Landmark open problem in quantum computing theory solved: Physical Superintelligence proved the Aaronson-Ambainis Conjecture using AI, establishing a lower bound on polynomial influence with implications for quantum query complexity.
#QuantumAlgorithms #QuantumComplexity #News
#QuantumAlgorithms #QuantumComplexity #News
Aaronson-Ambainis Conjecture Proved Using AI
iq.fp2.dev
November 8, 2026 at 10:53 PM
Landmark open problem in quantum computing theory solved: Physical Superintelligence proved the Aaronson-Ambainis Conjecture using AI, establishing a lower bound on polynomial influence with implications for quantum query complexity.
#QuantumAlgorithms #QuantumComplexity #News
#QuantumAlgorithms #QuantumComplexity #News
PSI's AI system running an unreleased Anthropic model proved the Aaronson-Ambainis conjecture—a landmark theoretical result showing quantum computers cannot achieve exponential speedups on random, unstructured data, verified through Lean formal proof.
#QuantumComplexity #QuantumAlgorithms #News
#QuantumComplexity #QuantumAlgorithms #News
PSI's AI System Proves 18-Year-Old Aaronson-Ambainis Conjecture in Quantum Complexity
quantumzeitgeist.com
November 8, 2026 at 10:08 AM
PSI's AI system running an unreleased Anthropic model proved the Aaronson-Ambainis conjecture—a landmark theoretical result showing quantum computers cannot achieve exponential speedups on random, unstructured data, verified through Lean formal proof.
#QuantumComplexity #QuantumAlgorithms #News
#QuantumComplexity #QuantumAlgorithms #News
New theoretical breakthrough demonstrates asymptotic quantum advantage: a Boolean function requiring O(√n) quantum communication bits versus Ω(n) classical bits, establishing exponential separation.
#QuantumCommunication #QuantumComplexity #Research
#QuantumCommunication #QuantumComplexity #Research
Quantum Advantage in One-Way and SMP Communication Complexity
arxiv.org
November 6, 2026 at 4:04 AM
New theoretical breakthrough demonstrates asymptotic quantum advantage: a Boolean function requiring O(√n) quantum communication bits versus Ω(n) classical bits, establishing exponential separation.
#QuantumCommunication #QuantumComplexity #Research
#QuantumCommunication #QuantumComplexity #Research
Establishes quantum analogues of classical complexity results: if UP⊈BQP, then NP∩coNP problems remain hard for quantum algorithms relative to random oracles, while ruling out black-box constructions from post-quantum cryptographic primitives.
#QuantumComplexity #PostQuantumCrypto #Research
#QuantumComplexity #PostQuantumCrypto #Research
Quantum Hardness in NP∩coNP from Unstructured Assumptions
arxiv.org
November 6, 2026 at 3:23 AM
Establishes quantum analogues of classical complexity results: if UP⊈BQP, then NP∩coNP problems remain hard for quantum algorithms relative to random oracles, while ruling out black-box constructions from post-quantum cryptographic primitives.
#QuantumComplexity #PostQuantumCrypto #Research
#QuantumComplexity #PostQuantumCrypto #Research
Researchers constructed an oracle where quantum advantage proofs can coexist with P=NP, showing quantum speedup doesn't necessarily imply classical limitations. BQP equals PSPACE in this theoretical scenario.
#QuantumComplexity #ProofsOfQuantumness #News
#QuantumComplexity #ProofsOfQuantumness #News
Quantum Advantage Can Coexist with P=NP, New Oracle Construction Reveals
quantumzeitgeist.com
November 5, 2026 at 3:27 PM
Researchers constructed an oracle where quantum advantage proofs can coexist with P=NP, showing quantum speedup doesn't necessarily imply classical limitations. BQP equals PSPACE in this theoretical scenario.
#QuantumComplexity #ProofsOfQuantumness #News
#QuantumComplexity #ProofsOfQuantumness #News
Establishes that approximate quantum circuit optimization is PP-hard—proving no efficient algorithm exists for key compilation tasks across standard metrics and gate architectures.
#QuantumComplexity #CircuitOptimization #Research
#QuantumComplexity #CircuitOptimization #Research
Hardness of Approximate Quantum Circuit Membership and Optimization
iq.fp2.dev
November 4, 2026 at 5:33 AM
Establishes that approximate quantum circuit optimization is PP-hard—proving no efficient algorithm exists for key compilation tasks across standard metrics and gate architectures.
