We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a function of the number of processors and suggest that the simulation software described in this paper may also serve as benchmark for testing high-end parallel computers.
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 computing is a radical new paradigm for a technology that is capable to revolutionize information processing. Simulators of universal quantum computer are important for understanding the basic principles and operations of the current noisy intermediate-scale quantum (NISQ) processors, and for building in future fault-tolerant quantum computers. In this work, we present simulation of universal quantum computers by introducing Psitrum -- a universal gate-model quantum computer simulator implemented on classical hardware. The simulator allows to emulate and debug quantum algorithms in for…
Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the ability to perform the logic gates that make up algorithms. We propose a method for learning how to construct these gates efficiently by using the simulator to perform optimal control on itself. This bypasses two major problems of purely classical approaches to the control problem: the need to have an accurate model of the system, and a classical computer mo…
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, the simulation methods using parallel processing are required. We have developed a general-purpose simulator for quantum computing on the parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We have performed Shor's factoriz…
In this work, we present a new large-scale quantum circuit simulator. It is based on the tensor network contraction technique to represent quantum circuits. We propose a novel parallelization algorithm based on \stepslice . In this paper, we push the requirement on the size of a quantum computer that will be needed to demonstrate the advantage of quantum computation with Quantum Approximate Optimization Algorithm (QAOA). We computed 210 qubit QAOA circuits with 1,785 gates on 1,024 nodes of the the Cray XC 40 supercomputer Theta. To the best of our knowledge, this constitutes the largest QAOA …
Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM) protocol with negligible soundness error and all but possibly the last message being classical. We prove that if this protocol is zero knowledge with a black-box, quantum simulator S, then L in BQP. Our result also applies to any language having a three-round quantum interactive proof (QIP), with all but possibly the last message being classical, with negligible soundness error and a black-box quantum simulator. These results in particular make it unlikely that certain protocols can be composed in parallel in order to …
It is discussed, why classical simulators of quantum computers escape from some no-go claims like Kochen-Specker, Bell, or recent Conway-Kochen "Free Will" theorems.
Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a function of the number of quantum operations applied. However, this exponential-space requirement can be avoided by using general space-time tradeoffs long known to complexity theorists, which can be appropriately optimized for this particular problem in a way that also illustrates some interesting reformulations of quantum mechanics. In this paper, we descr…
With quantum computers being out of reach for now, quantum simulators are the alternative devices for efficient and more exact simulation of problems that are challenging on conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing "hybrid" simulators by combining both techniques. In this paper, we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bact…
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.
The Quantum Fourier Transform is a famous example in quantum computing for being the first demonstration of a useful algorithm in which a quantum computer is exponentially faster than a classical computer. However when giving an explanation of the speed up, understanding computational complexity of a classical calculation has to be taken on faith. Moreover, the explanation also comes with the caveat that the current classical calculations might be improved. In this paper we present a quantum computer code for a Galton Board Simulator that is exponentially faster than a classical calculation us…
In May 2016 IBM released access to its 5-qubit quantum computer to the scientific community, its "IBM Quantum Experience" since acquiring over 25,000 users from students, educators and researchers around the globe. In the short time since the "IBM Quantum Experience" became available, a flurry of research results on 5-qubit systems have been published derived from the platform hardware. Quintuple is an open-source object-oriented Python module implementing the simulation of the "IBM Quantum Experience" hardware. Quintuple quantum algorithms can be programmed and run via a custom language fully…
A revised version of the massively parallel simulator of a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based quantum algorithms on some of the most powerful supercomputers that exist today. Adaptive encoding of the wave function reduces the memory requirement by a factor of eight, making it possible to simulate universal quantum computers with up to 48 qubits on the Sunway TaihuLight and on the K computer. The simulator exhibits close-to-ideal weak-scaling behavior on the Sunway TaihuLight,on the K computer, on an IBM Blue Gene/Q, a…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest--neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.
