum-inspired neural network is one of the interesting researches at the junction of the two fields of quantum computing and deep learning. Several models of quantum-inspired neurons with real parameters have been proposed, which are mainly used for three-layer feedforward neural networks. In this work, we improve the quantum-inspired neurons by exploiting the complex-valued weights which have richer representational capacity and better non-linearity. We then extend the method of implementing the quantum-inspired neurons to the convolutional operations, and naturally draw the models of quan…
A new gravitational-wave detector, which is devised based on quantum weak measurement amplification, is introduced and shown has the potential to significantly improve the strain sensitivity of gravitational-wave detection.
We show a representation of Quantum Computers defines Quantum Turing Machines with associated Quantum Grammars. We then create examples of Quantum Grammars. Lastly we develop an algebraic approach to high level Quantum Languages using Quantum Assembly language and Quantum C language as examples.
We introduce qprof, a new and extensible quantum program profiler able to generate profiling reports of various quantum circuits. We describe the internal structure and working of qprof and provide three practical examples on practical quantum circuits with increasing complexity. This tool will allow researchers to visualise their quantum implementation in a different way and reliably localise the bottlenecks for efficient code optimisation.
Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques
Univ. Grenoble Alpes, CEA, IRIG-PHELIQS GT（格勒诺布尔阿尔卑斯大学、法国原子能和替代能源委员会、IRIG-PHELIQS GT）；Department of Physics and Nanoscience Center, University of Jyväskylä（于韦斯屈莱大学物理系和纳米科学中心）
Quantum oracles play key roles in the studies of quantum computation and quantum information. But implementing quantum oracles efficiently with universal quantum gates is a hard work. Motivated by genetic programming, this paper proposes a novel approach to evolve quantum oracles with a hybrid quantum-inspired evolutionary algorithm. The approach codes quantum circuits with numerical values and combines the cost and correctness of quantum circuits into the fitness function. To speed up the calculation of matrix multiplication in the evaluation of individuals, a fast algorithm of matrix multipl…
We show that low-depth random quantum circuits can be efficiently simulated by a quantum teleportation-inspired algorithm. By using logical qubits to redirect and teleport the quantum information in quantum circuits, the original circuits can be renormalized to new circuits with a smaller number of logical qubits. We demonstrate the algorithm to simulate several random quantum circuits, including 1D-chain 1000-qubit 42-depth, 2D-grid 125*8-qubit 42-depth and 2D-Bristlecone 72-qubit 32-depth circuits. Our results present a memory-efficient method with a clear physical picture to simulate low-de…
We provide a new, quantum inspired, proof for the celebrated claim of [LFKN92] that $P^{\#P} \subseteq IP$. The protocol is fundamentally different from the original sum-check protocol of [LFKN92, Sha92], as well as from variants of this proof [GKR08, Mei09], though it still possesses the overall structure of inductively checking consistency between subsequent step. The protocol is inspired by [AAV13]. Hopefully, this protocol will be helpful in making progress towards two major open problems: resolving the quantum PCP question, and verification of quantum computations using a classical BPP ve…
Quantum(-inspired) annealers show promise in solving combinatorial optimisation problems in practice. There has been extensive researches demonstrating the utility of D-Wave quantum annealer and quantum-inspired annealer, i.e., Fujitsu Digital Annealer on various applications, but few works are comparing these platforms. In this paper, we benchmark quantum(-inspired) annealers with three combinatorial optimisation problems ranging from generic scientific problems to complex problems in practical use. In the case where the problem size goes beyond the capacity of a quantum(-inspired) computer, …
Quantum inspired protocols e.g. [AAV13,AG17] attempt to achieve a single-prover interactive protocol where a classical machine can verify quantum computations in an information-theoretically secure manner. We define a family of protocols which seem natural for verifying quantum computations and generalizes such known protocols, namely those of [AAV13,AG17]. We show that any protocol from this family is bound to require an extremely powerful prover, much like the classical protocols of [LFKN92] and [Sha92]. Using our analysis, we also hint at possible ways one might try to realize a protocol wh…
Could the theories with hidden variables be employed for creation of a quantum computer? A particular scheme of quasiclassical model quantum computer structure is describe.
