Decoherence as an obstacle in quantum computation is viewed as a struggle between two forces [1]: the computation which uses the exponential dimension of Hilbert space, and decoherence which destroys this entanglement by collapse. In this model of decohered quantum computation, a sequential quantum computer loses the battle, because at each time step, only a local operation is carried out but g*(t) number of gates collapse. With quantum circuits computing in parallel way the situation is different- g(t) number of gates can be applied at each time step and number gates collapse because of decoherence. As g(t) ≈ g*(t) competition here is even [1]. Our paper improves on this model by slowing down g*(t) by encoding the circuit in parallel computing architectures and running it in Single Instruction Multiple Data (SIMD) paradigm. We have proposed a parallel ion trap architecture for single-bit rotation of a qubit.
Decoherence as an obstacle in quantum computation is viewed as a struggle between two forces [1]: the computation which uses the exponential dimension of Hilbert space, and decoherence which destroys this entanglement by collapse. In this model of decohered quantum computation, a sequential quantum computer loses the battle, because at each time step, only a local operation is carried out but g*(t) number of gates collapse. With quantum circuits computing in parallel way the situation is different- g(t) number of gates can be applied at each time step and number gates collapse because of decoherence. As g(t) ≈ g*(t) competition here is even [1]. Our paper improves on this model by slowing down g*(t) by encoding the circuit in parallel computing architectures and running it in Single Instruction Multiple Data (SIMD) paradigm. We have proposed a parallel ion trap architecture for single-bit rotation of a qubit.
Abstract The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations1. The ability to execute parallel entangling quantum gates offers efficiency gains in numerous quantum circuits2–4, as well as for entire algorithms—such as Shor’s factoring algorithm5—and quantum simulations6, 7. In circuits such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time through the divide-and-conquer technique8. More importantly, quantum gate parallelism is essential for fault-tolerant error correction of qubits that suffer from idle errors9, 10. However, the implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits that are fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions11, 12 or cavity-coupled superconducting transmons13. Here we present experimental results for parallel two-qubit entangling gates in an array of fully connected trapped 171Yb+ ion qubits. We perform a one-bit full-addition operation on a quantum computer using a depth-four quantum circuit4, 14, 15, where circuit depth denotes the number of runtime steps required. Our method exploits the power of highly connected qubit systems using classical control techniques and will help to speed up quantum circuits and achieve fault tolerance in trapped-ion quantum computers.
Recently it has become clear, that a key issue in quantum computation is understanding how interaction with the environment, or "decoherence", affects the computational power of quantum computers. We adopt the standard physical method of describing systems which are interwound with their environment by "density matrices", and within this framework define a model of decoherence in quantum computation. Our results show that the computational power of decohered quantum computers depends strongly on the amount of parallelism in the computation. We first present a simulation of decohered sequential quantum computers, on a classical probabilistic Turing machine, and prove that the expected slowdown of this simulation is polynomial in time and space of the quantum computation, for any non zero decoherence rate. Similar results hold for quantum computers that are allowed to operate on logarithmic number of qubits at a time. For decohered quantum circuits (with local gates), the situation is more subtle and depends on the decoherence rate, /spl eta/. We find that our simulation is efficient for circuits with decoherence rate /spl eta/ higher than some constant /spl eta//sub 1/ but exponential for a general (random) circuit subjected to decoherence rate lower than some constant /spl eta//sub 2/. The transition from exponential cost to polynomial cost happens in a short range of decoherence rates. We use computer experiments to exhibit the phase transitions in various quantum circuits.
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling,'' is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature (London) 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the S\o{}rensen-M\o{}lmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme directly to the encoded qubits, are capable of further reducing various other sources of qubit decoherence, such as due to differential dephasing and due to decohered vibrational modes. The feasibility of using the relatively slow SM pulses in a decoupling scheme quenching the latter source of decoherence follows from the observed 1/f spectrum of the vibrational bath.
Quantum computing (QC) offers huge promise to accelerate a range of computationally intensive benchmarks. Quantum computing is limited, however, by the challenges of decoherence: i.e., a quantum state can only be maintained for short windows of time before it decoheres. While quantum error correction codes can protect against decoherence, fast execution time is the best defense against decoherence, so efficient architectures and effective scheduling algorithms are necessary. This paper proposes the Multi-SIMD QC architecture and then proposes and evaluates effective schedulers to map benchmark descriptions onto Multi-SIMD architectures. The Multi-SIMD model consists of a small number of SIMD regions, each of which may support operations on up to thousands of qubits per cycle.
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary operations on a finite-dimensional Hilbert space, are not unique to quantum systems but may be found in certain classical systems as well. Previously, it has been shown that one can represent an arbitrary multi-qubit quantum state in terms of classical analog signals using nested quadrature amplitude modulated signals. Furthermore, using digitally controlled analog electronics one may manipulate these signals to perform quantum gate operations and thereby execute quantum algorithms. The computational capacity of a single signal is, however, limited by the required bandwidth, which scales exponentially with the number of qubits when represented using frequency-based encoding. To overcome this limitation, we introduce a method to extend this approach to multiple parallel signals. Doing so allows a larger quantum state to be emulated with the same gate time required for processing frequency-encoded signals. In the proposed representation, each doubling of the number of signals corresponds to an additional qubit in the spatial domain. Single quit gate operations are similarly extended so as to operate on qubits represented using either frequency-based or spatial encoding schemes. Furthermore, we describe a method to perform gate operations between pairs of qubits represented using frequency or spatial encoding or between frequency-based and spatially encoded qubits. Finally, we describe how this approach may be extended to represent qubits in the time domain as well.
Quantum computing is emerging as a revolutionary paradigm in the field of computing, promising an exponential leap in computing power and problemsolving that challenges even the most advanced supercomputers of the classical era.At the heart of this revolution lies the peculiarity of the quantum world, where subatomic particles can exist in multiple states simultaneously, a phenomenon known as superposition, and entangle their states in a way that defies classical logic.It is this capacity for superposition and entanglement that gives quantum computing its disruptive power.One of the most intriguing properties of quantum computing is its ability to process information using Qubits, the quantum analogues of classical bits.While a classical bit can only be in a single 0 or 1 state, a Qubit can simultaneously represent a 0, a 1, or any superposition of these states, allowing multiple calculations to be performed in parallel.This massively parallel processing capability is the basis for the potential superiority of quantum computers over their classical counterparts in a wide range of applications.The architecture of quantum computers is inherently different from classical computers.While the latter use transistors to store and manipulate information in bits, quantum computers use Qubits, which can be implemented in a variety of physical systems, such as atoms, ion traps, photons, superconductors or nuclear magnetic resonance.The manipulation of the Qubits is carried out through quantum gates, fundamental operations that transform the quantum state of the Qubits and allow quantum calculations to be carried out.Furthermore, to maintain quantum coherence, the control and isolation of the quantum system from its environment is crucial, posing significant challenges in terms of designing and building scalable and robust quantum systems.