MPStab: an hybrid stabilizers tensor-network quantum circuit simulator
University of Trieste（的里雅斯特大学）；Istituto Nazionale di Fisica Nucleare, Trieste Section（意大利国家核物理研究所的里雅斯特分部）；University of Helsinki（赫尔辛基大学）；European Organization for Nuclear Research (CERN)（欧洲核子研究组织（日内瓦））；Chalmers University of Technology（查尔姆斯理工大学）
We use a massively parallel simulator of a universal quantum computer to benchmark some of the most powerful supercomputers in the world. We find nearly ideal scaling behavior on the Sunway TaihuLight, the K computer, the IBM BlueGene/Q JUQUEEN, and the Intel Xeon based clusters JURECA and JUWELS. On the Sunway TaihuLight and the K computer, universal quantum computers with up to 48 qubits can be simulated by means of an adaptive two-byte encoding to reduce the memory requirements by a factor of eight. Additionally, we discuss an alternative approach to alleviate the memory bottleneck by decom…
The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present review aims at giving a comprehensive outlook on the state of art capabilities offered from these near-term noisy devices as universal quantum simulators, i.e. programmable quantum computers potentially able to c…
The optimal design of a fault-tolerant quantum computer involves finding an appropriate balance between the burden of large-scale integration of noisy components and the load of improving the reliability of hardware technology. This balance can be evaluated by quantitatively modeling the execution of quantum logic operations on a realistic quantum hardware containing limited computational resources. In this work, we report a complete performance simulation software tool capable of (1) searching the hardware design space by varying resource architecture and technology parameters, (2) synthesizi…
In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the entanglements specify a quantum algorithm. As scalable and reliable quantum computers have not been implemented yet, quantum computation simulators are the only widely available tools to design and test quantum algorithms. However, simulating the quantum computations on a standard classical computer in most cases requires exponential memory and time. In this pape…
With the rapid progress made by industry and academia, quantum computers with dozens of qubits or even larger size are being realized. However, the fidelity of existing quantum computers often sharply decreases as the circuit depth increases. Thus, an ideal quantum circuit simulator on classical computers, especially on high-performance computers, is needed for benchmarking and validation. We design a large-scale simulator of universal random quantum circuits, often called 'quantum supremacy circuits', and implement it on Sunway TaihuLight. The simulator can be used to accomplish the following…
As the first useful Quantum Computers will be quantum simulators, here the minimum number of qubits necessary for the solution of the Schroedinger equation in simple test problems is evaluated. From the present preliminary results it appears that it is possible to realize a useful quantum simulator with a register of only 10-15 qbits. The intrinsic sensitivity to some errors appears to be moderate without the need of error correcting methods. At present there is at least some indication that the amplitude errors are more dangerous than phase and decoherence errors. So corrections limited to am…
Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-q…
Quantum computing, an innovative computing system carrying prominent processing rate, is meant to be the solutions to problems in many fields. Among these realms, the most intuitive application is to help chemical researchers correctly de-scribe strong correlation and complex systems, which are the great challenge in current chemistry simulation. In this paper, we will present a standalone quantum simulation tool for chemistry, ChemiQ, which is designed to assist people carry out chemical research or molecular calculation on real or virtual quantum computers. Under the idea of modular programm…
We propose a parallel quantum computing mode for ensemble quantum computer. In this mode, some qubits can be in pure states while other qubits in mixed states. It enables a single ensemble quantum computer to perform $"$single-instruction-multi-data" type of parallel computation. In Grover's algorithm and Shor's algorithm, parallel quantum computing can provide additional speedup. In addition, it also makes a fuller use of qubit resources in an ensemble quantum computer. As a result, some qubits discarded in the preparation of an effective pure state in the Schulman-Varizani, and the Cleve-DiV…
Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary e…
We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical-quantum feedback loop, bypass the barren plateau problem and does not necessitate any complicated measurements such as the Hadamard test. We introduce the notion of the hybrid density matrix, which allows us to disentangle the different steps of our algorithm and delegate classically demanding tasks to the quantum computer. Our algorithm proceeds in thr…
By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability-making quantum software and hardware development heavily reliant on quantum simulators running on conventional hardware. However, most of those simulators mimic perfect quantum computers and, hence, ignore the fragile nature of quantum mechanical effects which frequently yield to decoherence errors in real quantum devices. Considering those errors during the simulation is …
Quantum computing is an emerging technology, promising a paradigm shift in computing, and allowing for speedups in many different problems. However, quantum devices are still in their early stages, most with only a small number qubits. This places a reliance on simulation to develop quantum algorithms and to verify these devices. While there exists many algorithms for the simulation of quantum circuits, there is (at the time of writing) no tools which use OpenCL to parallelize this simulation, thereby taking advantage of devices such as GPUs while still remaining portable. In this paper, such …