#QuantumComplexity #CircuitOptimization #Research
#QuantumComplexity #CircuitOptimization #Research
Proves finding paths in welded trees requires Ω̃(2^(n/3)) quantum queries, establishing that quantum interference enables exit-finding speedup but discovering explicit paths demands exponentially more queries—a quantum analog of wave-particle duality.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Quantum Query Complexity Lower Bounds for Pathfinding in Welded Trees via Algorithmic Wave-Particle Duality
iq.fp2.dev
November 5, 2026 at 6:59 AM
Proves finding paths in welded trees requires Ω̃(2^(n/3)) quantum queries, establishing that quantum interference enables exit-finding speedup but discovering explicit paths demands exponentially more queries—a quantum analog of wave-particle duality.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
New quantum algorithms improve graph collision complexity from n^(2/3) to n^(11/17) while establishing matching Ω(√n log n) lower bounds using adversary methods, advancing fundamental quantum query complexity theory.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Breaking the Quantum Barriers for Graph Collision
arxiv.org
November 4, 2026 at 5:50 AM
New quantum algorithms improve graph collision complexity from n^(2/3) to n^(11/17) while establishing matching Ω(√n log n) lower bounds using adversary methods, advancing fundamental quantum query complexity theory.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Proved unitaryQIP = unitaryPSPACE: interactive quantum verifiers characterize polynomial-space unitary synthesis. Novel acceptance rigidity lemma and techniques establish complexity barriers for EFI cryptographic pairs.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Quantum Unitary Synthesis Equality: Interactive Proofs Characterize Polynomial Space
arxiv.org
November 3, 2026 at 7:36 AM
Proved unitaryQIP = unitaryPSPACE: interactive quantum verifiers characterize polynomial-space unitary synthesis. Novel acceptance rigidity lemma and techniques establish complexity barriers for EFI cryptographic pairs.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Establishes matching quantum lower bounds for k-to-one collision finding and testing, proving adaptivity is essential for quantum speedup. Harmonic framework resolves open questions about exact-promise collision problems.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Tight Quantum Query Complexity Lower Bounds for Collision Problems
iq.fp2.dev
November 3, 2026 at 9:35 AM
Establishes matching quantum lower bounds for k-to-one collision finding and testing, proving adaptivity is essential for quantum speedup. Harmonic framework resolves open questions about exact-promise collision problems.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
We present sample- and query-efficient quantum algorithms for estimating quantum divergences with p-power means and prove the problem is BQP-complete in the low-rank case, advancing quantum divergence estimation theory.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Estimating Quantum Divergences with p-Power Means
arxiv.org
November 3, 2026 at 4:31 AM
We present sample- and query-efficient quantum algorithms for estimating quantum divergences with p-power means and prove the problem is BQP-complete in the low-rank case, advancing quantum divergence estimation theory.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Complete complexity classification of NSPS problems reveals NP-completeness for most variants with applications to classical simulation algorithms and entanglement measures in quantum computing.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Complexity Classification of Nearest Stabilizer Product State Problems
iq.fp2.dev
November 1, 2026 at 4:03 PM
Complete complexity classification of NSPS problems reveals NP-completeness for most variants with applications to classical simulation algorithms and entanglement measures in quantum computing.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Establishes superpolynomial query lower bounds for random-oracle unitary synthesis, ruling out scalable pseudorandom unitaries at O(N²) security. Constructs matching O(N)-query secure designs in ROM, surpassing the prior O(√N) barrier.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Random-Oracle Unitary Synthesis is Impossible
iq.fp2.dev
October 31, 2026 at 1:00 PM
Establishes superpolynomial query lower bounds for random-oracle unitary synthesis, ruling out scalable pseudorandom unitaries at O(N²) security. Constructs matching O(N)-query secure designs in ROM, surpassing the prior O(√N) barrier.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Using representation theory and symmetry groups, we derive methods to construct optimal transducers for quantum algorithmic primitives including unstructured search, amplitude amplification, and amplitude estimation with explicit quantum algorithms.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Optimal Transducers Using Symmetries
arxiv.org
November 1, 2026 at 3:00 PM
Using representation theory and symmetry groups, we derive methods to construct optimal transducers for quantum algorithmic primitives including unstructured search, amplitude amplification, and amplitude estimation with explicit quantum algorithms.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
QAC0 demonstrates remarkable robustness: exact error-free TC0 simulation using polynomial input copies, plus preservation of computational power when restricted to discrete gate-set (Toffoli, Hadamard, S) via novel amplitude amplification techniques.
#QuantumComplexity #QuantumCircuits #Research
#QuantumComplexity #QuantumCircuits #Research
The Robustness of QAC0
arxiv.org
November 1, 2026 at 2:40 PM
QAC0 demonstrates remarkable robustness: exact error-free TC0 simulation using polynomial input copies, plus preservation of computational power when restricted to discrete gate-set (Toffoli, Hadamard, S) via novel amplitude amplification techniques.
#QuantumComplexity #QuantumCircuits #Research
#QuantumComplexity #QuantumCircuits #Research
Proves quantum verifiers require exponential oracle queries to find hidden quantum states even with unlimited classical interactive communication, establishing oracle separation between UniqueQMA and QCIP.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Quantum State Search with Classical Interactive Advice
arxiv.org
November 1, 2026 at 12:02 AM
Proves quantum verifiers require exponential oracle queries to find hidden quantum states even with unlimited classical interactive communication, establishing oracle separation between UniqueQMA and QCIP.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Develops microscopic boundary theory framework for finite-cutoff holography using deformed SYK, connecting chord Hamiltonians to (A)dS geometries, CMC-Krylov complexity, and eternal traversable wormholes with end-of-the-world branes.
