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We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
Quantum computing promises to solve some important problems faster than conventional computations ever could. Currently available NISQ devices on which first practical applications are already executed demonstrate the potential -- with…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
Current methods for verifying quantum computers are predominately based on interactive or automatic theorem provers. Considering that quantum computers are dynamical in nature, this paper employs and extends the concepts from the…
Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for calculation of eigenstates. Recently, it has been shown that a variety of these networks can be…
Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based on Pfaffians. In particular, they…
In order to achieve speedup over conventional classical computing for finding solution of computationally hard problems, quantum computing was introduced. Quantum algorithms can be simulated in a pseudo quantum environment, but…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…
We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…
The utility of near-term quantum computers and simulators is likely to rely upon software-hardware co-design, with error-aware algorithms and protocols optimized for the platforms they are run on. Here, we show how knowledge of noise in a…