scholarly journals Optimal two-qubit circuits for universal fault-tolerant quantum computation

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Andrew N. Glaudell ◽  
Neil J. Ross ◽  
Jacob M. Taylor
Keyword(s):  
Lower Bound ◽  
Normal Form ◽  
Quantum Computation ◽  
Normal Forms ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Worst Case ◽  
Synthesis Algorithm ◽  
Phase Gate ◽  
Controlled Phase Gate

AbstractWe study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS gates. In the present paper, we introduce an efficient and optimal synthesis algorithm for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and outputs a Clifford+CS circuit for U, which uses the least possible number of CS gates. Because the algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for that operator. We give an explicit description of these normal forms and use this description to derive a worst-case lower bound of $$5{{\rm{log}}}_{2}(\frac{1}{\epsilon })+O(1)$$ 5 log 2 ( 1 ϵ ) + O ( 1 ) on the number of CS gates required to ϵ-approximate elements of SU(4). Our work leverages a wide variety of mathematical tools that may find further applications in the study of fault-tolerant quantum circuits.

scholarly journals Accuracy threshold for postselected quantum computation

2008 ◽  
Vol 8 (3&4) ◽  
pp. 181-244 ◽  
Author(s):  
P. Aliferis ◽  
D. Gottesman ◽  
J. Preskill
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Correcting Codes ◽  
Stochastic Noise ◽  
Strongly Correlated ◽  
Error Detecting ◽  
Error Detecting Code

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated error-correcting codes) not to strongly-correlated adversarial noise. Our rigorously established lower bound on the accuracy threshold, $1.04\times 10^{-3}$, is well below Knill's numerical estimates.

scholarly journals Path-optimized nonadiabatic geometric quantum computation on superconducting qubits

2021 ◽  
Author(s):  
Cheng-Yun Ding ◽  
Li-Na Ji ◽  
Tao Chen ◽  
Zheng-Yuan Xue
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Fault Tolerant ◽  
High Fidelity ◽  
Noise Resistance ◽  
Geometric Phases ◽  
Single Qubit ◽  
Phase Gate ◽  
New Perspective ◽  
Geometric Quantum Computation

Abstract Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric Phase, $\pi/8$ and Hadamard gates can be obtained as $99.93\%$, $99.95\%$ and $99.95\%$, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as $99.87\%$. Therefore, our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.

Universal fault tolerant quantum computation on bilinear nearest neighbor arrays

2008 ◽  
Vol 8 (3&4) ◽  
pp. 330-344
Author(s):  
A.M. Stephens ◽  
A.G. Fowler ◽  
L.C.L. Hollenberg
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
Error Rate ◽  
Nearest Neighbor ◽  
Fault Tolerant ◽  
Quantum Code ◽  
Memory Errors ◽  
Memory Failure ◽  
Qubit Gate ◽  
Readout Error

Assuming an array that consists of two parallel lines of qubits and that permits only nearest neighbor interactions, we construct physical and logical circuitry to enable universal fault tolerant quantum computation under the $[[7,1,3]]$ quantum code. A rigorous lower bound to the fault tolerant threshold for this array is determined in a number of physical settings. Adversarial memory errors, two-qubit gate errors and readout errors are included in our analysis. In the setting where the physical memory failure rate is equal to one-tenth of the physical gate error rate, the physical readout error rate is equal to the physical gate error rate, and the duration of physical readout is ten times the duration of a physical gate, we obtain a lower bound to the asymptotic threshold of $1.96\times10^{-6}$.

scholarly journals Demonstration of a Controlled-Phase Gate for Continuous-Variable One-Way Quantum Computation

2011 ◽  
Vol 107 (25) ◽  
Author(s):  
Ryuji Ukai ◽  
Shota Yokoyama ◽  
Jun-ichi Yoshikawa ◽  
Peter van Loock ◽  
Akira Furusawa
Keyword(s):  
Quantum Computation ◽  
Continuous Variable ◽  
Phase Gate ◽  
Controlled Phase Gate

scholarly journals Fault-tolerant quantum computation for local leakage faults

2007 ◽  
Vol 7 (1&2) ◽  
pp. 139-156
Author(s):  
P. Aliferis ◽  
B.M. Terhal
Keyword(s):  
Quantum Computation ◽  
Quantum Teleportation ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Rigorous Analysis ◽  
Leakage Reduction

We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described microscopically, by Hamiltonian couplings, and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. \cite{Terhal04} and \cite{Aliferis05b}. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.

scholarly journals Is error detection helpful on IBM 5Q chips?

2018 ◽  
Vol 18 (11&12) ◽  
pp. 949-964 ◽  
Author(s):  
Christophe Vuillot
Keyword(s):  
Quantum Computation ◽  
Error Detection ◽  
Fault Tolerant ◽  
Quantum Circuits ◽  
Average Improvement ◽  
Show Evidence ◽  
Fault Tolerant Design

This paper reports on experiments realized on several IBM~5Q chips which show evidence for the advantage of using error detection and fault-tolerant design of quantum circuits. We show an average improvement of the task of sampling from states that can be fault-tolerantly prepared in the [4,2,2] code, when using a fault-tolerant technique well suited to the layout of the chip. By showing that fault-tolerant quantum computation is already within our reach, the author hopes to encourage this approach.

scholarly journals Cross-Platform Comparison of Arbitrary Quantum Computations

2021 ◽  
Author(s):  
Ze-Pei Cian ◽  
Daiwei Zhu ◽  
Crystal Noel ◽  
Andrew Risinger ◽  
Debopriyo Biswas ◽  
...  
Keyword(s):  
Lower Bound ◽  
Quantum Computation ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Platform Comparison ◽  
Cross Platform ◽  
Difficult Challenge ◽  
Classical Computer ◽  
Arbitrary Quantum

Abstract As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

scholarly journals Digital Quantum Simulation of Nonadiabatic Geometric Gates via Shortcuts to Adiabaticity

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1175
Author(s):  
Yapeng Wang ◽  
Yongcheng Ding ◽  
Jianan Wang ◽  
Xi Chen
Keyword(s):  
Quantum Computing ◽  
Fault Tolerant ◽  
Digital Simulation ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Geometric Phases ◽  
Shortcuts To Adiabaticity ◽  
Phase Gate ◽  
Ideal Quantum ◽  
Quantum Error

Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.

scholarly journals Fast and high-fidelity entangling gate through parametrically modulated longitudinal coupling

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 11 ◽  
Author(s):  
Baptiste Royer ◽  
Arne L. Grimsmo ◽  
Nicolas Didier ◽  
Alexandre Blais
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Effective Interaction ◽  
Interaction Strength ◽  
High Fidelity ◽  
Spin Qubits ◽  
Universal Quantum ◽  
Phase Gate ◽  
Controlled Phase Gate

We investigate an approach to universal quantum computation based on the modulation of longitudinal qubit-oscillator coupling. We show how to realize a controlled-phase gate by simultaneously modulating the longitudinal coupling of two qubits to a common oscillator mode. In contrast to the more familiar transversal qubit-oscillator coupling, the magnitude of the effective qubit-qubit interaction does not rely on a small perturbative parameter. As a result, this effective interaction strength can be made large, leading to short gate times and high gate fidelities. We moreover show how the gate infidelity can be exponentially suppressed with squeezing and how the entangling gate can be generalized to qubits coupled to separate oscillators. Our proposal can be realized in multiple physical platforms for quantum computing, including superconducting and spin qubits.

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

Sign in / Sign up

Export Citation Format

Share Document