Related papers: Identity Testing for +-Regular Noncommutative Arit…
We prove super-polynomial lower bounds on the size of propositional proof systems operating with constant-depth algebraic circuits over fields of zero characteristic. Specifically, we show that the subset-sum variant…
In this paper we study algebraic branching programs (ABPs) with restrictions on the order and the number of reads of variables in the program. Given a permutation $\pi$ of $n$ variables, for a $\pi$-ordered ABP ($\pi$-OABP), for any…
In gate-defined semiconductor spin qubits, the highly tunable Heisenberg exchange interaction is leveraged to implement fermionic two-qubit gates such as CZ and SWAP. However, the broader family of fermionic simulation (fSim) gates remains…
We discuss the advantages and limitations of cyclotomic fields to have fast polynomial arithmetic within homomorphic encryption, and show how these limitations can be overcome by replacing cyclotomic fields by a family that we refer to as…
The problem of constructing explicit functions which cannot be approximated by low degree polynomials has been extensively studied in computational complexity, motivated by applications in circuit lower bounds, pseudo-randomness,…
Mulmuley recently gave an explicit version of Noether's Normalization lemma for ring of invariants of matrices under simultaneous conjugation, under the conjecture that there are deterministic black-box algorithms for polynomial identity…
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be…
Choiceless Polynomial Time (CPT) is one of the few remaining candidate logics for capturing PTIME. In this paper, we make progress towards separating CPT from polynomial time by firstly establishing a connection between the expressive power…
In this paper, we study the computational complexity of the commutative determinant polynomial computed by a class of set-multilinear circuits which we call regular set-multilinear circuits. Regular set-multilinear circuits are commutative…
We generalize the usual relationship between irreducible Zariski closed subsets of the affine space, their defining ideals, coordinate rings, and function fields, to a non-commutative setting, where "varieties" carry a PGL_n-action, regular…
We consider three classification systems for distributed decision tasks: With unbounded computation and certificates, defined by Balliu, D'Angelo, Fraigniaud, and Olivetti [JCSS'18], and with (two flavors of) polynomially bounded local…
Based on a theorem of Bergman we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely, we show the following:…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
We introduce the polynomial coefficient matrix and identify maximum rank of this matrix under variable substitution as a complexity measure for multivariate polynomials. We use our techniques to prove super-polynomial lower bounds against…
Dawar and Wilsenach (ICALP 2020) introduce the model of symmetric arithmetic circuits and show an exponential separation between the sizes of symmetric circuits for computing the determinant and the permanent. The symmetry restriction is…
While efficient randomized algorithms for factorization of polynomials given by algebraic circuits have been known for decades, obtaining an even slightly non-trivial deterministic algorithm for this problem has remained an open question of…
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
Barrier certificates, serving as differential invariants that witness system safety, play a crucial role in the verification of cyber-physical systems (CPS). Prevailing computational methods for synthesizing barrier certificates are based…