526 research outputs found
How many qubits are needed for quantum computational supremacy?
Quantum computational supremacy arguments, which describe a way for a quantum
computer to perform a task that cannot also be done by a classical computer,
typically require some sort of computational assumption related to the
limitations of classical computation. One common assumption is that the
polynomial hierarchy (PH) does not collapse, a stronger version of the
statement that P NP, which leads to the conclusion that any classical
simulation of certain families of quantum circuits requires time scaling worse
than any polynomial in the size of the circuits. However, the asymptotic nature
of this conclusion prevents us from calculating exactly how many qubits these
quantum circuits must have for their classical simulation to be intractable on
modern classical supercomputers. We refine these quantum computational
supremacy arguments and perform such a calculation by imposing fine-grained
versions of the non-collapse assumption. Each version is parameterized by a
constant and asserts that certain specific computational problems with
input size require time steps to be solved by a non-deterministic
algorithm. Then, we choose a specific value of for each version that we
argue makes the assumption plausible, and based on these conjectures we
conclude that Instantaneous Quantum Polynomial-Time (IQP) circuits with 208
qubits, Quantum Approximate Optimization Algorithm (QAOA) circuits with 420
qubits and boson sampling circuits (i.e. linear optical networks) with 98
photons are large enough for the task of producing samples from their output
distributions up to constant multiplicative error to be intractable on current
technology. In the first two cases, we extend this to constant additive error
by introducing an average-case fine-grained conjecture.Comment: 24 pages + 3 appendices, 8 figures. v2: number of qubits calculation
updated and conjectures clarified after becoming aware of Ref. [42]. v3:
Section IV and Appendix C added to incorporate additive-error simulation
Quantum information in the Posner model of quantum cognition
Matthew Fisher recently postulated a mechanism by which quantum phenomena
could influence cognition: Phosphorus nuclear spins may resist decoherence for
long times, especially when in Posner molecules. The spins would serve as
biological qubits. We imagine that Fisher postulates correctly. How adroitly
could biological systems process quantum information (QI)? We establish a
framework for answering. Additionally, we construct applications of biological
qubits to quantum error correction, quantum communication, and quantum
computation. First, we posit how the QI encoded by the spins transforms as
Posner molecules form. The transformation points to a natural computational
basis for qubits in Posner molecules. From the basis, we construct a quantum
code that detects arbitrary single-qubit errors. Each molecule encodes one
qutrit. Shifting from information storage to computation, we define the model
of Posner quantum computation. To illustrate the model's quantum-communication
ability, we show how it can teleport information incoherently: A state's
weights are teleported. Dephasing results from the entangling operation's
simulation of a coarse-grained Bell measurement. Whether Posner quantum
computation is universal remains an open question. However, the model's
operations can efficiently prepare a Posner state usable as a resource in
universal measurement-based quantum computation. The state results from
deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected
entangled-pair state (PEPS). Finally, we show that entanglement can affect
molecular-binding rates, boosting a binding probability from 33.6% to 100% in
an example. This work opens the door for the QI-theoretic analysis of
biological qubits and Posner molecules.Comment: Published versio
Quantum Computing in the NISQ era and beyond
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the
near future. Quantum computers with 50-100 qubits may be able to perform tasks
which surpass the capabilities of today's classical digital computers, but
noise in quantum gates will limit the size of quantum circuits that can be
executed reliably. NISQ devices will be useful tools for exploring many-body
quantum physics, and may have other useful applications, but the 100-qubit
quantum computer will not change the world right away --- we should regard it
as a significant step toward the more powerful quantum technologies of the
future. Quantum technologists should continue to strive for more accurate
quantum gates and, eventually, fully fault-tolerant quantum computing.Comment: 20 pages. Based on a Keynote Address at Quantum Computing for
Business, 5 December 2017. (v3) Formatted for publication in Quantum, minor
revision
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