#QuantumGravity #Holography #QuantumComplexity
#QuantumGravity #Holography #QuantumComplexity
Finite-Cutoff Holographic Description of Double-Scaled SYK: Geometry, Complexity, and ETW Branes
arxiv.org
November 1, 2026 at 7:53 AM
Develops microscopic boundary theory framework for finite-cutoff holography using deformed SYK, connecting chord Hamiltonians to (A)dS geometries, CMC-Krylov complexity, and eternal traversable wormholes with end-of-the-world branes.
#QuantumGravity #Holography #QuantumComplexity
#QuantumGravity #Holography #QuantumComplexity
Clonable quantum proofs are strictly more powerful than classical proofs relative to a classical oracle, proving unclonability is unnecessary for quantum advantage in proof systems.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Separating Clonable QMA and QCMA Relative to a Classical Oracle
iq.fp2.dev
October 31, 2026 at 12:32 PM
Clonable quantum proofs are strictly more powerful than classical proofs relative to a classical oracle, proving unclonability is unnecessary for quantum advantage in proof systems.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Develops robust subspace designs with probabilistic and explicit constructions, introducing kernel peeling technique to isolate unique quantum witnesses in space-bounded protocols with inverse-polynomial robustness.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Robust Subspace Designs and the Power of a Unique Small Quantum Witness
arxiv.org
October 31, 2026 at 2:46 PM
Develops robust subspace designs with probabilistic and explicit constructions, introducing kernel peeling technique to isolate unique quantum witnesses in space-bounded protocols with inverse-polynomial robustness.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
First classical oracle separation between QMA and QMA(2) quantum complexity classes, demonstrating unentanglement's computational power. Advances understanding of quantum proof systems beyond previously known quantum oracle results.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Classical Oracle Separation Between QMA and QMA(2)
arxiv.org
October 31, 2026 at 12:06 PM
First classical oracle separation between QMA and QMA(2) quantum complexity classes, demonstrating unentanglement's computational power. Advances understanding of quantum proof systems beyond previously known quantum oracle results.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Proves RQL=RQUL for quantum logspace: intermediate measurements can be eliminated while preserving polynomial time, logarithmic space, and exact zero acceptance on no-instances, extending prior results to general gate sets with exact inverses.
#QuantumComplexity #QuantumAlgorithms #Research
#QuantumComplexity #QuantumAlgorithms #Research
Measurement Elimination in Logarithmic-Space Quantum Computation
iq.fp2.dev
October 31, 2026 at 3:08 PM
Proves RQL=RQUL for quantum logspace: intermediate measurements can be eliminated while preserving polynomial time, logarithmic space, and exact zero acceptance on no-instances, extending prior results to general gate sets with exact inverses.
#QuantumComplexity #QuantumAlgorithms #Research
#QuantumComplexity #QuantumAlgorithms #Research
Clonable quantum proofs are strictly more powerful than classical proofs relative to a classical oracle, proving unclonability is unnecessary for quantum advantage in proof systems.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Separating Clonable QMA and QCMA Relative to a Classical Oracle
iq.fp2.dev
October 31, 2026 at 12:32 PM
Clonable quantum proofs are strictly more powerful than classical proofs relative to a classical oracle, proving unclonability is unnecessary for quantum advantage in proof systems.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Develops robust subspace designs with probabilistic and explicit constructions, introducing kernel peeling technique to isolate unique quantum witnesses in space-bounded protocols with inverse-polynomial robustness.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Robust Subspace Designs and the Power of a Unique Small Quantum Witness
arxiv.org
October 31, 2026 at 2:46 PM
Develops robust subspace designs with probabilistic and explicit constructions, introducing kernel peeling technique to isolate unique quantum witnesses in space-bounded protocols with inverse-polynomial robustness.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
First classical oracle separation between QMA and QMA(2) quantum complexity classes, demonstrating unentanglement's computational power. Advances understanding of quantum proof systems beyond previously known quantum oracle results.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Classical Oracle Separation Between QMA and QMA(2)
arxiv.org
October 31, 2026 at 12:06 PM
First classical oracle separation between QMA and QMA(2) quantum complexity classes, demonstrating unentanglement's computational power. Advances understanding of quantum proof systems beyond previously known quantum oracle results.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Establishes superpolynomial query lower bounds for random-oracle unitary synthesis, ruling out scalable pseudorandom unitaries at O(N²) security. Constructs matching O(N)-query secure designs in ROM, surpassing the prior O(√N) barrier.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research
Random-Oracle Unitary Synthesis is Impossible
iq.fp2.dev
October 31, 2026 at 1:00 PM
Establishes superpolynomial query lower bounds for random-oracle unitary synthesis, ruling out scalable pseudorandom unitaries at O(N²) security. Constructs matching O(N)-query secure designs in ROM, surpassing the prior O(√N) barrier.
#QuantumComplexity #QuantumCryptography #Research
#QuantumComplexity #QuantumCryptography #Research