Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and degree of parallelism. I present an analysis of error correction with block codes, made fault-tolerant through the use of prepared ancilla blocks. The preparation and verification of the ancillas is described in detail. It is shown that the ancillas need only be verified against a small set of errors. This, combined with previously known advantages, makes this `ancilla factory' the best method to apply error correction, whether in concatenated or block coding. I then consider the resources required to achieve $2 \times 10^{10}$ computational steps reliably in a computer of 2150 logical qubits, finding that the simplest $[[n,1,d]]$ block codes can tolerate more noise with smaller overheads than the $7^L$-bit concatenated code. The scaling is such that block codes remain the better choice for all computations one is likely to contemplate.
We investigate distinguishability (measured by fidelity) of the initial and the final state of a qubit, which is an object of the so-called nonideal quantum measurement of the first kind. We show that the fidelity of a nonideal measurement can be greater than the fidelity of the corresponding ideal measurement. This result is somewhat counterintuitive, and can be traced back to the quantum parallelism in quantum operations, in analogy with the quantum parallelism manifested in the quantum computing theory. In particular, while the quantum parallelism in quantum computing underlies efficient qu…
The assumption of maximum parallelism support for the successful realization of scalable quantum computers has led to homogeneous, ``sea-of-qubits'' architectures. The resulting architectures overcome the primary challenges of reliability and scalability at the cost of physically unacceptable system area. We find that by exploiting the natural serialization at both the application and the physical microarchitecture level of a quantum computer, we can reduce the area requirement while improving performance. In particular we present a scalable quantum architecture design that employs specializat…
Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum Mechanics seems to support some infinite variant of classical parallel computing. We compare this new one with other attempts towards hypercomputation by separating 1) its principal computing capabilities from 2) realizability issues. The first are shown to coincide with recursive enumerability; the second are considered in analogy to `existence' in mathematical log…
We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's algorithm succeeding after n iterations. We show that the fully generalized formula reduces to the special cases considered by previous authors. We then use the generalized formula to determine the optimal strategy for using the unstructured quantum search algorithm. On average the optimal strategy is about 12% better than the naive use of Grover's algorithm…
This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of quantum parallelism is important both for theoretical and applied research, cf. e.g. David Deutsch \cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed …
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…
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing …
Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The imp…
Quantum computing has the potential to offer substantial computational advantages over conventional computing. Recent advances in quantum computing hardware and algorithms have enabled a class of classically parallel quantum workloads, whereby individual quantum circuits can execute independently on many quantum processing units. Here, we present the full-stack software framework developed at Quantum Brilliance to enable multi-modal parallelism for hybrid quantum workloads. Our software provides the capability to distribute quantum workloads across multiple quantum accelerators hosted by nodes…
We present a proposal for quantum information processing with neutral atoms trapped in optical lattices as qubits. Initialization and coherent control of single qubits can be achieved with standard laser cooling and spectroscopic techniques. We consider entangling two-qubit logic gates based on optically induced dipole-dipole interactions, calculating a figure-of-merit for various protocols. Massive parallelism intrinsic to the lattice geometry makes this an intriguing system for scalable, fault-tolerant quantum computation.
There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation) as soon as the technology can accommodate reasonably sized computations. Interest in quantum computing has been sparked by both the realization that increasing miniaturisation will eventually bring computer scientists face-to-face with quantum effects, and by the grasping of the potential for massive parallelism inherent in the Hilbert space representation of…
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that target the entire structure indiscriminately. But large-scale quantum computation imposes several requirements in terms of noise level, time, space (scaling) and in particular parallelism. Keeping in mind these requirements, we prove GC can support error-correction, by implementing two simple codes. This opens the way to fault-tolerant computation with this ty…
This is an expository talk written for the Bourbaki Seminar. After a brief introduction, Section 1 discusses in the categorical language the structure of the classical deterministic computations. Basic notions of complexity icluding the P/NP problem are reviewed. Section 2 introduces the notion of quantum parallelism and explains the main issues of quantum computing. Section 3 is devoted to four quantum subroutines: initialization, quantum computing of classical Boolean functions, quantum Fourier transform, and Grover's search algorithm. The central Section 4 explains Shor's factoring algorith…
As current Noisy Intermediate Scale Quantum (NISQ) devices suffer from decoherence errors, any delay in the instruction execution of quantum control microarchitecture can lead to the loss of quantum information and incorrect computation results. Hence, it is crucial for the control microarchitecture to issue quantum operations to the Quantum Processing Unit (QPU) in time. As in classical microarchitecture, parallelism in quantum programs needs to be exploited for speedup. However, three challenges emerge in the quantum scenario: 1) the quantum feedback control can introduce significant pipelin…
