Playing Pong Game on a Quantum Computer Chaitanya Varma, 1, * Bikash K. Behera, 2, † and Prasanta K. Panigrahi 2, ‡ 1 Department of Physics, St.Stephen’s College, University of Delhi, New Delhi - 110007, India 2 Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India Pong, an arcade game, was initially designed as a training exercise and became one of the most popular games ever that paved the way for many of the personal-console games in the future. Here, we undertake the task of modeling the above game which can be played on a quantum computer. We create a static 3-space model of the game that follows a sequential approach and includes a user- based choice system on the positioning of the paddles. We develop new quantum circuits, design and simulate those, and verify the results using IBM quantum experience platform. Keywords: Quantum Computation, Quantum Logic Gates, Pong Game, Sequential Game Theory, IBM Quantum Computer, Foosball I. INTRODUCTION Quantum computation and quantum information is the study of the information processing tasks that can be accomplished using quantum mechanical systems [1]. The information presented here will be well understood with a basic understanding of classical computation like what bits are, how logic gates work and basic knowledge of matrices and linear algebra. FIG. 1: Comparison between a classical bit and a qubit. The basic unit of information processing in a modern- day computer is the bit, which can assume one of the two states: 0 and 1. How quantum computing differs from regular computing is that it uses qubits (short for “Quantum Bits”) instead of bits. Unlike a bit, a qubit can exist in more than two states (Fig. 1). The states that a qubit can exist in are |0i, |1i, a superposition of these two states. The notation used here can be called a “state” or a “vector” or a “ket”. The superposed state is somewhat special. For the superposed state given here [2]: |ψi = α|0i + β|1i (1) * chaitanyamvarma@gmail.com † bkb18rs025@iiserkol.ac.in ‡ pprasanta@iiserkol.ac.in Both α and β are complex numbers such that |α| 2 + |β| 2 = 1. However, when measured, the qubit is seen either in |0i or in |1i state. Here, |α| 2 and |β| 2 gives the probability of finding |ψi in |0i or |1i state. With all this basic information, and taking a brief look over some other papers on quantum games such as quan- tum Shooting game [3], quantum Bingo [4], quantum Su- doku [5], the solution to the Monty Hall problem [6], Diner’s Dilemma [7] and quantum robots [8], quantum go [9], quantum tic-tac-toe [10], one realizes that some further knowledge about the algebra of quantum infor- mation is required. The next section will brief you about the basic knowledge of qubits, single-qubit and two-qubit gates. II. BRA-KET NOTATION AND DIFFERENT TYPES OF PRODUCTS Bra-Ket notation. The bra-ket notation notation is also known as Dirac notation. An elementary idea of this notation can be provided as follows:  c|v  is a “bracket”; now we may divide it into two parts as  c| and |v  [11]. It can be mentioned that a bra-state is a row vector while a ket-state is a column vector. Different types of products • An inner product of two states is a bra state (row vector) premultiplied to a ket state (column vec- tor). This results in a single-digit answer as a row vector when premultiplied to a column vector re- sembles very closely to a dot product. • An outer product of two states is treated as a ket state (column vector) premultiplied to a bra state (row vector). This results in a matrix with dimen- sions of the given vectors. • A tensor product is defined as follows: