Using the methods for optimal simulation of quantum logic gates developed in Ref. [1], we perform a numerical estimation of time and spatial resources involved in the execution of one and two qubit gates for the case of three representative models of quantum computation based on global control. The importance of such models stems from the solution to the problem of experimentally addressing and locally manipulating the qubits in a given quantum register. The numerical estimation of the temporal efficiency for each model is performed by assuming that the qubits are coupled to each other via the Ising interaction
whose strength is considered to be of the order of 50 MHz (33 neV).
Using the methods for optimal simulation of quantum logic gates developed in Ref. [1], we perform a numerical estimation of time and spatial resources involved in the execution of one and two qubit gates for the case of three representative models of quantum computation based on global control. The importance of such models stems from the solution to the problem of experimentally addressing and locally manipulating the qubits in a given quantum register. The numerical estimation of the temporal efficiency for each model is performed by assuming that the qubits are coupled to each other via the Ising interaction
whose strength is considered to be of the order of 50 MHz (33 neV).
Using the methods for optimal simulation of quantum logic gates, we perform a quantitative estimation of the time resources involved in the execution of universal gate sets for the case of three representative models of quantum computation based on global control. The importance of such models stems from the solution to the problem of experimentally addressing and locally manipulating the qubits in a given quantum register. The numerical estimation of the temporal efficiency for each model is performed by assuming that the qubits in the register can be coupled to each other via the Ising and the Förster interactions. Finally, we discuss the feasibility of the physical realization of such architectures under quantum error correction conditions.
Multi-qubit entangling interactions arise naturally in several quantum computing platforms and promise advantages over traditional two-qubit gates. In particular, a fixed multi-qubit Ising-type interaction together with single-qubit X-gates can be used to synthesize global ZZ-gates (GZZ gates). In this work, we first show that the synthesis of such quantum gates that are time-optimal is NP-hard. Second, we provide explicit constructions of special time-optimal multi-qubit gates. They have constant gate times and can be implemented with linearly many X-gate layers. Third, we develop a heuristic algorithm with polynomial runtime for synthesizing fast multi-qubit gates. Fourth, we derive lower and upper bounds on the optimal GZZ gate-time. Based on explicit constructions of GZZ gates and numerical studies, we conjecture that any GZZ gate can be executed in a time O( n ) for n qubits. Our heuristic synthesis algorithm leads to GZZ gate-times with a similar scaling, which is optimal in this sense. We expect that our efficient synthesis of fast multi-qubit gates allows for faster and, hence, also more error-robust execution of quantum algorithms.
Currently, the theory of quantum computing is actively developing. Despite the fact that a quantum computer has some features, any algorithm designed for a classical computer can be implemented for a quantum one. The relevance of the topic of quantum computers is confirmed by the fact that even now banking systems, cryptography and encryption of information require enormous resources of computing systems, these are just some examples, but the most important and vivid ones that relate to the everyday life of a huge part of the world's population. A hardware computing core has been developed and simulated, which is the main part of an accelerator based on field-programmable gate array with computer aided design Altera Quartus. Considering the obtained time dependence of the number of cycles required for the impact of a single-qubit quantum gate on a quantum register on the number of qubits and parallel arithmetic logic units in the hardware computing core, when simulating quantum computing, a method was developed to determine the increase in hardware performance and ways to improve the performance of an accelerator based on a hardware computing core were developed. based on field-programmable gate array.
Quantum computing and quantum information science are two recently discovered and rapidly growing fields of physics that show substantial promise in providing new and valuable technologies in the foreseeable future. Large-scale quantum computers, if ever realized experimentally, are likely to outperform their classical counterparts in a number of important computational tasks, the most important of which may be the accurate simulation of many-body quantum systems such as the ones encountered in physics, chemistry and life sciences. This thesis investigates the problem of controlling quantum systems for the purpose of performing quantum information processing tasks. The problem is approached from a theoretical and simulational viewpoint. The work contained here encompasses a range of levels of abstraction. Firstly, we discuss the decomposition of abstract multiqubit logic gates into sequences of simple elementary gates. Secondly, we study the local commutational properties of two-qubit gates using local gate invariants. Thirdly, we develop methods for the physical implementation of the elementary gates through the control of specific quantum systems, possibly in the presence of noise and decoherence. We present a new, almost optimal n-qubit gate decomposition based on the cosine-sine decomposition, which utilizes a likewise new intermediate quantum circuit structure we call a uniformly controlled gate. We then show how they can be used in constructing a general state transformation circuit. Both of the resulting circuits can be efficiently implemented using nearest-neighbor gates which makes their physical realization simpler. A local gate invariant is introduced which can be used to assess the suitability of two-qubit gates for serving as the entangling gate in elementary gate libraries. Finally, we develop numerical optimization methods for finding near-optimal control sequences for generating oneand two-qubit gates, both in closed quantum systems and in the presence of Markovian noise.
In this paper, we study the optimal simulation of three-qubit unitary by using two-qubit gates. First, we give a lower bound on the two-qubit gates cost of simulating a multi-qubit gate. Secondly, we completely characterize the two-qubit gate cost of simulating a three-qubit controlled controlled gate by generalizing our result on the cost of Toffoli gate. The function of controlled controlled gate is simply a three-qubit controlled unitary gate and can be intuitively explained as follows: the gate will output the states of the two control qubit directly, and apply the given one-qubit unitary u on the target qubit only if both the states of the control are ∣1⟩. Previously, it is only known that five two-qubit gates is sufficient for implementing such a gate [Sleator and Weinfurter, Phys. Rev. Lett. 74, 4087 (1995)]. Our result shows that if the determinant of u is 1, four two-qubit gates is achievable optimal. Otherwise, five is optimal. Thirdly, we show that five two-qubit gates are necessary and sufficient for implementing the Fredkin gate(the controlled swap gate), which settles the open problem introduced in [Smolin and DiVincenzo, Phys. Rev. A, 53, 2855 (1996)]. The Fredkin gate is one of the most important quantum logic gates because it is universal alone for classical reversible computation, and thus with little help, universal for quantum computation. Before our work, a five two-qubit gates decomposition of the Fredkin gate was already known, and numerical evidence of showing five is optimal is found.
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 more powerful than the quantum one to carry out the required simulations. Strong evidence that the scheme scales polynomially in the number of qubits, for systems of up to 9 qubits with Ising interactions, is presented from numerical simulations carried out in different topologies. This suggests that this in situ approach is a practical way of upgrading quantum simulators to computers.