Related papers: QMA(2) with postselection equals to NEXP
The framework of postselection is becoming more and more important in various recent directions in Quantum Computation research. Postselection renders simple computational models able to perform general quantum computation. This was first…
It was recently shown by Atserias, Buss and Mueller that the standard complexity-theoretic conjecture NEXP not in P / poly is consistent with the relatively strong bounded arithmetic theory V^0_2, which can prove a substantial part of…
We study the following problem: with the power of postselection (classically or quantumly), what is your ability to answer adaptive queries to certain languages? More specifically, for what kind of computational classes $\mathcal{C}$, we…
Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with one-sided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible…
The modular representation theory of the queer Lie superalgebra q(n) over characteristic p>2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters and a criterion for the…
We give an alternative proof of PreciseQMA = PSPACE, first proved by Fefferman and Lin (Innov. Theor. Comp. Sci. 2018), where PreciseQMA is the class Quantum Merlin-Arthur with inverse exponential completeness-soundness gap. We adapt the…
We demonstrate that theories $\text{Z}^-$, $\text{ZF}^-$, $\text{ZFC}^-$ (minus means the absence of the Power Set axiom) and $\text{PA}_2$, $\text{PA}_2^-$ (minus means the absence of the Countable Choice schema) are equiconsistent to each…
Certain quasi-exactly solvable systems exhibit an energy reflection property that relates the energy levels of a potential or of a pair of potentials. We investigate two sister potentials and show the existence of this energy reflection…
Quantum multiprover interactive proof systems with entanglement MIP* are much more powerful than its classical counterpart MIP (Babai et al. '91, Ji et al. '20): while MIP = NEXP, the quantum class MIP* is equal to RE, a class including the…
We suggest an optical method which tests a nonclassical feature with a coherent state input. The test is designed with a multiplexer of on/off detectors and post-selection, adopting sub-binomiality as a nonclassical feature, replacing…
We investigate the expressive power of Higher-Order Datalog$^\neg$ under both the well-founded and the stable model semantics, establishing tight connections with complexity classes. We prove that under the well-founded semantics, for all…
We develop a new lower bound method for analysing the complexity of the Equality function (EQ) in the Simultaneous Message Passing (SMP) model of communication complexity. The new technique gives tight lower bounds of $\Omega(\sqrt n)$ for…
Space-bounded computation has been a central topic in classical and quantum complexity theory. In the quantum case, every elementary gate must be unitary. This restriction makes it unclear whether the power of space-bounded computation…
This is a reply to the above comment (hep-th/9509028). We argue that QED displays a class of symmetries which may be used to select out the various velocity dependent superselection sectors.
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also…
A long-standing open problem in quantum complexity theory is whether ${\sf QMA}$, the quantum analogue of ${\sf NP}$, is equal to ${\sf QMA}_1$, its one-sided error variant. We show that ${\sf QMA}={\sf QMA}^{\infty}= {\sf QMA}_1^{\infty}$,…
Two-way quantum computers (2WQC) are proposed extension of standard 1WQC: adding conjugated state preparation operation $\langle 0|$ similar to postselection $|0\ra \langle 0|$, by performing a process which from perspective of CPT symmetry…