1.isQ编程语言用户手册.pdf
1.isQ编程语言用户手册.pdf
The help document of quantum compiler Qsoftware Team in ISCAS 1 Introduction This is a brief introduction to our quantum compiler, a part of quantum software toolkit of Institute of Software, Chinese Academy of Science. The main function of this tool is compiling the high-level source language in to a lowlevel intermediate representation (IR). The high-level language, named isQ, is based on [1] and similar to qWhile [2], besides we add some new features such as recursion and local variables. The IR is similar to Rigetti’s Quil [3], but we make some moderate changes to enable recursion stacks for recursion and local variables. As we have not connected it to a real quantum hardware device, we write a simulator to execute the current IR instructions. Further applying the IR (and modifying it if necessary) to hardware like superconducting or ion-trap will be a following step. As the compiler in a rather raw version, if you find any bugs, please feel free to inform us and we will be very grateful. We also appreciate any kind suggestions. :) 2 Grammar In [1], the high-level language supports several quantum instructions: initialization, unitary operation, measurement. Classical control like if-statement and loop-statement is also involved. To make the language more portable to users and more feasible to existing quantum architectures, we permit explicitly declaration of both classical and quantum variables in the source language. This indicates that in the IR both quantum registers and classical registers are needed, as Quil does. 2.1 Structure A program written in our source language usually composes of three parts: gate definition, global variable definition and procedure definition. For readability and convenience, we require these three parts in strict order for the moment, 1 that is: Gate Def inition ... Global V ariable Def inition ... P rocedure Def inition ... And they can not overlap with each other. Only when previous part is finished could the users write the next part. 2.2 Gate Definition We permit the users to define their own desired unitary operators at the very beginning of programs. Note that some basic gates are automatically defined and need no definition by users: H,T,X,Y,Z,CX(CNOT),CZ. They are reserved words and cannot be used as user-defined gate names, variable names or procedure names. Another reserve word is M, which acts as the projection measurement operator. To define a new gate the user should input a complex matrix and name the gate like below: Def gate U 1 =[c1,1 , c1,2 , · · · , c1,n ; c2,1 , c2,2 , · · · , c2,n ; ... cn,1 , cn,2 , · · · , cn,n ]; where U 1 is the gate name and n must be a power of 2. ci,j is a complex number, such as 0 or −0.5 + 0.5j. 2.3 Global Variable Definition There are two types of variables are supported currently: int and qbit. Define a new int or qbit is like: int a; qbit b; By the way, the user can define multiple variable of same type in one clause: qbit q0, q1, q2, q3; We also allow definition of variable arrays now, like: qbit q[3]; 2 2.4 Procedure Definition For flexibility, we permit the user to define custom procedures which can recursively call each other. But a main procedure must exist and can not be called by other procedures: p r o c e d u r e A( ) { PROCEDURE BODY A } p r o c e d u r e main ( ) { PROCEDURE BODY MAIN } A is a proc name. PROCEDURE BODY A and PROCEDURE BODY MAIN can contain five kinds of statements, which will be introduced in the following. 2.5 Statement the permitted statements include: while statement, if statement, initialization, assignment statement, procedure call statement. For classical control, the guard in while and if statement can only contains classical variables. Initialization is used to reset a quantum variable. Assignment statements include assignment of arithmetic value, unitary operation and measurement operation. 2.5.1 while statement while statement provides the loop structure, it has the form: w h i l e (GUARD) do LOOPBODY od Currently the GUARD only permits the comparison of two expressions composed of integers and int variables. LOOPBODY has no restrictions, with all five statements permitted. Note that brackets are necessary for the GUARD. See an example below: w h i l e ( x<2) do x = x + 1; od 2.5.2 if statement Similar to while statement, the structure is below: i f (GUARD) then IFBODY fi 3 or i f (GUARD) then IFBODY 1 else IFBODY 2 fi in while and if statements, ’do’,’od’,’if’,’fi’ are reserved words to indicate the scope of such statements. 