With the advent of near-term quantum computers, the simulation of properties of solids using quantum algorithms becomes possible. By an adequate description of the system's Hamiltonian, variational methods enable to fetch the band structure and other fundamental properties as transition probabilities. Here, we use k$\cdot$p Hamiltonians to describe semiconductor structures of the III-V family and obtain their band structures using a state vector solver, a probabilistic simulator, and a real noisy-device simulator. The resulting band structures are in good agreement with the ones obtained by di…
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by mimicking thermal noise. By slow cooling, it freezes the system in a low-energy configuration, but the algorithm often gets stuck in local minima. In quantum annealing, the thermal noise is replaced by controllable quantum fluctuations, and the technique can be implemented in modern quantum simulators. However, quantum-adiabatic schemes become prohibitively slow i…
This paper presents the benchmark score definitions of QPack, an application-oriented cross-platform benchmarking suite for quantum computers and simulators, which makes use of scalable Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver applications. Using a varied set of benchmark applications, an insight of how well a quantum computer or its simulator performs on a general NISQ-era application can be quantitatively made. This paper presents what quantum execution data can be collected and transformed into benchmark scores for application-oriented quantum benchmark…
Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC an…
We propose a physical setup that can be used to simulate the quantum dynamics of the Ising model with present-day technology. Our scheme consists of electrons floating on superfluid helium which interact via Coulomb forces. In the limit of low temperatures, the system will stay near the ground state where its Hamiltonian is equivalent to the Ising model and thus shows phenomena such as quantum criticality. Furthermore, the proposed design could be generalized in order to study interacting field theories (e.g., $λϕ^4$) and adiabatic quantum computers.
Classical simulation of quantum computation is vital for verifying quantum devices and assessing quantum algorithms. We present a new quantum circuit simulator developed on the Sunway TaihuLight supercomputer. Compared with other simulators, the present one is distinguished in two aspects. First, our simulator is more versatile. The simulator consists of three mutually independent parts to compute the full, partial and single amplitudes of a quantum state with different methods. It has the function of emulating the effect of noise and support more kinds of quantum operations. Second, our simul…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. Fidelity of the target states corresponding to each algorithm is numerically …
Vertex amplitudes are elementary contributions to the transition amplitudes in the spin foam models of quantum gravity. The purpose of this article is make the first step towards computing vertex amplitudes with the use of quantum algorithms. In our studies we are focused on a vertex amplitude of 3+1 D gravity, associated with a pentagram spin-network. Furthermore, all spin labels of the spin network are assumed to be equal $j=1/2$, which is crucial for the introduction of the \emph{intertwiner qubits}. A procedure of determining modulus squares of vertex amplitudes on universal quantum comput…
One of the major objectives of the experimental programs at the LHC is the discovery of new physics. This requires the identification of rare signals in immense backgrounds. Using machine learning algorithms greatly enhances our ability to achieve this objective. With the progress of quantum technologies, quantum machine learning could become a powerful tool for data analysis in high energy physics. In this study, using IBM gate-model quantum computing systems, we employ the quantum variational classifier method in two recent LHC flagship physics analyses: $t\bar{t}H$ (Higgs boson production i…
Quantum computing has demonstrated the potential to revolutionize our understanding of nuclear, atomic, and molecular structure by obtaining forefront solutions in non-relativistic quantum many-body theory. In this work, we show that quantum computing can be used to solve for the structure of hadrons, governed by strongly-interacting relativistic quantum field theory. Following our previous work on light unflavored mesons as a relativistic bound-state problem within the nonperturbative Hamiltonian formalism, we present the numerical calculations on simulated quantum devices using the basis lig…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms and the avenue of its application in multiple domains. Availability of efficient quantum simulators will enable the researchers to quickly verify their results and concepts in order to establish a working proof of correctness. One important algorithm that has become one of the basic ingredients to build other algorithms and models is the Grover's search Algor…
Classical simulation of quantum computers will continue to play an essential role in the progress of quantum information science, both for numerical studies of quantum algorithms and for modeling noise and errors. Here we introduce the latest release of Intel Quantum Simulator (IQS), formerly known as qHiPSTER. The high-performance computing (HPC) capability of the software allows users to leverage the available hardware resources provided by supercomputers, as well as available public cloud computing infrastructure. To take advantage of the latter platform, together with the distributed simul…
A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical…
A custom-built and precisely controlled quantum system may offer access to a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analog quantum simulator that makes the relevant observables, interactions, and states of a quantum model accessible could permit experimental insight into complex quantum dynamics that are intractable on conventional computers. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here we characterise two-dimensional arrays of three ions trapp…
An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is l…
Electric Field Gradient Calculations for Ice VIII and IX using Polarizable Embedding: A Comparative Study on Classical Computers and Quantum Simulators
Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose …
