scholarly journals A Threshold for Quantum Advantage in Derivative Pricing

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 463
Author(s):  
Shouvanik Chakrabarti ◽  
Rajiv Krishnakumar ◽  
Guglielmo Mazzola ◽  
Nikitas Stamatopoulos ◽  
Stefan Woerner ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Upper Bound ◽  
Fault Tolerant ◽  
Use Cases ◽  
Derivative Pricing ◽  
Resource Requirements ◽  
Hardware Architectures ◽  
Logical Qubits ◽  
Current Systems ◽  
Do So

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing – the re-parameterization method – that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 8k logical qubits and a T-depth of 54 million. We estimate that quantum advantage would require executing this program at the order of a second. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.

scholarly journals Measurement-free preparation of grid states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Jacob Hastrup ◽  
Kimin Park ◽  
Jonatan Bohr Brask ◽  
Radim Filip ◽  
Ulrik Lund Andersen
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Fault Tolerant ◽  
Hexagonal Lattice ◽  
Harmonic Oscillators ◽  
Noise Levels ◽  
Logical Qubits ◽  
Classical Computing ◽  
Current Systems

AbstractQuantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any length or size can be realized in the presence of noise. The Gottesman-Kitaev-Preskill code is a promising approach toward fault-tolerant quantum computing, encoding logical qubits into grid states of harmonic oscillators. However, for the code to be fault tolerant, the quality of the grid states has to be extremely high. Approximate grid states have recently been realized experimentally, but their quality is still insufficient for fault tolerance. Current implementable protocols for generating grid states rely on measurements of ancillary qubits combined with either postselection or feed forward. Implementing such measurements take up significant time during which the states decohere, thus limiting their quality. Here, we propose a measurement-free preparation protocol, which deterministically prepares arbitrary logical grid states with a rectangular or hexagonal lattice. The protocol can be readily implemented in trapped-ion or superconducting-circuit platforms to generate high-quality grid states using only a few interactions, even with the noise levels found in current systems.

Virtual Logical Qubits: A Compact Architecture for Fault-Tolerant Quantum Computing

IEEE Micro ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jonathan M. Baker ◽  
Casey Duckering ◽  
David Schuster ◽  
Fred Chong
Keyword(s):  
Quantum Computing ◽  
Fault Tolerant ◽  
Logical Qubits

Efficient reversible quantum design of sig-magnitude to two's complement converters

2020 ◽  
Vol 20 (9&10) ◽  
pp. 747-765
Author(s):  
F. Orts ◽  
G. Ortega ◽  
E.M. E.M. Garzon
Keyword(s):  
Quantum Computing ◽  
Scientific Community ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
State Of The Art ◽  
The Other ◽  
Quantum Computers ◽  
Binary Number ◽  
Quantum Cost ◽  
The One

Despite the great interest that the scientific community has in quantum computing, the scarcity and high cost of resources prevent to advance in this field. Specifically, qubits are very expensive to build, causing the few available quantum computers are tremendously limited in their number of qubits and delaying their progress. This work presents new reversible circuits that optimize the necessary resources for the conversion of a sign binary number into two's complement of N digits. The benefits of our work are two: on the one hand, the proposed two's complement converters are fault tolerant circuits and also are more efficient in terms of resources (essentially, quantum cost, number of qubits, and T-count) than the described in the literature. On the other hand, valuable information about available converters and, what is more, quantum adders, is summarized in tables for interested researchers. The converters have been measured using robust metrics and have been compared with the state-of-the-art circuits. The code to build them in a real quantum computer is given.

Fault-tolerant blind quantum computing using GHZ states over depolarization channel

2021 ◽  
Vol 20 (9) ◽  
Author(s):  
Xiaoqing Tan ◽  
Hong Tao ◽  
Xiaoqian Zhang ◽  
Xiaodan Zeng ◽  
Qingshan Xu
Keyword(s):  
Quantum Computing ◽  
Fault Tolerant ◽  
Ghz States

scholarly journals A silicon-based surface code quantum computer

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Joe O’Gorman ◽  
Naomi H Nickerson ◽  
Philipp Ross ◽  
John JL Morton ◽  
Simon C Benjamin
Keyword(s):  
Quantum Computing ◽  
Solid State ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Device Fabrication ◽  
Impurity Atoms ◽  
Dipole Interactions ◽  
Total Phase ◽  
Surface Code ◽  
Silicon Based

Abstract Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

Optimal Bacon-Shor codes

2013 ◽  
Vol 13 (5&6) ◽  
pp. 490-510
Author(s):  
John Napp ◽  
John Preskill
Keyword(s):  
Error Rate ◽  
Upper Bound ◽  
Error Probability ◽  
Fault Tolerant ◽  
Phase Error ◽  
Block Size ◽  
Effective Protection ◽  
Logical Error ◽  
Logical Errors ◽  
Bit Flip

We study the performance of Bacon-Shor codes, quantum subsystem codes which are well suited for applications to fault-tolerant quantum memory because the error syndrome can be extracted by performing two-qubit measurements. Assuming independent noise, we find the optimal block size in terms of the bit-flip error probability $p_X$ and the phase error probability $p_Z$, and determine how the probability of a logical error depends on $p_X$ and $p_Z$. We show that a single Bacon-Shor code block, used by itself without concatenation, can provide very effective protection against logical errors if the noise is highly biased ($p_Z/p_X\gg 1)$ and the physical error rate $p_Z$ is a few percent or below. We also derive an upper bound on the logical error rate for the case where the syndrome data is noisy.

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