Scientists / Open questions

Peter W. Shor

Quantum computing; quantum information; algorithms

15 questions

Exact resource costs of remote state preparation: Lo's conjecture beyond the oblivious and qubit cases, the mixed-state entanglement–communication tradeoff, multipartite preparation, and RSP capacities of noisy channels
Quantum capacity of the qubit depolarizing channel and the optimal asymptotic rate of quantum error-correcting codes
Shor's open questions: can quantum computers efficiently solve NP-complete problems and find short vectors in lattices?
Computing the Voronoi diagram of a subset of sites in linear time from the Voronoi diagram of the full set
Interaction locality and coding limits for energy-gap-protected universal adiabatic quantum computation: the surviving open core of the Jordan–Farhi–Shor questions
Strong uncompletability versus bound entanglement: the complementary projector of uncompletable product bases and its cut-wise entanglement structure
Asymptotic minimum-gap scaling, avoided-crossing structure, and stoquasticity limits of the quantum adiabatic algorithm on random 3-regular Max-Cut instances
Nonadditive versus stabilizer quantum error-correcting codes: constructions, optimal parameters, and structure
Single-Letterization of the Simultaneous Classical-Quantum Capacity Region of a Quantum Channel and Its Conjectured Analogues
Molecular and mathematical foundations of the local-rule theory of icosahedral virus shell assembly: what enforces the rules, and do local rules exist for every triangulation number?
Open problems for the Movassagh–Shor supercritical-entanglement spin chains: excited-state spectrum, continuum limit, sharp gap asymptotics, and the entanglement limits of physically reasonable one-dimensional local systems
Entanglement limits of frustration-free spin-1 chains: upper bounds, boundary-free translation-invariant constructions, and stability of long-range entanglement
Undistillability of the canonical NPT family of DiVincenzo et al. and the existence of bound entanglement with negative partial transpose
NPT bound entanglement in Werner states: the Shor–Smolin–Terhal conjecture and its activation consequences
Optimality of approximate randomization of quantum states: key rates for private quantum channels, the 1:2 quantum data-hiding ratio, and the entropy statistics of random bases

Back to open problems

Exact resource costs of remote state preparation: Lo's conjecture beyond the oblivious and qubit cases, the mixed-state entanglement–communication tradeoff, multipartite preparation, and RSP capacities of noisy channels

Quantum capacity of the qubit depolarizing channel and the optimal asymptotic rate of quantum error-correcting codes

Shor's open questions: can quantum computers efficiently solve NP-complete problems and find short vectors in lattices?

Computing the Voronoi diagram of a subset of sites in linear time from the Voronoi diagram of the full set

Interaction locality and coding limits for energy-gap-protected universal adiabatic quantum computation: the surviving open core of the Jordan–Farhi–Shor questions

Strong uncompletability versus bound entanglement: the complementary projector of uncompletable product bases and its cut-wise entanglement structure

Asymptotic minimum-gap scaling, avoided-crossing structure, and stoquasticity limits of the quantum adiabatic algorithm on random 3-regular Max-Cut instances

Nonadditive versus stabilizer quantum error-correcting codes: constructions, optimal parameters, and structure

Single-Letterization of the Simultaneous Classical-Quantum Capacity Region of a Quantum Channel and Its Conjectured Analogues

Molecular and mathematical foundations of the local-rule theory of icosahedral virus shell assembly: what enforces the rules, and do local rules exist for every triangulation number?

Open problems for the Movassagh–Shor supercritical-entanglement spin chains: excited-state spectrum, continuum limit, sharp gap asymptotics, and the entanglement limits of physically reasonable one-dimensional local systems

Entanglement limits of frustration-free spin-1 chains: upper bounds, boundary-free translation-invariant constructions, and stability of long-range entanglement

Undistillability of the canonical NPT family of DiVincenzo et al. and the existence of bound entanglement with negative partial transpose

NPT bound entanglement in Werner states: the Shor–Smolin–Terhal conjecture and its activation consequences

Optimality of approximate randomization of quantum states: key rates for private quantum channels, the 1:2 quantum data-hiding ratio, and the entropy statistics of random bases