2.5.3 initialization Initialization statement are used to reset a qubit to state |0i. See an example below: q0 = |0 >; q1 = |0 >; where q0, q1 are qbit variables. The structure for this statement is fixed, and reset a qubit to state |1i is not permitted. 2.5.4 assignment statement There are three types of assignment. The first type is assigning expression value to a int variable. For example: a = a + 2; The second type is assigning measurement outcome of a qubit to a int variable: a = M [q]; where q must be a qbit variable and a must be a int variable. The third type is unitary operation: H ; CNOT ; x = M[ p ] ; od y = M[ p ] ; print x ; print y ; } The compiling results: main : MOV REGS 0 MOV SPEC1 2 MOV SPEC2 2 Measure q [ 0 ] c [ SPEC1 ] JUMP−IF @IF0 c [ SPEC1]==0 1 In fact, there is an instruction set called QPU-executable Quil for Rigetti’s current quan- tum devices, but in this doc we discuss the original Quil 5 X q [0] LABEL @IF0 Measure q [ 1 ] c [ SPEC1 ] JUMP−IF @IF1 c [ SPEC1]==0 X q [1] LABEL @IF1 MOV c [ 0 ] 0 LABEL @LOOPGUARD0 MOV SPEC3 c [ 0 ] MOV SPEC4 0 JUMP−UNLESS @LOOPEND0 SPEC3==SPEC4 H q [1] CNOT q [ 1 ] q [ 0 ] Measure q [ 1 ] c [ 0 ] JUMP @LOOPGUARD0 LABEL @LOOPEND0 Measure q [ 1 ] c [ 1 ] PRINT c [ 0 ] PRINT c [ 1 ] Example 3.2 (Grover’s fixed-point quantum search[4]) initial state |si, target state |ti, where hs|ti = 0. To search |ti, we use following three gates U, Rs , Rt , which satisfies: ||ht|U |si||2 = (1 − ) < 1 π Rs = I − [1 − exp(i )]|sihs| 3 π Rt = I − [1 − exp(i )]|tiht| 3 define Um as following: • when m = 0, Um = U ; † • ∀m ≥ 0, Um+1 = Um Rs Um Rt U m . it can be proved by induction: m ∀m > 0, ||ht|Um |si||2 = 1 − 3 program code: D e f g a t e Rs = [ 0 . 5 + 0 . 8 6 6 0 2 5 4 j , 0 , 0 , 0 ; 0 ,1 ,0 ,0; 0 ,0 ,1 ,0; 0 ,0 ,0 ,1]; D e f g a t e Rs2 =[0.5 −0.8660254 j , 0 , 0 , 0 ; 0 ,1 ,0 ,0; 6 0 ,0 ,1 ,0; 0 ,0 ,0 ,1]; D e f g a t e Rt = [ 1 , 0 , 0 , 0 ; 0 ,1 ,0 ,0; 0 ,0 ,1 ,0; 0 ,0 ,0 ,0.5+0.8660254 j ] ; D e f g a t e Rt2 = [ 1 , 0 , 0 , 0 ; 0 ,1 ,0 ,0; 0 ,0 ,1 ,0; 0 ,0 ,0 ,0.5 −0.8660254 j ] ; qbit p,q , r ; qbit t [5]; int a ,x , y ; p r o c e d u r e A1( i n t a ) { i f ( a==0) t h e n H ; H ; B1 ( a ) ; Rs ; A1( a ) ; a = a +1; fi } p r o c e d u r e B1 ( i n t a ) { i f ( a==0) t h e n H ; H ; A1( a ) ; Rt2 ; B1 ( a ) ; a = a + 1; 7 fi } p r o c e d u r e main ( ) { a = 2; A1( a ) ; x = M [p]; y = M [q ]; print x ; print y ; } the compiling result (omitted lines represented by ”...”): LABEL @PROC A1 MOV SPEC3 REGS SUB SPEC3 2 MOV SPEC3 s [ SPEC3 ] MOV SPEC3 c [ SPEC3 ] MOV SPEC4 0 JUMP−UNLESS @IF0 SPEC3==SPEC4 H q [0] H q [1] ... MOV c [ SPEC4 ] c [ SPEC3 ] ADD c [ SPEC4 ] 1 LABEL @IF1 SUB REGS 1 JUMP−IF @CALL END A10 s [REGS]==0 JUMP−IF @CALL END A11 s [REGS]==1 JUMP−IF @CALL END A12 s [REGS]==2 JUMP−IF @CALL END A13 s [REGS]==3 LABEL @PROC B1 MOV SPEC3 REGS SUB SPEC3 2 MOV SPEC3 s [ SPEC3 ] MOV SPEC3 c [ SPEC3 ] MOV SPEC4 0 JUMP−UNLESS @IF2 SPEC3==SPEC4 H q [0] H q [1] LABEL @IF2 ... LABEL @IF3 SUB REGS 1 JUMP−IF @CALL END B10 s [REGS]==0 8 JUMP−IF @CALL END B11 s [REGS]==1 JUMP−IF @CALL END B12 s [REGS]==2 main : MOV REGS 0 MOV SPEC1 3 MOV SPEC2 8 MOV c [ 0 ] 2 MOV SPEC3 REGS MOV s [ SPEC3 ] 0 ADD REGS 1 MOV s [REGS] 3 ADD REGS 1 JUMP @PROC A1 LABEL @CALL END A13 SUB REGS 1 Measure q [ 0 ] c [ 1 ] Measure q [ 1 ] c [ 2 ] PRINT c [ 1 ] PRINT c [ 2 ] 4 Discussion As our compiler might adjust the target IR, we expect to apply our compiler on real classic-quantum hybrid systems in the future. And the optimization of compilers, which plays a pivotal role in classical computer science, has tremendous potential in quantum computing. We will keep on updating the compiler. References [1] M. S. Ying, Foundations of Quantum Programming, Morgan-Kaufmann, 2016. [2] Liu, Shusen, Wang, Xin, Zhou, Li, et al. Q|SIi: A Quantum Programming Environment[J]. Scientia Sinica, 2017. [3] Smith R S, Curtis M J, Zeng W, et al. A Practical Quantum Instruction Set Architecture.[J]. arXiv: Quantum Physics, 2016. [4] Grover L K. Fixed-point quantum search.[J]. Physical Review Letters, 2005, 95(15): 150501.Grover L K. Fixed-point quantum search.[J]. Physical Review Letters, 2005, 95(15): 150501. 9 ; CX
; fi i f ( a >0) t h e n a = a − 1; A1( a ) ; Rt
; fi i f ( a >0) t h e n a = a − 1; B1 ( a ) ; Rs2