Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction

Paetznick, Adam; Reichardt, Ben W.

doi:10.1103/physrevlett.111.090505

Cited by 235 publications

(265 citation statements)

References 29 publications

Supporting

Mentioning

263

Contrasting

Order By: Relevance

“…This can be done in a variety of ways and has become, now, highly optimised. [116][117][118][119][120] The original distillation protocol 71,121 proceeds by taking 15 approximate copies of |a〉: 9ã 1 〉;…”

Section: Quantum Information Processing With Mzmsmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

View full text Add to dashboard Cite

We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localised at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic MZMs in solid-state systems. We also discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC. We describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC. INTRODUCTIONTopological quantum computation 1,2 is an approach to faulttolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called 'anyons'. Anyons braid non-trivially: two counterclockwise exchanges do not leave the state of the system invariant, unlike in the cases of bosons or fermions. Anyons can arise in two ways: as localised excitations of an interacting quantum Hamiltonian 3 or as defects in an ordered system.

show abstract

Section: Quantum Information Processing With Mzmsmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

View full text Add to dashboard Cite

show abstract

“…VII we show how a universal gate set can be achieved via gauge fixing or by defining a gauge color code. Although these results follow directly from the qubit cases presented in [15,26] without the need for any further technical innovations, we include a discussion and explanation of these techniques for completeness.…”

Section: Gauge Fixing To Implement the Logical Hadamard Gatementioning

confidence: 99%

“…The fact that color codes can be shown to saturate this bound with transversal gates is a very promising feature and when combined with gauge fixing techniques [15,[26][27][28] enables universal quantum computation without the need of magic state distillation [5,6,[29][30][31][32][33][34]. The structure of the qudit Clifford group is very different from its qubit counterpart [4,35].…”

Section: Introductionmentioning

confidence: 99%

Qudit color codes and gauge color codes in all spatial dimensions

et al. 2015

View full text Add to dashboard Cite

Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological quantum codes with remarkable transversality properties, can be generalized to the qudit paradigm. In recent developments it was found that in three spatial dimensions a qubit color code can support a transversal non-Clifford gate and that in higher spatial dimensions additional non-Clifford gates can be found, saturating Bravyi and König's bound [S. Bravyi and R. König, Phys. Rev. Lett. 111, 170502 (2013)]. Furthermore, by using gauge fixing techniques, an effective set of Clifford gates can be achieved, removing the need for state distillation. We show that the qudit color code can support the qudit analogs of these gates and also show that in higher spatial dimensions a color code can support a phase gate from higher levels of the Clifford hierarchy that can be proven to saturate Bravyi and König's bound in all but a finite number of special cases. The methodology used is a generalization of Bravyi and Haah's method of triorthogonal matrices [S. Bravyi and J. Haah, Phys. Rev. A 86, 052329 (2012)], which may be of independent interest. For completeness, we show explicitly that the qudit color codes generalize to gauge color codes and share many of the favorable properties of their qubit counterparts.

show abstract

“…Most leading laboratories are following designs [3][4][5] within this paradigm of distill-thensynthesize combined with surface codes. While alternative ideas to magic state distillation exist [6][7][8][9], so far they lack the appealing high tolerance to noise [10,11]. We propose a framework where both distillation and synthesis occur simultaneously, which we call synthillation.…”

mentioning

confidence: 99%

“…[22][23][24], resource states for small-angle single-qubit rotations are distilled, whereas in Refs. [8,14,25] the resource state for a Toffoli gate is distilled. While inspirational to our approach, these techniques do not apply to a general class of multi-qubit circuits and are formally quite distinct from any gate-synthesis protocols.…”

mentioning

confidence: 99%

Unifying Gate Synthesis and Magic State Distillation

Campbell

Howard

2017

Phys. Rev. Lett.

View full text Add to dashboard Cite

The leading paradigm for performing computation on quantum memories can be encapsulated as distill-thensynthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T gate, an essential quantum logic gate. Subsequently, gate synthesis intersperses many T gates with Clifford gates to realise a desired circuit. We introduce a unified framework that implements one round of distillation and multi-qubit gate synthesis in a single step. Typically, our method uses the same number of T -gates as conventional synthesis, but with the added benefit of quadratic error suppression. Because of this, one less round of magic state distillation needs to be performed, leading to significant resource savings.Development of quantum computers has intensified, spurred on by the prospect that fully fault-tolerant devices are within reach. A major impetus has been new theoretical advances showing practical designs of fault-tolerant devices can tolerate up to one percent noise [1]. The topological surface code or toric code is the most widely known breakthrough, which allows for a robust storage of quantum information. Augmenting the surface code from a static memory to a computer requires additional information processing gadgets. Fault-tolerant information processing can be achieved by a two-step process. In the first step, logical qubits are distilled from noisy resources into high-fidelity magic states [2]. Each magic state can provide a fault-tolerant T -gate, also known as a π/8 phase gate. In the second step, gate-synthesis techniques decompose any desired unitary into a sequence of many T -gates interspersed with Clifford gates. This approach to processing quantum information can be paraphrased as distill-then-synthesize. Most leading laboratories are following designs [3][4][5] within this paradigm of distill-thensynthesize combined with surface codes. While alternative ideas to magic state distillation exist [6][7][8][9], so far they lack the appealing high tolerance to noise [10,11]. We propose a framework where both distillation and synthesis occur simultaneously, which we call synthillation.Fault-tolerance protocols come with a price-tag, an overhead of extra qubits. Consequently, genuinely useful applications may need millions or billions of physical qubits. Improved protocols for magic state distillation [12][13][14] and gate synthesis [15][16][17][18][19][20][21] have reduced resource overheads, but the cost remains formidable and further overhead reduction is extremely valuable. Notable is the Bravyi-Haah magic state distillation (BHMSD) protocol [13] that converts 3k + 8 magic states into k magic states with quadratic error suppression. For large computations, with between 10 10 and 10 15 logical operations, the required precision can be reached by concatenating BHMSD two or three times, assuming an initial physical error rate of order ∼ 0.1%. Multilevel distillation is an effective tool when many rounds are required [14]. Gate synthesis has advanced on tw...

show abstract

Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error Correction

Cited by 235 publications

References 29 publications

Majorana zero modes and topological quantum computation

Majorana zero modes and topological quantum computation

Qudit color codes and gauge color codes in all spatial dimensions

Unifying Gate Synthesis and Magic State Distillation

Contact Info

Product

Resources

About