Fault‐tolerant quantum implementation of conventional decoder logic with enable input (original) (raw)
Related papers
Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction
Physical Review Letters, 2013
A general scheme to perform universal quantum computation within decoherence-free subspaces (DFSs) of a system's Hilbert space is presented. This scheme leads to the first fault-tolerant realization of universal quantum computation on DFSs with the properties that (i) only one-and two-qubit interactions are required, and (ii) the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under "collective decoherence" (qubit-permutation-invariant system-bath coupling). Our results have immediate relevance to a number of solid-state quantum computer implementations, in particular those in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled GaAs quantum dot arrays and the Si: 31 P nuclear spin arrays.
Implementation of fault-tolerant quantum logic gates via optimal control
New Journal of Physics, 2009
The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T -gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control. arXiv:0907.1635v2 [quant-ph]
A Low-Overhead Hybrid Approach for Universal Fault-Tolerant Quantum Computation
arXiv: Quantum Physics, 2016
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, a hybrid approach is proposed which combines the code concatenation technique with the other mentioned approaches. The proposed approach outperforms code concatenation in terms of both number of qubits and error threshold and also significantly reduces the resource overhead of code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.
On Universal and Fault-Tolerant Quantum Computing
Ipl, 1999
A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and σ z 1 4), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of π) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed in [25, 17].
A comparative code study for quantum fault tolerance
Quantum Information and Computation, 2009
We study a comprehensive list of quantum codes as candidates for codes used at the physical level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the pseudo-threshold for these codes against depolarizing noise at various levels of overhead. We estimate the logical noise rate as a function of overhead at a physical error rate of p_0=1times10−4p_0=1 \times 10^{-4}p_0=1times10−4. The Bacon-Shor codes and the Golay code are the best performers in our study.
Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error detection codes have been proposed and realized for lower number of qubit systems. Here we present an error detection code for a (2n + 1)-qubit entangled state using two syndrome qubits and simulate it on IBM's 16-qubit quantum computer for a 13-qubit entangled system. The code is able to detect an arbitrary quantum error in any one of the first 2n qubits of the (2n+1)-qubit entangled state and detects any bit-flip error on the last qubit of the (2n + 1)-qubit entangled state via measurements on a pair of ancillary error syndrome qubits. The protocol presented here paves the way for designing error detection codes for the general higher number of entangled qubit *
Fault-Tolerant Quantum Computing
The team is now exploring how to develop other useful quantum algorithms based on fault-tolerant quantum codes. [58] A Rice University-led study is forcing physicists to rethink superconductivity in uranium ditelluride, an A-list material in the worldwide race to create fault-tolerant quantum computers.[57] Quantum computation represents a fundamental shift that is now under way. What is most exciting is not what we can do with with a quantum computer today, but the undiscovered truths it will reveal tomorrow. [56]
Algorithms and Architectures for Quantum Computers
This research group seeks to understand and develop the experimental and theoretical potential for information processing and communications using the laws of quantum physics. Two fundamental questions motivate our work: (1) How can a large-scale, reliable quantum computer be realized? (2) What new algorithms, cryptographic primitives, and metrology techniques are enabled by quantum information? The first question is primarily experimental. We intend to build a large-scale, reliable quantum computer over the next few decades. Based on our successes with realizing small quantum computers, and after three years of testing, modeling, and planning, we have come to understand how this can be achieved by combining fault tolerance techniques developed by von Neumann, with methods from atomic physics.
Grover's algorithm in a four-qubit silicon processor above the fault-tolerant threshold
arXiv (Cornell University), 2024
Spin qubits in silicon are strong contenders for realizing a practical quantum computer [1-4]. This technology has made remarkable progress in recent years with the demonstration of single and two-qubit gates with fidelities above the fault-tolerant threshold [5-13] and entanglement of up to three qubits [8, 14-16]. However, maintaining high fidelity operations while executing multiqubit algorithms has remained elusive and only achieved for two spin qubits to date [5, 6] due to the small qubit size, which makes it difficult to control individual qubits without creating errors on neighbouring qubits [3-5]. Here, we use a four-qubit silicon processor with every operation above the fault tolerant limit and demonstrate Grover's search algorithm with a ∼95% probability of finding the marked state, one of the most successful implementations of this algorithm in any qubit platform to date. Our four-qubit processor is made of three phosphorus atoms and one electron spin precisionpatterned into 1.5 nm 2 isotopically pure silicon. The strong resulting confinement potential, without additional confinement gates that can increase cross-talk, leverages the benefits of having both electron and phosphorus nuclear spins. Significantly, the all-to-all connectivity of the nuclear spins provided by the hyperfine interaction not only allows for efficient multi-qubit operations in which a single gate operation on the electron spin can entangle multiple nuclear spins, but also provides individual qubit addressability, in which the frequency of each nuclear spin qubit is easily separated. Together with the long coherence times of the phosphorus nuclear and electron spins, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity. The high control fidelities, combined with >99% fidelity non-demolition readout of all nuclear spins, allows for the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with 96.2% fidelity, the highest reported for semiconductor spin qubits so far. Neighbouring nuclear spin registers can additionally be coupled via electron-electron exchange [17, 18], which when combined with this result establishes a path for making larger fault-tolerant quantum processors.
A template-based technique for efficient Clifford+T-based quantum circuit implementation
Microelectronics Journal, 2018
The near-future possibility of Quantum supremacy, which aspires to establish a set of algorithms running efficiently on a Quantum computer-have significantly fuelled the interest in design and automation of Quantum circuits. Multiple technologies such as Ion-Trap, Nuclear Magnetic Resonance (NMR), have made great progress in recent years towards a practical Quantum circuit implementation. For all these technologies, in order to suppress the inherent computation noise, fault-tolerance is a desirable feature. Fault tolerance is achieved by Quantum error correction codes, such as surface code. Due to the efficient realization of surface codes using Clifford + T gate library of Quantum logic gates, it is now becoming de facto gate library for Quantum circuit implementation. In this paper, we improve two key performance metrics, T − depth and T − count, for Quantum circuit realization using Clifford + T gates. In contrast with the previous approaches, we have incorporated two techniques-1) restructuring of the gate positions in the designs to make it amenable towards a lower T − depth 2) using Binary Decision Diagrams (BDD) as an intermediate representation for achieving scalability. To validate our proposed optimizations, we have tested a wide spectrum of benchmarks, registering an average improvement of 74% and 21% on T − depth and T − count in compared works.