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.

scholarly journals GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Geometric Phases ◽  
Quantum Phases ◽  
Topological Quantum ◽  
Universal Quantum ◽  
The Subject ◽  
Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

scholarly journals Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 62 ◽  
Author(s):  
Daniel Litinski ◽  
Felix von Oppen
Keyword(s):  
Quantum Computation ◽  
Long Range ◽  
Fault Tolerant ◽  
Planar Surface ◽  
Single Qubit ◽  
Control Target ◽  
Surface Code ◽  
Time Overhead

We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.

scholarly journals Counterexamples to Kalai's conjecture C

2013 ◽  
Vol 13 (1&2) ◽  
pp. 1-8
Author(s):  
Steven T. Flammia ◽  
Aram W. Harrow
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Fault Tolerant

We provide two simple counterexamples to Kalai's Conjecture C and discuss our perspective on the implications for the prospect of large-scale fault-tolerant quantum computation.

scholarly journals Nodal free geometric phases: Concept and application to geometric quantum computation

2008 ◽  
Vol 372 (5) ◽  
pp. 596-599 ◽  
Author(s):  
Marie Ericsson ◽  
David Kult ◽  
Erik Sjöqvist ◽  
Johan Åberg
Keyword(s):  
Quantum Computation ◽  
Geometric Phases ◽  
Geometric Quantum Computation

scholarly journals High-fidelity single-qubit gates using non-adiabatic rapid passage

2007 ◽  
Vol 7 (7) ◽  
pp. 594-608
Author(s):  
R. Li ◽  
M. Hoover ◽  
F. Gaitan
Keyword(s):  
Quantum Interference ◽  
Fault Tolerant ◽  
Quantum Gates ◽  
High Fidelity ◽  
Interference Effects ◽  
Adiabatic Rapid Passage ◽  
Single Qubit ◽  
The One ◽  
Error Probabilities ◽  
Rapid Passage

Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991 should be capable of implementing a set of quantum gates that is universal for one-qubit unitary operations and whose elements operate with error probabilities $P_{e}<10^{-4}$. The sweeps are non-composite and generate controllable quantum interference effects which allow the one-qubit gates produced to operate non-adiabatically while maintaining high accuracy. The simulations suggest that the one-qubit gates produced by these sweeps show promise as possible elements of a fault-tolerant scheme for quantum computing.

scholarly journals The XZZX surface code

2020 ◽  
Author(s):  
J. Bonilla Ataides ◽  
David Tuckett ◽  
Stephen Bartlett ◽  
Steven Flammia ◽  
Benjamin Brown
Keyword(s):  
Quantum Computation ◽  
High Performance ◽  
Fault Tolerant ◽  
Small Scale ◽  
Single Qubit ◽  
The Common ◽  
Surface Code ◽  
Random Codes ◽  
Relevant Range ◽  
Common Situation

Abstract We show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favorable sub-threshold resource scaling that can be obtained by specializing a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation. We finally suggest some small-scale experiments that could exploit noise bias to reduce qubit overhead in two-dimensional architectures

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 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 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.

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