The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. Taking advantage of this connection, we give quantum-inspired proofs of many existing as well as new remarkable permanent identities. Most notably, we give a quantum-inspired proof of the MacMahon master theorem as well as proofs for new generalizations of this theorem. Previous proofs of this theorem used completely different ideas. Beyond their purely combinatorial applicat…
Do quantum computers already exist in Nature? It is proposed that they do. Photosynthesis is one example in which a 'quantum computer' component may play a role in the 'classical' world of complex biological systems. A 'translation' of the standard metabolic description of the 'front-end' light harvesting complex in photosynthesis into the language of quantum computers is presented. Biological systems represent an untapped resource for thinking about the design and operation of hybrid quantum-classical computers and expanding our current conceptions of what defines a 'quantum computer' in Natu…
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource consumption caused by complexity and failure of Moore's Law. Quantum-inspired Ising machines, as a new computing paradigm, can be used to solve integer programming problems by reducing them into Ising models. Therefore, it is necessary to understand the technical evolution of quantum inspired solvers to break the bottleneck. In this paper, the concept and tradition…
We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for complex temperatures. The latter, for real temperatures, achieves performance comparable to a state-of-the-art DQC1 algorithm [Chowdhury et al. Phys. Rev. A 103, 032422 (2021)]. Both our algorithms take as input the Hamiltonian decomposed as a linear combination Pauli operators. We show this decomposition to be DQC1-hard for a given Hamiltonian, providing new ins…
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…
Motivated by recent progress in quantum technologies and in particular quantum software, research and industrial communities have been trying to discover new applications of quantum algorithms such as quantum optimization and machine learning. Regardless of which hardware platform these novel algorithms operate on, whether it is adiabatic or gate based, from theoretical point of view, they are performing drastically better than their classical counterparts. Two promising areas of quantum algorithms quantum machine learning and quantum optimization. These are based on performing matrix operatio…
Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we can solve linear equation system via algorithm inspired by adiabatic quantum computing. Here we demonstrate the algorithm and realize the solution of 8-dimensional linear equations $A\textbf{x}=\textbf{b}$ in a 4-qubit nuclear magnetic resonance system. The result is by far the solution of maximum-dimensional linear equation with a limited number of qubits in…
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 t…
Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundarie…
One of the major approaches to neuromorphic computing is using memristors as analogue synapses. We propose unitary quantum gates that exhibit memristive behaviours, including Ohm's law, pinched hysteresis loop and synaptic plasticity. Hysteresis depending on the quantum phase and long-term plasticity that encodes the quantum state are observed. We also propose a three-layer neural network with the capability of universal quantum computing. Quantum state classification on the memristive neural network is demonstrated. Our results pave the way towards brain-inspired quantum computing. We obtain …
There have been suggestions within the Information Retrieval (IR) community that quantum mechanics (QM) can be used to help formalise the foundations of IR. The invoked connection to QM is mathematical rather than physical. The proposed ideas are concerned with information which is encoded, processed and accessed in classical computers. However, some of the suggestions have been thoroughly muddled with questions about applying techniques of quantum information theory in IR, and it is often unclear whether or not the suggestion is to perform actual quantum information processing on the informat…
We describe a quantum computer emulator for a generic, general purpose quantum computer. This emulator consists of a simulator of the physical realization of the quantum computer and a graphical user interface to program and control the simulator. We illustrate the use of the quantum computer emulator through various implementations of the Deutsch-Jozsa and Grover's database search algorithm.
Quantum annealing inspired algorithms for the NISQ Era
Jülich Supercomputing Centre, Forschungszentrum Jülich（于利希超级计算中心，于利希研究中心）；RWTH Aachen University（亚琛工业大学）；Modular Supercomputing and Quantum Computing, Goethe University Frankfurt（法兰克福歌德大学模块化超算与量子计算）；Department of Computer Science, University of Cologne（科隆大学计算机科学系）
A Quantum Computer is a new type of computer which can efficiently solve complex problems such as prime factorization. A quantum computer threatens the security of public key encryption systems because these systems rely on the fact that prime factorization is computationally difficult. Errors limit the effectiveness of quantum computers. Because of the exponential nature of quantum com puters, simulating the effect of errors on them requires a vast amount of processing and memory resources. In this paper we describe a parallel simulator which accesses the feasibility of quantum computers. We …
Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible through the efficient sampling of matrix elements according to their norms. Here, we apply it to extreme learning which is a machine learning framework that performs linear regression using random feature vectors generated through a random neural network. The extreme learning is suited for the application of quantum-inspired SVD in that it first requires tran…
